EP2680262A1 - Method for suppressing noise in an acoustic signal for a multi-microphone audio device operating in a noisy environment - Google Patents

Abstract

The method involves denoising two parts of a spectrum with implementation of an adaptive algorithm estimator by denoising and exploiting a character of a useful signal from a sensor to another sensor between first sub-array sensors by a first adaptive algorithm estimator (14) for a high frequency part and by denoising by prediction of noise from the sensor to another sensor between second sub-array sensors by a second adaptive algorithm estimator (18) for a low frequency part. The spectrum is reconstructed (22) by combining signals delivered after denoising the two parts of the spectrum. The character is a predictable character. The sensors of the first sub-array of sensors are unidirectional sensors oriented along direction of a speech source.

Description

The invention relates to the treatment of speech in a noisy environment.

It relates in particular to the processing of speech signals picked up by "hands-free" telephony devices intended to be used in a noisy environment.

These devices include one or more microphones ("microphones") sensitive, capturing not only the voice of the user, but also the surrounding noise, noise that is a disruptive element that can go in some cases to make unintelligible the speaker's words . It is the same if one wants to implement speech recognition techniques, because it is very difficult to perform a form recognition on words embedded in a high noise level.

This difficulty related to surrounding noise is particularly restrictive in the case of devices "hands free" for motor vehicles, whether in-vehicle equipment or accessories in the form of removable housing incorporating all components and functions signal processing for telephone communication.

Indeed, in this application, the significant distance between the microphone (placed at the dashboard or in an angle of the cockpit of the passenger compartment) and the speaker (whose distance is constrained by the driving position) entails capturing a relatively high noise level, which makes it difficult to extract the useful signal embedded in the noise. In addition, the very noisy environment typical of the automotive environment has spectral characteristics that evolve unpredictably depending on driving conditions: passage on deformed or paved roads, car radio in operation, etc.

Comparable difficulties arise when the device is a headset type microphone / headset combined used for communication functions such as hands-free telephony functions, in addition to listening to an audio source (music for example ) from a device to which the headphones are connected.

In this case, it is a question of ensuring sufficient intelligibility of the signal picked up by the microphone, that is to say the speech signal of the close speaker (the helmet wearer). But the headset can be used in a noisy environment (subway, busy street, train, etc.), so that the microphone will not only pick up the word of the wearer of the helmet, but also the noise surrounding. The wearer is protected from this noise by the headphones, especially if it is a model with closed headphones isolating the ear from the outside, and even more if the headset is provided with an "active noise control"". On the other hand, the distant speaker (the one at the other end of the communication channel) will suffer from the noise picked up by the microphone and being superimposed and interfere with the speech signal of the near speaker (the helmet wearer). In particular, certain speech formers essential to the understanding of the voice are often embedded in noise components commonly encountered in the usual environments.

The invention more particularly relates to denoising techniques using a network of several microphones, judiciously combining the signals simultaneously picked up by these microphones to discriminate the useful components of speech from the noise noise components.

A conventional technique consists in placing and orienting one of the microphones so that it mainly captures the voice of the speaker, while the other is arranged to capture a greater noise component than the main microphone. The comparison of the signals captured makes it possible to extract the voice of the ambient noise by spatial coherence analysis of the two signals, with relatively simple software means.

The US 2008/0280653 A1 describes such a configuration, where one of the pickups (the one that mainly picks up the voice) is that of a wireless headset carried by the driver of the vehicle, while the other (the one that captures the noise) is that of the telephone device, placed remotely in the passenger compartment of the vehicle, for example hung on the dashboard.

However, this technique has the disadvantage of requiring two remote microphones, the efficiency being even higher than the two microphones are remote. Therefore, this technique is not applicable to a device in which the two microphones are close together, for example two microphones incorporated in the facade of a car radio, or two microphones that would be arranged on one of the shells an earphone.

Another technique, called beamforming, consists of creating by software means a directivity that improves the signal / noise ratio of the network or "antenna" microphones. The US 2007/0165879 A1 describes such a technique, applied to a pair of non-directional microphones placed back to back. An adaptive filtering of the captured signals makes it possible to derive at the output a signal in which the voice component has been reinforced.

However, it is estimated that a method of multi-sensor denoising only provides good results provided to have a network of at least eight microphones, the performance is extremely limited when only two microphones are used.

The EP 2 293 594 A1 and EP 2 309 499 A1 (Parrot ) describe other techniques, also based on the assumption that the wanted signal and / or spurious noises have a certain directivity, which combine the signals from the different microphones so as to improve the signal / noise ratio according to these conditions of directivity. These denoising techniques are based on the assumption that speech generally has a higher spatial coherence than noise and that, moreover, the direction of speech incidence is generally well defined and can be assumed to be known (in the case of motor vehicle, it is defined by the position of the driver, to which are turned the microphones). This assumption, however, takes into account the reverberation effect typical of the cabin of a car, where powerful reflections and many make it difficult to calculate a direction of arrival. They can also be faulted by noises with a certain directivity, such as blows of horn, passage of a scooter, overtaking by a car, etc.

Yet another method is described in the article of I. McCowan and S. Sridharan, "Adaptive Parameter Compensation for Robust Hands-free Speech Recognition Using a Dual-Beamforming Microphone Array", Proceedings on 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing, May 2001 .

In general, these techniques based on directivity assumptions all have limited performance against the noise components in the region of the lowest frequencies - there where, precisely, the noise can be concentrated at a relatively high energy level.

In fact, the directivity is all the more marked as the frequency is high, so that this criterion becomes less discriminating for the lower frequencies. In fact, to remain sufficiently effective, it is necessary to remove many microphones, for example 15 to 20 cm, or even more depending on the desired performance, so as to decorrelate enough noise picked up by these microphones.

Consequently, it is not possible to incorporate such a network of microphones, for example, into the housing of a car radio or to a stand-alone "hands-free" housing placed in the vehicle, let alone on vehicles. earphone shells of a headphone.

• présente des performances accrues dans le bas du spectre des fréquences, là où sont le plus souvent concentrées les composantes de bruit parasite les plus gênantes, notamment du point de vue du masquage du signal de parole ;
• ne requière pour sa mise en oeuvre qu'un nombre réduit de micros (typiquement, pas plus de trois à cinq micros) ; et
• avec une configuration géométrique suffisamment ramassée du réseau de micros (typiquement avec un écartement entre micros de quelques centimètres seulement), pour permettre notamment son intégration à des produits compacts de type "tout-en-un".

The problem of the invention is, in such a context, to be able to have an effective noise reduction technique for delivering to the remote speaker a voice signal representative of the speech transmitted by the close speaker (driver of the vehicle or carrier of the helmet), by eliminating this signal of the external noise noise components present in the environment of this close speaker, a technique which:

• shows increased performance in the lower frequency spectrum, where the most troublesome parasitic noise components are most often concentrated, particularly from the point of view of masking the speech signal;
• require for its implementation a small number of microphones (typically no more than three to five microphones); and
• with a sufficiently compact geometric configuration of the network of microphones (typically with a gap between microphones of a few centimeters only), to allow including its integration with compact products of "all-in-one" type.

• le bruit dans l'habitacle est spatialement cohérent dans les basses fréquences (au-dessous de 1000 Hz environ) ;
• il perd en cohérence dans les hautes fréquences (au-dessus de 1000 Hz) ; et
• selon le type de micro utilisé, unidirectionnel ou omnidirectionnel, la cohérence spatiale est modifiée.

The starting point of the invention lies in the analysis of the typical noise field in the passenger compartment of a motor vehicle, which leads to the following observations:

• the noise in the passenger compartment is spatially coherent at low frequencies (below about 1000 Hz);
• it loses coherence in the high frequencies (above 1000 Hz); and
• depending on the type of microphone used, unidirectional or omnidirectional, the spatial coherence is modified.

• la forte cohérence des bruits en BF permet d'envisager un algorithme exploitant une prédiction du bruit d'un micro sur l'autre, ce qui est possible car on peut observer des périodes de silence du locuteur, avec absence de signal utile et présence exclusive du bruit ;
• en revanche, en HF le bruit est faiblement cohérent et il est difficilement prédictible, sauf à prévoir un nombre élevé de micros (ce qui n'est pas souhaité) ou à rapprocher les micros pour rendre les bruits plus cohérents (mais l'on n'obtiendra jamais de grande cohérence dans cette bande, sauf à confondre les micros : les signaux captés seraient alors les mêmes, et l'on n'aurait aucune information spatiale). Pour cette partie HF, on utilisera alors un algorithme exploitant le caractère prédictible du signal utile d'un micro sur l'autre (et non plus une prédiction du bruit), ce qui est par hypothèse possible car on sait que ce signal utile est produit par une source ponctuelle (la bouche du locuteur).

These observations, which will be specified and justified later, lead to propose a hybrid denoising strategy, using low frequency (BF) and high frequency (HF) two different algorithms, exploiting the coherence or non-coherence of the components. of noise according to the part of the spectrum considered:

• the high coherence of the noise in BF makes it possible to envisage an algorithm exploiting a prediction of the noise of a microphone on the other, which is possible because one can observe periods of silence of the speaker, with absence of useful signal and exclusive presence noise ;
• on the other hand, in HF the noise is weakly coherent and it is difficult to predict, except to foresee a high number of microphones (which is not desired) or to bring the microphones closer to make the noises more coherent (but one does not will never get much consistency in this band, except to confuse the pickups: the signals picked up would then be the same, and we would have no spatial information). For this HF part, we will then use an algorithm exploiting the predictability of the useful signal from one microphone to the other (and no longer a noise prediction), which is hypothetically possible because we know that this useful signal is produced by a point source (the mouth of the speaker).

More specifically, the invention provides a method of denoising a noisy acoustic signal for a multi-microphone audio device of the general type disclosed by the aforementioned article by McCowan and S. Sridharan, wherein the device comprises a sensor network consisting of a plurality of microphone sensors arranged in a predetermined configuration and able to collect the noisy signal, the sensors being grouped into two sub-networks, with a first sub-network able to collect an RF portion of the spectrum, and a second sub-network of sensors able to collect a part BF of the spectrum distinct from the part HF.

1. a) partition du spectre du signal bruité entre ladite partie HF et ladite partie BF, par filtrage respectivement au-delà et en deçà d'une fréquence pivot prédéterminée,
2. b) débruitage de chacune des deux parties du spectre avec mise en oeuvre d'un estimateur à algorithme adaptatif ; et
3. c) reconstruction du spectre par combinaison des signaux délivrés après débruitage des deux parties du spectre aux étapes b1) et b2),

This process comprises steps of:

1. a) partition of the spectrum of the noisy signal between said RF portion and said BF portion, by filtering respectively beyond and below a predetermined pivot frequency,
2. b) denoising each of the two parts of the spectrum with implementation of an adaptive algorithm estimator; and
3. c) reconstruction of the spectrum by combining the signals delivered after denoising the two parts of the spectrum in steps b1) and b2),

• b1) pour la partie HF, un débruitage exploitant le caractère prédictible du signal utile d'un capteur sur l'autre entre capteurs du premier sous-réseau, au moyen d'un premier estimateur (14) à algorithme adaptatif, et
• b2) pour la partie BF, un débruitage par prédiction du bruit d'un capteur sur l'autre entre capteurs du second sous-réseau, au moyen d'un second estimateur (18) à algorithme adaptatif.

In a characteristic manner of the invention, the denoising step b) is carried out by separate treatments for each of the two parts of the spectrum, with:

• b1) for the HF part, a denoising exploiting the predictability of the useful signal from one sensor to the other between sensors of the first sub-network, by means of a first adaptive algorithm estimator (14), and
• b2) for the BF part, a prediction noise denoising of one sensor on the other between sensors of the second sub-network, by means of a second adaptive algorithm estimator (18).

With regard to the geometry of the sensor array, the first sub-array of sensors able to collect the RF portion of the spectrum may in particular comprise a linear array of at least two sensors aligned perpendicularly to the direction of the speech source, and the second sub-array of sensors adapted to collect the spectrum portion BF may comprise a linear network of at least two sensors aligned parallel to the direction of the speech source.

The sensors of the first sub-array of sensors are advantageously unidirectional sensors, oriented in the direction of the speech source.

The denoising processing of the HF part of the spectrum in step b1) can be differentially performed for a lower band and an upper band of this HF part, with the selection of different sensors among the sensors of the first sub-network, the distance between the sensors selected for denoising the upper band being smaller than the distance of the selected sensors for denoising the lower band.

• d) réduction sélective du bruit par un traitement de type gain à amplitude log-spectrale modifié optimisé, OM-LSA, à partir du signal reconstruit produit à l'étape c) et d'une probabilité de présence de parole.

The denoising treatment preferably provides, after step c) of spectrum reconstruction, a step of:

• d) selective noise reduction by optimized modified log-spectral amplitude gain processing, OM-LSA, from the reconstructed signal produced in step c) and a speech presence probability.

• b11) estimation d'une probabilité de présence de parole dans le signal bruité recueilli ;
• b12) estimation d'une matrice spectrale de covariance des bruits recueillis par les capteurs du premier sous-réseau, cette estimation étant modulée par la probabilité de présence de parole ;
• b13) estimation de la fonction de transfert des canaux acoustiques entre la source de parole et au moins certains des capteurs du premier sous-réseau, cette estimation étant opérée par rapport à une référence de signal utile constituée par le signal recueilli par l'un des capteurs du premier sous-réseau, et étant en outre modulée par la probabilité de présence de parole ; et
• b14) calcul, notamment par un estimateur de type beamforming à réponse sans distorsion à variance minimale, MVDR, d'un projecteur linéaire optimal donnant un signal combiné débruité unique à partir des signaux recueillis par au moins certains des capteurs du premier sous-réseau, de la matrice spectrale de covariance estimée à l'étape b12), et des fonctions de transfert estimées à l'étape b13).

With regard to the denoising of the RF portion of the spectrum, step b1), exploiting the predictability of the useful signal from one sensor to the other, can be operated in the frequency domain, in particular by:

• b11) estimating a probability of speech in the collected noisy signal;
• b12) estimation of a spectral matrix of covariance of the noises collected by the sensors of the first sub-network, this estimation being modulated by the probability of presence of speech;
• b13) estimation of the transfer function of the acoustic channels between the speech source and at least some of the sensors of the first sub-network, this estimation being made with respect to a useful signal reference constituted by the signal collected by one of the sensors of the first sub-network, and further being modulated by the probability of presence of speech; and
• b14) calculating, in particular by a minimally variance-minimum distortion-response beamforming estimator, MVDR, of an optimal linear projector giving a combined single-ended signal from the signals collected by at least some of the sensors of the first sub-array, the estimated covariance spectral matrix in step b12), and transfer functions estimated in step b13).

The step b13) of estimating the transfer function of the acoustic channels can in particular be implemented by an LMS-type linear least linear adaptive adaptive filter, with modulation by the probability of presence of speech, notably a modulation. by variation of the iteration step of the adaptive filter LMS.

For the denoising of the part BF in step b2), the prediction of the noise of one sensor on the other can be made in the time domain, in particular by a Wiener filter multichannel filter with weighting by the Speech distortion, SDW-MWF, including an SDW-MWF filter adaptively estimated by a gradient descent algorithm.

• La Figure 1 illustre de façon schématique un exemple de réseau de micros, comprenant quatre micros utilisables de façon sélective pour la mise en oeuvre de l'invention.
• Les Figures 2a et 2b sont des caractéristiques, respectivement pour un micro omnidirectionnel et pour un micro unidirectionnel, montrant les variations, en fonction de la fréquence, de la corrélation (fonction de cohérence quadratique) entre deux micros pour un champ de bruit diffus, ceci pour plusieurs valeurs d'écartement entre ces deux micros.
• La Figure 3 est un schéma d'ensemble, sous forme de blocs fonctionnels, montrant les différents traitements selon l'invention pour le débruitage des signaux recueillis par le réseau de micros de la Figure 1.
• La Figure 4 est une représentation schématique par blocs fonctionnels, généralisée à un nombre de micros supérieur à deux, d'un filtre adaptatif pour l'estimation de la fonction de transfert d'un canal acoustique, utilisable pour le traitement de débruitage de la partie BF du spectre dans le traitement d'ensemble de la Figure 3.

An embodiment of the device of the invention will now be described with reference to the appended drawings in which the same reference numerals designate identical or functionally similar elements from one figure to another.

• The Figure 1 schematically illustrates an example of a network of microphones, comprising four microphones used selectively for the implementation of the invention.
• The Figures 2a and 2b are characteristics, respectively for an omnidirectional microphone and for a unidirectional microphone, showing the variations, as a function of frequency, of the correlation (quadratic coherence function) between two microphones for a diffuse noise field, this for several values of spacing between these two pickups.
• The Figure 3 is a block diagram, in the form of functional blocks, showing the different treatments according to the invention for the denoising of the signals collected by the network of microphones of the Figure 1 .
• The Figure 4 is a functional block schematic representation, generalized to a number of micros greater than two, of an adaptive filter for the estimation of the transfer function of an acoustic channel, usable for the denoising processing of the spectrum part BF in the overall treatment of the Figure 3 .

An example of a denoising technique embodying the teachings of the invention will now be described in detail.

Configuration of the microphone sensor network

We will consider, as illustrated Figure 1 , a network R of microphonic sensors M ₁ ... M ₄ , each sensor being able to be likened to a single microphone picking up a noisy version of a speech signal emitted by a useful signal source (speaker) of direction of incidence Δ .

Each microphone thus captures a component of the useful signal (the speech signal) and a component of the surrounding noise, in all its forms (directive or diffuse, stationary or evolving unpredictably, etc.).

The network R is configured in two subnetworks R ₁ and R ₂ dedicated respectively to the capture and processing of the signals in the upper part (hereinafter "high frequency", HF) of the spectrum and in the lower part (hereinafter after "low frequency", BF) of this same spectrum.

The sub-network R ₁ dedicated to the HF part of the spectrum consists of three microphones M ₁ , M ₃ , M ₄ which are aligned perpendicularly to the direction of incidence Δ, with a respective spacing of d = 2 cm in the illustrated example. These microphones are preferably unidirectional microphones whose main lobe is oriented in the direction Δ of the speaker.

The sub-network R ₂ dedicated to the part BF of the spectrum consists of two microphones M ₁ and M ₂ , aligned parallel to the direction Δand spaced apart by d = 3 cm in the illustrated example. It will be noted that the microphone M ₁ , which belongs to the two subnetworks R ₁ and R ₂ , is shared, which makes it possible to reduce the total number of microphones of the network. This pooling is advantageous, but it is not necessary. On the other hand, a shaped configuration is illustrated in "L" when the microphone is shared the microphone M _1, but this configuration is not restrictive, the microphone can be shared eg micro M _3, giving the whole network a configuration in the form of "T".

Moreover, the microphone M ₂ of the BF network may be an omnidirectional microphone, since the directivity is much less marked in BF than in HF.

Finally, the illustrated configuration showing two subnets R ₁ + R ₂ comprising 3 + 2 microphones (a total of 4 microphones given the pooling of one of the microphones) is not limiting. The minimum configuration is a configuration with 2 + 2 microphones (a minimum of 3 microphones if one of them is shared). Conversely, it is possible to increase the number of microphones, with configurations to 4 + 2 pickups, 4 + 3 pickups, etc.

The increase in the number of microphones makes it possible, particularly in the high frequencies, to select different microphone configurations depending on the parts of the RF spectrum processed.

Thus, in the illustrated example, if one operates in wideband telephony with a frequency range up to 8000 Hz (instead of 4000 Hz), for the lower band (1000 to 4000 Hz) of the HF part of the spectrum we will choose the two extreme microphones {M ₁ , M ₄ } distant from each other by d = 4 cm, while for the upper band (4000 to 8000 Hz) of this same HF part we will use a pair of two neighboring microphones {M ₁ , M ₃ } or {M ₃ , M ₄ }, or the three microphones {M ₁ , M ₃ , M ₄ } together, these microphones being each spaced apart by d = 2 cm only: it thus benefits in the lower band of the HF spectrum of the maximum spacing of the microphones, which maximizes the decorrelation of the sensed noises, while avoiding in the upper band a refolding of the high frequencies of the signal to be restored; such a refolding would appear if not because of a too low spatial sampling frequency, insofar as it is necessary that the maximum phase delay of a signal picked up by a microphone then by the other is less than the period of time. sampling of the signal digitizer. We will now expose, with reference to Figures 2a and 2b , the manner of choosing the pivot frequency between the two parts BF and HF of the spectrum, and the preferred choice of the unidirectional / omnidirectional microphone type according to the part of the spectrum to be treated, HF or BF.

These Figures 2a and 2b illustrate, respectively for an omnidirectional microphone and for a unidirectional microphone, characteristics giving, as a function of frequency, the value of the correlation function between two microphones, for several distance values d between these microphones.

f étant la fréquence considérée et τ étant le retard de propagation entre les micros soit τ = d/c, où d est la distance entre les micros et c la vitesse du son.The correlation function between two microphones distant from a distance d , for a diffuse noise field model, is a globally decreasing function of the distance between the microphones. This correlation function is represented by mean squared coherence MSC ( Mean Squared Coherence ) , which varies between 1 (the two signals are perfectly coherent, they differ only from a linear filter) and 0 (totally decorrelated signals). In the case of an omnidirectional microphone, this coherence can be modeled according to the frequency by the function: $$\mathit{MSC}\left(f\right)={\left|\frac{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">sin</figure-callout>}\left(2\mathit{<figure-callout\; id="2"\; label="\pi f\tau "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\pi f\tau </figure-callout>}\right)}{2\mathit{\pi f\tau }}\right|}^2$$

f being the frequency considered and τ being the propagation delay between the microphones is τ = d / c, where d is the distance between the microphones and c the speed of sound.

This modeled curve has been illustrated on the Figure 2a , the Figures 2a and 2b also setting the MSC consistency function actually measured for both types of microphones and for various distance values d.

If one considers that there are actually coherent signals when the value of MSC > 0.9, the noise can be considered as being coherent when one is below a frequency f ₀ such than : ${\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=\frac{0787\mathrm{<figure-callout\; id="2"\; label="vs"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">vs</figure-callout>}}{2\mathrm{\pi d}}\mathrm{.}$

This gives a pivot frequency f ₀ of about 1000 Hz for microphones spaced apart by d = 4 cm (distance between the microphones M ₁ and M ₄ of the network example of FIG. Figure 1 ).

In the present example, in particular corresponding to the array of microphones having the dimensions indicated above, a pivot frequency is thus chosen f ₀ = 1000 Hz below which (part BF) will be considered that the noise is coherent, thereby consider an algorithm based on a prediction of this noise from one microphone to the other (prediction made during periods of silence of the speaker, where only the noise is present).

Preferably, for this part BF, unidirectional microphones will be used because, as can be seen by comparing the Figures 2a and 2b the variation of the coherence function is much more abrupt in this case than with an omnidirectional microphone.

In the HF part of the spectrum, where the noise is weakly coherent, it is no longer possible to predict this noise satisfactorily; another algorithm will then be implemented, exploiting the predictability of the useful signal (and no longer noise) from one microphone to the other.

Note finally that the choice of the pivot frequency ( f ₀ = 1000 Hz for d = 2 cm) also depends on the spacing between microphones, a larger gap corresponding to a lower pivot frequency, and vice versa.

Denoising treatment: description of a preferential mode

We will now describe, with reference to the Figure 3 , a preferred mode of implementation of denoising of the signals collected by the network of microphones of the Figure 1 , of course without limitation.

As explained above, different treatments are performed for the high-frequency spectrum (high frequencies, HF) and for the low-end spectrum (low frequencies, BF).

For the high end of the spectrum, a high-pass filter HF 10 receives the signals from the microphones M ₁ , M ₃ and M ₄ of the sub-network R ₁ , used jointly. These signals are first subject to a fast FFT Fourier transform (block 12), then to a frequency-domain processing by an algorithm (block 14) exploiting the predictability of the useful signal of a signal. microphone on the other, in this example a type estimator MMSE-STSA (Minimum Mean-Squared Error Short-Time Spectral Amplitude), which will be described in detail below.

In the lower spectrum, a low-pass filter BF 16 receives as input the signals picked up by the microphones M ₁ and M ₂ subnet R _2. These signals are the subject of a denoising processing (block 18) operated in the time domain by an algorithm exploiting a prediction of the noise of a microphone on the other during the periods of silence of the speaker. In this example, we use an SDW-MWF ( Speech Distortion Weighted Multichannel Wiener Filter ) type algorithm, which will be described in more detail below. The resulting denoised signal is then subjected to a fast Fourier transform FFT (block 20).

Thus, from two multichannel treatments, two resulting single-channel signals are available, one for the HF part originating from block 14, the other for part BF coming from block 18 after passing into the frequency domain by block 20. .

These two resulting denoised signals are combined (block 22) so as to perform a reconstruction of the complete spectrum, HF + BF.

Very advantageously, an additional (single channel) processing of selective denoising (block 24) is performed on the corresponding reconstructed signal. The signal resulting from this treatment is finally the subject of a transformation of Fourier fast inverse iFFT (block 26) to return to the time domain.

More specifically, this final selective denoising processing consists in applying a variable gain specific to each frequency band, this denoising being also modulated by a probability of presence of speech.

1. [1] I. Cohen, "Optimal Speech Enhancement under Signal Presence Uncertainty Using Log-Spectral Amplitude Estimator", Signal Processing Letters, IEEE, Vol. 9, No 4, pp. 113-116, Apr. 2002 .
   Essentiellement, l'application d'un gain nommé "gain LSA" (Log-Spectral Amplitude) permet de minimiser la distance quadratique moyenne entre le logarithme de l'amplitude du signal estimé et le logarithme de l'amplitude du signal de parole originel. Ce second critère se montre supérieur au premier car la distance choisie est en meilleure adéquation avec le comportement de l'oreille humaine et donne donc qualitativement de meilleurs résultats.
   Dans tous les cas, il s'agit de diminuer l'énergie des composantes fréquentielles très parasitées en leur appliquant un gain faible, tout en laissant intactes (par l'application d'un gain égal à 1) celles qui le sont peu ou pas du tout.
   L'algorithme "OM-LSA" (Optimally-Modified LSA) améliore le calcul du gain LSA à appliquer en le pondérant par une probabilité conditionnelle de présence de parole SPP (Speech Presence Probability), qui intervient à deux niveaux :
   • pour l'estimation de l'énergie du bruit : la probabilité module le facteur d'oubli dans le sens d'une mise à jour plus rapide de l'estimation du bruit sur le signal bruité lorsque la probabilité de présence de parole est faible ;
   • pour le calcul du gain final : la réduction de bruit appliquée est d'autant plus importante (c'est-à-dire que le gain appliqué est d'autant plus faible) que la probabilité de présence de parole est faible.

Can be advantageously used for the block 24 a denoising method type OM / LSA (Optimally Modified - Log Spectral Amplitude) as described by

1. [1] I. Cohen, "Optimal Speech Enhancement Under Signal Presence Uncertainty Using Log-Spectral Amplitude Estimator," Signal Processing Letters, IEEE, Vol. 9, No. 4, pp. 113-116, Apr. 2002 .
   Essentially, the application of a gain called Log-Spectral Amplitude (LSA) is used to minimize the mean squared distance between the logarithm of the amplitude of the estimated signal and the logarithm of the amplitude of the original speech signal. This second criterion is superior to the first because the distance chosen is in better adequacy with the behavior of the human ear and thus gives qualitatively better results.
   In all cases, it is a question of reducing the energy of the highly parasitized frequency components by applying them a weak gain, while leaving intact (by the application of a gain equal to 1) those which are it little or not at all.
   The algorithm "OM-LSA" ( Optimally-Modified LSA ) improves the calculation of the LSA gain to be applied by weighting it by a conditional probability of speech presence SPP ( Speech Presence Probability ), which intervenes on two levels:
   • for estimating the noise energy: the probability modulates the forgetting factor in the direction of a faster update of the estimate of the noise on the noisy signal when the probability of presence of speech is low;
   • for the calculation of the final gain: the noise reduction applied is all the more important (that is to say, the applied gain is even lower) that the probability of presence of speech is low.

• [2] I. Cohen et B. Berdugo, "Two-Channel Signal Detection and Speech Enhancement Based on the Transient Beam-to-Reference Ratio", IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2003, Hong-Kong, pp. 233-236, Apr. 2003 .

The probability of presence of speech SPP is a parameter that can take several different values between 0 and 100%. This parameter is calculated according to a technique in itself known, examples of which are notably set forth in:

• [2] I. Cohen and B. Berdugo, "Two-Channel Signal Detection and Speech Enhancement Based on the Transient Beam-to-Reference Ratio," IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2003, Hong Kong, pp. 233-236, Apr. 2003 .

We can also refer to WO 2007/099222 A1 (Parrot ), which describes a denoising technique implementing a probability calculation of presence of speech.

MMSE-STSA HF Denoising Algorithm (block 14)

An example of denoising processing applied to the HF portion of the spectrum will be described by an MMSE-STSA estimator operating in the frequency domain.

This particular implementation is of course not limiting, other denoising techniques can be envisaged, since they are based on the predictability of the useful signal of a microphone on the other. In addition, this HF denoising is not necessarily operated in the frequency domain, it can also be operated in the time domain, by equivalent means.

The proposed technique consists of searching for an optimal linear "projector" for each frequency, that is to say an operator corresponding to a transformation of a plurality of signals (those collected concurrently by the various microphones of the sub-network R ₁ ). in a single single channel signal.

This projection, estimated by the block 28, is an "optimal" linear projection in that it is sought that the residual noise component on the single-channel signal output is minimized and that the useful speech component is the less distorted possible.

• la projection A^TX contienne le moins de bruit possible, c'est-à-dire que la puissance du bruit résiduel, qui vaut E[ A^TVV^TA] = A^TR_nA, soit minimisée, et
• la voix du locuteur ne soit pas déformée, ce qui se traduit par la contrainte A^TH =1, où R_n est la matrice de corrélation entre les micros, pour chaque fréquence, et H est le canal acoustique considéré.

This optimization involves searching for each frequency a vector A such that:

• the projection A ^T X contains the least amount of noise, that is to say, the power of the residual noise, which is E [VV A ^{T T} A] = A ^T R _n A, is minimized, and
• the voice of the speaker is not distorted, which results in stress A ^T H = 1, where R _n is the correlation matrix between the microphones for each frequency, and H is the acoustic channel considered.

This problem is a constrained optimization problem, namely the search for min ( A ^T R _n A ) under the constraint A ^T H = 1.

It can be solved using the method of Lagrange multipliers, which leads to the solution: ${\mathrm{AT}}^T=\frac{H^T{R}_{\mathrm{not}}^{-1}}{H^T{R}_{\mathrm{not}}^{-1}H}\mathrm{.}$

In the case where the transfer function H corresponds to a pure delay, it recognizes the formula beamforming MVDR (Minimum Variance Distorsionless Response), also called beamforming Capon. It will be noted that the residual noise power is worth, after projection $\frac{1}{H^T{R}_{\mathrm{not}}^{-1}H}\mathrm{.}$

• [3] R. C. Hendriks et al., On optimal multichannel mean-squared error estimators for speech enhancement, IEEE Signal Processing Letters, vol. 16, no. 10, 2009 .

Moreover, if we consider MMSE ( Minimum Mean-Squared Error ) estimators on the amplitude and the phase of the signal at each frequency, we see that these estimators are written like a Capon beamforming followed by a single-channel selective denoising treatment, as has been stated by:

• [3] RC Hendriks et al., On Multichannel Optimal Mean-squared error estimators for speech enhancement, IEEE Signal Processing Letters, Vol. 16, no. 10, 2009 .

The selective noise denoising treatment, applied to the single-channel signal resulting from beamforming processing , is advantageously the OM-LSA type treatment described above, operated by block 24 on the complete spectrum after synthesis at 22.

α ₀ étant un facteur d'oubli.The interspectral matrix of noises is estimated recursively (block 32), using the probability of presence of speech SPP (block 34, see above): $$\begin{array}{c}{\mathrm{\Sigma }}_{\mathit{bb}}\left(t\right)=\alpha {\mathrm{\Sigma }}_{\mathit{bb}}\left(t\right)\left(t-1\right)+\left(1-\alpha \right)\mathrm{X}\left(t\right)\mathrm{X}{\left(t\right)}^T\\ \alpha ={\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0+\left(1-{\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0\right)\mathit{SPP}\end{array}$$

α ₀ being a forgetting factor.

With regard to the MVDR estimator (block 28), its implementation involves an estimation of the acoustic transfer functions H _i between the speech source and each of the microphones M _i (M ₁ , M ₃ or M ₄ ).

These transfer functions are advantageously evaluated by a frequency LMS estimator (block 30) receiving as input the signals from the different microphones and outputting the estimates of the various transfer functions H.

It is also necessary to estimate (block 32) the correlation matrix R _n (covariance spectral matrix, also called the interspectral noise matrix).

Finally, these various estimates imply the knowledge of a probability of presence of speech SPP , obtained from the signal collected by one of the microphones (block 34).

We will now describe in detail how the MMSE-STSA estimator operates.

• contenant le moins de bruit possible, et
• déformant le moins possible la voix du locuteur restituée en sortie.

This involves processing the multiple signals produced by the microphones to provide a unique noise signal that is as close as possible to the speech signal emitted by the speaker, that is to say:

• containing as little noise as possible, and
• distorting as little as possible the speaker's voice output.

où x_i est le signal capté, h_i est la réponse impulsionnelle entre la source de signal utile (signal de parole du locuteur) et le micro M_i, s est le signal utile produit par la source S et b_i est le bruit additif.On the microphone of rank i , the collected signal is: $$x_i\left(t\right)=h_i\otimes s\left(t\right)+b_i\left(t\right)$$

where x _i is the sensed signal, h _i is the impulse response between the useful signal source (speaker speech signal) and the microphone M _i , s is the useful signal produced by the source S and b _i is the additive noise .

For all the microphones, we can use the vector notation: $$\mathit{x}\left(t\right)=\mathit{h}\otimes s\left(t\right)+\mathit{b}\left(t\right)$$

In the frequency domain, this expression becomes (uppercase letters representing the corresponding Fourier transforms): $$X_i\left(\omega \right)=H_i\left(\omega \right)S\left(\omega \right)+B_i\left(\omega \right)$$

• le signal S(ω) est gaussien de moyenne nulle et de puissance spectrale ${\sigma }_s^2\left(\omega \right);$
  
• les bruits B_i (ω) sont gaussiens de moyenne nulle et ont une matrice interspectrale (E[BB ^T ]) notée Σ _bb (ω);
• le signal et les bruits considérés sont décorrélés, et chacun est décorrélé lorsque les fréquences sont différentes.

We will make the following assumptions, for all frequencies ω:

• the signal S (ω) is Gaussian of zero mean and spectral power ${\sigma }_s^{}$${}_2^{}\left(\omega \right);$
  
• the noise B _i (ω) is Gaussian of zero mean and has an interspectral matrix ( E [BB ^T ]) denoted Σ _bb (ω);
• the signal and noises considered are decorrelated, and each is decorrelated when the frequencies are different.

As mentioned above, in the multi-microphone case the MMSE-STSA estimator factorizes into a MVDR beamforming (block 28) followed by a single-channel estimator (the OM / LSA algorithm of block 24).

The MVDR beamforming is written: $$\mathit{MVDR}\left(\mathbf{X}\right)=\frac{{\mathbf{H}}^T{\mathrm{\Sigma }}_{\mathit{bb}}^{-1}\mathbf{X}}{{\mathbf{H}}^T{\mathrm{\Sigma }}_{\mathit{bb}}^{-1}\mathbf{H}}$$

The adaptive MVDR beamforming thus exploits the coherence of the useful signal to estimate a transfer function H corresponding to the acoustic channel between the speaker and each of the microphones of the sub-network.

• [4] J. Prado and E. Moulines, Frequency-Domain Adaptive Filtering with Applications to Acoustic Echo Cancellation, Springer, Ed. Annals of Telecommunications, 1994.

For the estimation of this acoustic channel, an LMS-block-type algorithm is used in the frequency domain (block 30) such as that described in particular by:

• [4] J. Prado and E. Mills, Frequency-Domain Adaptive Filtering with Applications to Acoustic Echo Cancellation, Springer, Ed. Annals of Telecommunications, 1994.

LMS algorithms - or NLMS ( Normalized LMS ) which is a standardized version of the LMS - are relatively simple and undemanding algorithms in terms of computing resources.

• [5] M.-S. Choi, C.-H. Baik, Y.-C. Park, and H.-G. Kang, "A Soft-Decision Adaptation Mode Controller for an Efficient Frequency-Domain Generalized Sidelobe Canceller," IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2007, Vol. 4, April 2007, pp. IV-893-IV-896.

For a type GSC beamforming (Generalized sidelobe canceller), this approach is similar to that proposed by:

• [5] M.-S. Choi, C.-H. Baik, Y.-C. Park, and H.-G. Kang, "A Soft-Decision Adaptation Mode Controller for an Efficient Frequency-Domain Generalized Sidelobe Canceller," IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2007, Vol. 4, April 2007, pp. IV-893-IV-896.

The useful signal s (t) is unknown, we can identify H than at a transfer function close. We therefore choose one of the channels as a reference for a useful signal, for example the channel of the microphone M ₁ , and the transfer functions H ₂ ... H _n are calculated for the other channels (which amounts to constraining H ₁ = 1). If the selected reference microphone does not bring major degradation to the useful signal, this choice has no significant influence on the performance of the algorithm.

As illustrated in the figure, the LMS algorithm aims (in known manner) to estimate a filter H (block 36) by means of an adaptive algorithm, corresponding to the signal x _i delivered by the microphone M ₁ , by estimating the transfer of voice between the microphone M _i and the microphone M ₁ (taken as a reference). The output of the filter 36 is subtracted at 38 from the signal x ₁ picked up by the microphone M ₁ , to give a prediction error signal allowing the iterative adaptation of the filter 36. It is thus possible to predict from the signal x _i the speech component contained in the signal x ₁ .

To avoid the problems related to the causality (that is to say, to be sure that the signals x _i arrive in advance with respect to the reference x ₁ ), the signal x ₁ is slightly delayed (block 40).

Moreover, the error signal of the adaptive filter 36 is weighted at 42 by the probability of presence of speech SPP delivered at the output of the block 34, so as to adapt the filter only when the probability of presence of speech is high.

This weighting can in particular be made by modifying the adaptation step of the algorithm, as a function of the SPP probability .

avec $$\mu ={\mu }_0\frac{\mathit{SPP}\left(tk\right)}{E\left[{\left|X_1\left(k\right)\right|}^2\right]}$$

t étant l'indice temporel de la trame courante, µ ₀ étant une constante choisie expérimentalement, et SPP étant la probabilité de présence de parole a posteriori, estimée comme indiqué plus haut (bloc 34).The adaptive filter update equation is, for frequency bin k and the microphone i: $$H_i\left(tk\right)=H_i\left(t-1,k\right)+\mu X_i\left(tk\right)*\left(X_1\left(tk\right)-H_i\left(t-1,k\right)X_i\left(tk\right)\right)$$

with $$\mu ={\mathrm{<figure-callout\; id="0"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_0\frac{\mathit{SPP}\left(tk\right)}{E\left[{\left|X_1\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)\right|}^2\right]}$$

t being the temporal index of the current frame, μ ₀ being an experimentally chosen constant, and SPP being the probability of presence of posterior speech , estimated as indicated above (block 34).

Μ not the adaptation of the algorithm, modulated by the probability of presence of speech SPP, is written in a standardized form of the LMS (the denominator corresponding to the spectral power of the signal x ₁ at the frequency considered): $$\mathrm{\mu }=\frac{\mathrm{<figure-callout\; id="1"\; label="p\; E\; X"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">p\; </figure-callout>}}{E\left[{\mathit{X}}_{}^{}\right]}$$

The hypothesis that the noises are decorrelated leads to a prediction of the voice, and not of the noise, by the LMS algorithm, so that the estimated transfer function effectively corresponds to the acoustic channel H between the speaker and the microphones.

SDW-MWF BF denoising algorithm (block 18)

An example of an SDW-MWF type time-domain denoising algorithm will be described, but this choice is not limitative, other denoising techniques may be envisaged, as long as they are based on the predicting the noise of one microphone on the other. In addition, this BF denoising is not necessarily operated in the time domain, it can also be operated in the frequency domain, by equivalent means.

• [6] A. Spriet, M. Moonen, and J. Wouters, "Stochastic Gradient-Based Implementation of Spatially Preprocessed Speech Distortion Weighted Multichannel Wiener Filtering for Noise Reduction in Hearing Aids," IEEE Transactions on Signal Processing, Vol. 53, pp. 911-925, Mar. 2005 .

The technique used by the invention is based on a prediction of the noise of a microphone on the other described, for a hearing aid, by:

• [6] A. Spriet, M. Moonen, and J. Wouters, "Stochastic Gradient-Based Implementation of Spatially Preprocessed Speech Distortion Weighted Multichannel Wiener Filtering for Noise Reduction in Hearing Aids," IEEE Transactions on Signal Processing, Vol. 53, pp. 911-925, Mar. 2005 .

où :

• x _i (t) est le vecteur [x_i (t - L + 1) ... x_i (t)] ^T et $$\mathrm{x}\left(t\right)={\left[\begin{array}{cccc}{\mathrm{x}}_1{\left(t\right)}^T& {\mathrm{x}}_2{\left(t\right)}^T& \dots & {\mathrm{x}}_M{\left(t\right)}^T\end{array}\right]}^T\mathrm{.}$$
  

Each microphone picks up a useful signal component and a noise component. For the micro of rank i , we have: x _i ( t ) = s _i ( t ) + b _i ( t ) s _i being the component of the useful signal and b _i the noise component. If it is desired to estimate a version of the useful signal present on a micro k by a linear least squares estimator, this amounts to estimating a size of W filter ML such that: $${\hat{\mathrm{W}}}_k=\underset{\mathrm{w}}{\min }E\left[{\left|s_k\left(t\right)-{\mathrm{w}}^T\mathrm{x}\left(\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)\right|}^2\right]$$

or :

• x _i ( t ) is the vector [ x _i ( t - L + 1) ... x _i ( t )] ^T and $$\mathrm{x}\left(t\right)={\left[\begin{array}{cccc}{\mathrm{x}}_1{\left(t\right)}^T& {\mathrm{x}}_2{\left(t\right)}^T& ...& {\mathrm{x}}_M{\left(t\right)}^T\end{array}\right]}^T\mathrm{.}$$
  

The solution is given by the Wiener filter: $${\hat{\mathrm{W}}}_k={\left[E\left[\mathrm{x}\left(t\right)\mathrm{x}{\left(t\right)}^T\right]\right]}^{-1}E\left[\mathrm{x}\left(t\right)s_k\left(t\right)\right]$$

Since, as we have explained in the introduction, for the BF part of the spectrum, we try to estimate the noise and not the useful signal, we obtain: $${\hat{\mathrm{W}}}_k^b=\underset{\mathrm{w}}{\min }E\left[{\left|b_k\left(t\right)-{\mathrm{w}}^T\mathrm{x}\left(\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)\right|}^2\right]$$

This prediction of the noise on a microphone is made from the noise on every microphone considered the second subnet R _2, and this in periods of silence the speaker, where only noise is present.

• [7] B. Widrow, J. Glover, J.R., J. McCool, J. Kaunitz, C. Williams, R. Hearn, J. Zeidler, J. Eugene Dong, and R. Goodlin, "Adaptive Noise Cancelling : Principles and applications," Proceedings of the IEEE, Vol. 63, No. 12, pp. 1692-1716, Dec. 1975 .

The technique used is close to that of the ANC ( Adaptive Noise Cancellation ) denoising, by using several microphones for the prediction and including in the filtering a reference microphone (for example the microphone M ₁ ). The ANC technique is exposed in particular by:

• [7] B. Widrow, J. Glover, JR, J. McCool, J. Kaunitz, C. Williams, R. Hearn, J. Zeidler, J. Eugene Dong, and R. Goodlin, "Adaptive Noise Canceling: Principles and Applications," Proceedings of the IEEE, Vol. 63, No. 12, pp. 1692-1716, Dec. 1975 .

As illustrated on the Figure 3 , the Wiener filter (block 44) provides a noise prediction which is subtracted at 46 from the collected, non-denoised signal after applying a delay (block 48) to avoid causation problems. The Wiener filter 44 is parameterized by a coefficient μ (represented at 50) which determines an adjustable weighting between, on the one hand, the distortion introduced by the processing on the speech signal denoised and, on the other hand, the noise level. residual.

In the case of a signal collected by a larger number of microphones, the generalization of this scheme of the weighted noise prediction is given Figure 4 .

la solution est donnée, de la même façon que précédemment, par le filtre de Wiener: $${\hat{\mathrm{W}}}_k^b={\left[E\left[\mathrm{x}\left(t\right)\mathrm{x}{\left(t\right)}^T\right]\right]}^{-1}E\left[\mathrm{x}\left(t\right)b_k\left(t\right)\right]$$

The estimated signal being: $$\hat{s}\left(t\right)=x_k\left(t\right)-{\mathbf{W}}_k^b$$

the solution is given, in the same way as before, by the Wiener filter: $${\hat{\mathrm{W}}}_k^b={\left[E\left[\mathrm{x}\left(t\right)\mathrm{x}{\left(t\right)}^T\right]\right]}^{-1}E\left[\mathrm{x}\left(t\right)b_k\left(t\right)\right]$$

The estimated signal is then strictly the same, because we can prove that ${\hat{\mathbf{W}}}_k+{\hat{\mathbf{W}}}_k^b={\mathrm{e}}_k,\mathrm{ave}{\mathrm{e}}_k=[0,0...\underset{\mathrm{position\; k}}{\underset{\}}{1}}...{0]}^T\mathrm{.}$

The Wiener filter used is advantageously a weighted Wiener filter (SDW-MVF), to take into account not only the energy of the noise to be eliminated by the filtering, but also the distortion introduced by this filtering, which should be minimized. .

où :

• s_i (t) est le vecteur [s_i (t - L + 1) ... s_i (t)] ^T
  • s(t) = [s₁(t) ^T s₂(t) ^T ... s _M (t) ^T ] ^T
  • b_i(t) est le vecteur [b_i (t - L + 1) ... b_i (t)] ^T et
  • b(t) = [b₁(t) ^T b₂(t) ^T ... b _M (t) ^T ] ^T
  • e_s est la distorsion introduite par le filtrage sur le signal utile, et
  • e_b est le bruit résiduel après filtrage.

In the case of the Wiener filter Ŵ _k , the "cost function" can be split into two, the mean square deviation can be written as the sum of two terms: $$E\left[{\left|s_k\left(t\right)-{\mathrm{w}}^T\mathrm{x}\left(\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)\right|}^2\right]=\underset{e_{\mathrm{at}}}{\underset{\}}{E\left[{\left|s_k\left(t\right)-{\mathrm{w}}^T\mathrm{s}\left(t\right)\right|}^2\right]}}+\underset{e_b}{\underset{\}}{E\left[{\left|{\mathrm{w}}^T\mathrm{b}\left(t\right)\right|}^2\right]}}$$

or :

• s _i ( t ) is the vector [ s _i ( t - L + 1) ... s _i ( t )] ^T
  • s ( t ) = [s ₁ ( t ) ^T s ₂ ( t ) ^T ... s _M ( t ) ^T ] ^T
  • b _i ( t ) is the vector [ b _i ( t - L + 1) ... b _i ( t )] ^T and
  • b ( t ) = [b ₁ ( t ) ^T b ₂ ( t ) ^T ... b _M ( t ) ^T ] ^T
  • e _s is the distortion introduced by the filter on the useful signal, and
  • e _b is the residual noise after filtering.

It is possible to weight these two errors e _s and e _b according to whether one favors the reduction of distortion or the reduction of the residual noise.

avec pour solution : $${\hat{\mathrm{W}}}_{\mathit{kr}}={\left[E\left[\mathrm{s}\left(t\right)\mathrm{s}{\left(t\right)}^T\right]+\mathit{\mu E}\left[\mathrm{b}\left(t\right)\mathrm{b}{\left(t\right)}^T\right]\right]}^{-1}E\left[\mathrm{s}\left(t\right)s_k\left(t\right)\right]$$

l'indice "_.r ' indiquant que l'on régularise la fonction de cout pour pondérer selon la distorsion, et µ étant un paramètre ajustable :

• plus µ est grand, plus l'on privilégie la réduction du bruit, mais au prix d'une distorsion plus importante sur le signal utile ;
• si µ est nul, aucune importance n'est accordée à la réduction du bruit, et la sortie vaut x_k (t) car les coefficients du filtre sont nuls ;
• si µ est infini, les coefficients du filtre sont nuls à l'exception du terme en position k*L (L étant la longueur du filtre) qui vaut 1, la sortie vaut donc zéro.

By invoking the decorrelation between noise and useful signal, the problem becomes: $${\hat{\mathrm{W}}}_{\mathit{kr}}=\underset{\mathrm{w}}{\min }\left[E\left[{\left|s_k\left(t\right)-{\mathrm{w}}^T\mathrm{s}\left(\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)\right|}^2\right]\right]+\left[\mathit{mE}\left[{\left|{\mathrm{w}}^T\mathrm{<figure-callout\; id="2"\; label="b\; t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b\; </figure-callout>}\left(t\right)\left(\right)\right|}^2\right]\right]$$

with for solution: $${\hat{\mathrm{W}}}_{\mathit{kr}}={\left[E\left[\mathrm{s}\left(t\right)\mathrm{s}{\left(t\right)}^T\right]+\mathit{mE}\left[\mathrm{b}\left(t\right)\mathrm{b}{\left(t\right)}^T\right]\right]}^{-1}E\left[\mathrm{s}\left(t\right)s_k\left(t\right)\right]$$

the index " _r " indicating that the function of cost is adjusted to weight according to the distortion, and μ being an adjustable parameter:

• the larger the μ, the more the reduction of noise is preferred, but at the cost of greater distortion on the useful signal;
• if μ is zero, no importance is given to the reduction of the noise, and the output is worth x _k ( t ) because the coefficients of the filter are zero;
• if μ is infinite, the coefficients of the filter are zero except for the term in position k * L ( L being the length of the filter) which is 1, the output is therefore zero.

le problème peut se réécrire : $${\hat{\mathrm{W}}}_{\mathit{kr}}^b=\underset{\mathrm{w}}{\min }\mu \left[E\left[{\left|b_k\left(t\right)-{\mathrm{w}}^T\mathrm{b}\left(t\right)\right|}^2\right]\right]+\left[\mathit{E}\left[{\left|{\mathrm{w}}^T\mathrm{s}\left(t\right)\right|}^2\right]\right]$$

avec pour solution : $${\hat{\mathrm{W}}}_{\mathit{kr}}^b={\left[\frac{1}{\mu }E\left[\mathrm{s}\left(t\right)\mathrm{s}{\left(t\right)}^T\right]+\mathit{E}\left[\mathrm{b}\left(t\right)\mathrm{b}{\left(t\right)}^T\right]\right]}^{-1}E\left[\mathrm{b}\left(t\right)b_k\left(t\right)\right]$$

For the dual filter ${\mathbf{W}}_k^b,$

the problem can be rewritten: $${\hat{\mathrm{W}}}_{\mathit{kr}}^b=\underset{\mathrm{w}}{\min }\mu \left[E\left[{\left|b_k\left(t\right)-{\mathrm{w}}^T\mathrm{<figure-callout\; id="2"\; label="b\; t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b\; </figure-callout>}\left(t\right)\left(\right)\right|}^2\right]\right]+\left[\mathit{E}\left[{\left|{\mathrm{w}}^T\mathrm{s}\left(\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)\right|}^2\right]\right]$$

with for solution: $${\hat{\mathrm{W}}}_{\mathit{kr}}^b={\left[\frac{1}{\mu }E\left[\mathrm{s}\left(t\right)\mathrm{s}{\left(t\right)}^T\right]+\mathit{E}\left[\mathrm{b}\left(t\right)\mathrm{b}{\left(t\right)}^T\right]\right]}^{-1}E\left[\mathrm{b}\left(t\right)b_k\left(t\right)\right]$$

It is also demonstrated that the output signal is the same regardless of the approach used.

This filter is implemented adaptively by a gradient descent algorithm such as that set forth in the aforementioned article [6].

The diagram is the one illustrated Figures 3 and 4 .

For the implementation of this filter, it is necessary to estimate the matrices R _s = E [s ( t ) s ( t ) ^T ], R _b = E [b ( t ) b ( t ) ^T ], the vector E [b ( t ) b _k ( t )] as well as the parameters L (the desired length for the filter) and μ (which adjusts the weighting between noise reduction and distortion).

λ étant un facteur d'oubli.If we assume that we have a voice activity detector (which makes it possible to discriminate between speech phases of the speaker and silence phases) and that the noise b ( t ) is stationary, we can estimate R _b during the silent phases, where only the noise is picked up by the pickups. During these phases of silence, the matrix R _b is estimated along the water: $${\mathrm{R}}_b\left(t\right)=\{\begin{array}{ll}\lambda {\mathrm{R}}_b\left(t-1\right)+\left(1-\lambda \right)\mathrm{x}\left(t\right)\mathrm{x}{\left(t\right)}^T& \mathrm{if\; there\; is\; no\; word}\\ {\mathrm{R}}_b\left(t-1\right)& \mathrm{if\; not}\end{array}$$

λ being a factor of forgetting.

We can estimate E [b ( t ) b _k ( t )], or notice that it is a column of R _b . To estimate R _s , we invoke the decorrelation of the noise and the useful signal. If we denote R _x = E [x ( t ) x ( t ) ^T ], we can write: R _x , R _s + R _b .

ce qui permet de déduire R _s (t) = R _x (t) - R _b (t).We can estimate R _x in the same way as R _b , but without condition on the presence of speech: $${\mathrm{R}}_x\left(t\right)=\lambda {\mathrm{R}}_x\left(t-1\right)+\left(1-\lambda \right)\mathrm{x}\left(t\right)\mathrm{x}{\left(t\right)}^T$$

which makes it possible to deduce R _s ( t ) = R _x ( t ) - R _b ( t ).

Regarding the length L of the filter, this parameter must correspond to a spatial and temporal reality, with a sufficient number of coefficients to predict the noise temporally (temporal coherence of the noise) and spatially (spatial transfer between the microphones).

The parameter μ is adjusted experimentally, increasing it until the distortion on the voice becomes perceptible to the ear.

These estimators are used to perform a gradient descent on the following cost function: $$J_{\mathit{kr}}=\mu \left[E\left[{\left|b_k\left(t\right)-{\mathrm{w}}^T\mathrm{<figure-callout\; id="2"\; label="b\; t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b\; </figure-callout>}\left(t\right)\left(\right)\right|}^2\right]\right]+\left[E\left[{\left|{\mathrm{w}}^T\mathrm{s}\left(\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)\right|}^2\right]\right]$$

The gradient of this function is: $$\delta J_{\mathit{kr}}=2\left[{\mathrm{R}}_s+\mu {\mathrm{R}}_b\right]\mathrm{w}-2\mathit{mE}\left[\mathrm{b}\left(t\right)b_k\left(t\right)\right]$$

où α est un pas d'adaptation proportionnel à $\frac{1}{{\mathrm{x}}^T\mathrm{x}}\mathrm{.}$

Hence the update equation: $$\mathrm{w}\left(t\right)=\mathrm{w}\left(t-1\right)-\mathit{\alpha \delta }{J}_{\mathit{kr}}$$

where α is a proportional adaptation step to $\frac{1}{{\mathrm{x}}^T\mathrm{x}}\mathrm{.}$

Claims (14)

A method of denoising a noisy acoustic signal for a multi-microphone audio device operating in a noisy medium,
the noisy acoustic signal comprising a useful component derived from a speech source and a noise noise component,
said device comprising a sensor array formed of a plurality of microphone sensors (M ₁ ... M ₄ ) arranged in a predetermined configuration and able to collect the noisy signal,
the sensors being grouped into two sub-networks, with a first sub-network (R ₁ ) of sensors able to collect a high-frequency part of the spectrum, and a second sub-network (R ₂ ) of sensors able to collect a low part spectrum frequency distinct from said high frequency part,
this process comprising the following steps: a) partition of the spectrum of the signal noisy in said high frequency portion (HF) and said low frequency portion (BF), by filtering (10, 16) respectively beyond and below a predetermined pivot frequency, b) denoising each of the two parts of the spectrum with implementation of an adaptive algorithm estimator; and c) reconstruction of the spectrum by combination (22) of the signals delivered after denoising the two parts of the spectrum in steps b1) and b2), characterized in that the denoising step b) is operated by separate treatments for each of the two parts of the spectrum, with: b1) for the high frequency part, a denoising exploiting the predictability of the useful signal from one sensor to the other between sensors of the first sub-network, by means of a first adaptive algorithm estimator (14), and b2) for the low-frequency part, a noise-canceling of the noise of one sensor on the other between sensors of the second sub-network, by means of a second adaptive algorithm estimator (18). The method of claim 1, wherein the first sensor sub-network (R ₁₎ adapted to collect the high frequency part of the spectrum comprises a linear array of at least two sensors (M ₁ , M ₃ , M ₄ ) aligned perpendicular to the direction (Δ) of the speech source. The method of claim 1, wherein the second sensor sub-network (R ₂₎ adapted to collect the low-frequency part of the spectrum comprises a linear array of at least two sensors (M _1, M ₂₎ aligned parallel to the direction (Δ) of the speech source. The method of claim 2, wherein the sensors (M ₁ , M ₃ , M ₄ ) of the first sensor subarray (R ₁ ) are unidirectional sensors oriented in the direction (Δ) of the speech source. The method of claim 2, wherein the denoising processing of the high frequency portion of the spectrum in step b1) is differentially performed for a lower band and an upper band of this high frequency portion, with selection of different sensors. among the sensors of the first sub-network (R ₁ ), the distance between the sensors (M ₁ , M ₄ ) selected for the denoising of the upper band being smaller than that of the sensors (M ₃ , M ₄ ) selected for the denoising the lower band. The method of claim 1 further comprising, after step c) of reconstructing the spectrum, a step of: d) selective noise reduction (24) by optimized modified log-spectral amplitude gain processing, OM-LSA, from the reconstructed signal produced in step c) and a speech presence probability. The method of claim 1 wherein the step b1) denoising the high frequency part, exploiting the predictability of the useful signal from one sensor to the other, is operated in the frequency domain. The method of claim 7 wherein the step b1) of denoising the high frequency part, exploiting the predictability of the useful signal from one sensor to the other, is operated by: b11) estimating (34) a probability of speech presence (SPP) in the collected noisy signal; b12) estimating (32) a spectral covariance matrix of the noises collected by the sensors of the first sub-array, this estimation being modulated by the probability of presence of speech; b13) estimation (30) of the transfer function of the acoustic channels between the speech source and at least some of the sensors of the first sub-network, this estimation being made with respect to a useful signal reference constituted by the signal collected by the one of the sensors of the first sub-network, and further being modulated by the probability of presence of speech; and b14) calculating (28) an optimal linear projector giving a combined single denoised signal from the signals collected by at least some of the first subarray sensors, the estimated covariance spectral matrix in step b12), and transfer functions estimated in step b13). The method of claim 8, wherein step (b14) of computing an optimal linear projector (28) is performed by a minimally variance-minimum distortion-response beamforming estimator, MVDR. The method of claim 9, wherein step b13) of estimating the transfer function of the acoustic channels (30) is performed by an adaptive filter (36, 38, 40) with linear least squares prediction means, LMS, with modulation (42) by the probability of presence of speech. The method of claim 10, wherein said speech presence probability modulation is a variation modulation of the iteration pitch of the LMS adaptive filter. The method of claim 1 wherein, for denoising the low frequency portion in step b2), the prediction of noise from one sensor to the other is operated in the time domain. The method of claim 12, wherein the prediction of noise from one sensor to the other is implemented by a filter (44, 46, 48) of Wiener multichannel filter type with speech distortion weighting, SDW-MWF. The method of claim 13, wherein the SDW-MWF filter is adaptively estimated by a gradient descent algorithm.

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