CN114528871B - A Noise Reduction Method Using Fractional Wavelet Decomposition and Reconstruction Technology - Google Patents

Abstract

The present invention provides a noise reduction method using fractional wavelet decomposition and reconstruction technology. Aiming at the defects of using wavelet decomposition and reconstruction technology for signal noise reduction processing, according to the theoretical ideas of fractional calculus, the fixed forms of wavelet decomposition high/low pass filters and reconstruction high/low pass filters are changed, and the original limited threshold algorithm form is changed, so that the filter form and the threshold algorithm form can be flexibly adjusted according to the actual situation of the processed signal, and finally the effect of improving noise reduction is achieved. The present invention makes the existing wavelet decomposition and reconstruction technology and threshold filtering technology have more and better technical effects, solves the technical problems of single fixed wavelet decomposition and reconstruction filter form and limited threshold algorithm form, and has made significant progress in improving the visual effect of image signals and improving noise reduction accuracy.

Description

A Noise Reduction Method Using Fractional Wavelet Decomposition and Reconstruction Technology

Technical Field

The present invention relates to the field of signal processing, and in particular to a signal noise reduction processing method.

Background technique

At present, the process of signal noise reduction using wavelet decomposition and reconstruction technology combined with threshold is as follows:

x＝X+40*randn(size(X)) is the noisy signal, where X is the original image woman that comes with the Matlab system, and 40*randn(size(X)) is the added white noise signal. The wavelet decomposition technology is used to decompose the noisy signal into one layer, two layers and three layers respectively, and the high-frequency component is filtered using the threshold. The wavelet function used is named ‘sym5’, and then wavelet reconstruction is performed to complete the denoising of the noisy signal. The processing results are divided into two parts: one part is the image simulation effect diagram, and the other part is the maximum error value between the denoised image and the original image. The results are shown in Figures 3, 4 and 5 (a), (b), (c) and Table 1.

Table 1 Maximum error values of wavelet decomposition and reconstruction relative to the original image

Serial number Wavelet decomposition level Threshold vector Maximum error value 1 1 [34 50] 146.36 2 2 [87 87] 146.23 3 3 [97 97] 147.18

Through analysis, the existing wavelet decomposition and reconstruction technology can only achieve the above results. In order to improve the noise reduction effect, many threshold modification technologies have also emerged, such as soft threshold and hard threshold technology. However, these technologies have limited effect on the improvement of noise reduction.

Summary of the invention

In order to overcome the shortcomings of the prior art, the present invention provides a noise reduction method using fractional wavelet decomposition and reconstruction technology. Aiming at the defects of using wavelet decomposition and reconstruction technology for signal noise reduction processing, the present invention changes the fixed form of wavelet decomposition high/low pass filter and reconstruction high/low pass filter according to the theoretical ideas of fractional calculus, and changes the original limited threshold algorithm form, so that the filter form and the threshold algorithm form can be flexibly adjusted according to the actual situation of the processed signal, and finally achieves the effect of improving noise reduction.

The specific steps of the technical solution adopted by the present invention to solve its technical problem are as follows:

Step 1: Call the noisy signal

In Matlab or other platforms, reading the noisy signal means calling the noisy signal.

Step 2: Perform fractional wavelet decomposition on the noisy signal to generate a new wavelet coefficient matrix;

First, the wavelet decomposition high-pass filter coefficients and low-pass filter coefficients are changed by fractional calculus, so that the filter form changes with the number of integration times of fractional calculus; secondly, the fractional wavelet decomposition high-pass filter coefficients and low-pass filter changed by fractional calculus are applied to the generation process of four sub-bands; the specific steps are as follows:

(a) LL sub-band;

After the two-dimensional noisy signal is extended in the horizontal direction, it is convolved with a fractional wavelet decomposition low-pass filter, and each row vector is downsampled. After the two-dimensional noisy signal is extended in the vertical direction, it is convolved with a fractional wavelet decomposition low-pass filter, and each column vector is downsampled to obtain the approximate wavelet coefficient matrix FCA of the image signal.

(b) HL subband

After the two-dimensional noisy signal is extended in the horizontal direction, it is convolved with a fractional wavelet decomposition low-pass filter, and each row vector is downsampled. After the vertical direction boundary is extended, it is convolved with a fractional wavelet decomposition high-pass filter, and each column vector is downsampled to obtain the wavelet coefficient matrix FCH of the image signal.

(c) LH subband

After the two-dimensional noisy signal is extended in the horizontal direction, it is convolved with a fractional wavelet decomposition high-pass filter, and each row vector is downsampled. After the vertical direction boundary is extended, it is convolved with a fractional wavelet decomposition low-pass filter, and each column vector is downsampled to obtain the wavelet coefficient matrix FCV of the image signal.

(d) HH subband

After the horizontal boundary extension, the two-dimensional noisy signal is processed by convolution with a fractional wavelet decomposition high-pass filter, and each row vector is downsampled. After the vertical boundary extension, the two-dimensional noisy signal is processed by convolution with a fractional wavelet decomposition high-pass filter, and each column vector is downsampled to obtain the wavelet coefficient matrix FCD of the image signal.

Step 3: Threshold processing is performed on the high-frequency coefficients in three directions;

Threshold processing is performed on the high-frequency coefficients in the horizontal, diagonal and vertical directions to generate new coefficient matrices FNA, FNH, FNV and FND;

Step 4: Signal wavelet reconstruction;

Firstly, the wavelet reconstruction high/low pass filter coefficients are transformed by fractional calculus to change the original fixed form, so that the filter form changes with the change of the number of integration times of fractional calculus; secondly, the wavelet reconstruction high/low pass filter after fractional calculus is applied to the generation process of four reconstruction coefficient matrices; the details are as follows:

(a) Approximate reconstruction coefficient matrix FCA’;

After upsampling and extending the boundaries of each column vector of the coefficient matrix FNA of the image signal, convolution is performed with the fractional wavelet reconstruction low-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, convolution is performed with the fractional wavelet reconstruction low-pass filter and the row vector is intercepted, and the approximate reconstruction coefficient matrix FCA' of the image signal is obtained.

(b) Reconstruction coefficient matrix FCH’

After upsampling and extending the boundaries of each column vector of the coefficient matrix FNH of the image signal, convolution is performed with the fractional wavelet reconstruction high-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, convolution is performed with the fractional wavelet reconstruction low-pass filter and the row vector is intercepted, and the reconstruction coefficient matrix FCH' of the image signal is obtained.

(c) Reconstruction coefficient matrix FCV’

After upsampling and extending the boundaries of each column vector of the coefficient matrix FNV of the image signal, it is convolved with the fractional wavelet reconstruction low-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, it is convolved with the fractional wavelet reconstruction high-pass filter and the row vector is intercepted to obtain the reconstructed coefficient matrix FCV’ of the image signal.

(d) Reconstruction coefficient matrix FCD’

After upsampling and extending the boundaries of each column vector of the coefficient matrix FND of the image signal, convolution is performed with the fractional wavelet reconstruction high-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, convolution is performed with the fractional wavelet reconstruction high-pass filter and the row vector is intercepted, and the reconstruction coefficient matrix FCD' of the image signal is obtained.

Step 5: Signal restoration after noise reduction;

The approximate reconstruction coefficient matrix obtained in step 4 is added to the reconstruction coefficient matrix to obtain the denoised signal, that is: FX’=FCA’+FCH’+FCV’+FCD’, where FX’ is the final denoised signal.

The present invention adopts a soft threshold algorithm to perform fractional calculus changes, so that the existing soft threshold algorithm changes continuously with the change of the number of integration times of the fractional calculus, better adapts to the processed signal, and achieves a better threshold filtering effect; the adopted soft threshold algorithm performs fractional calculus changes; according to actual needs, the noisy signal is respectively subjected to wavelet one-layer wavelet decomposition, two-layer wavelet decomposition and three-layer wavelet decomposition, the scale vector setting is determined by the number of wavelet decomposition layers, and the threshold vector is set according to actual needs; the coefficient matrices FCA, FCH, FCV and FCD of the LL, HL, LH and HH subbands are respectively subjected to soft threshold filtering processing in three directions of horizontal, diagonal and vertical directions, and new coefficient matrices FNA, FNH, FNV and FND are correspondingly generated.

The beneficial effect of the present invention is that due to the adoption of fractional calculus variation technology means of wavelet decomposition and reconstruction high/low pass filters and fractional calculus variation technology means of soft threshold algorithm, the existing wavelet decomposition and reconstruction technology and threshold filtering technology have more and better technical effects, and the technical problems of single fixed form of wavelet decomposition and reconstruction filters and limited form of threshold algorithms have been solved, and significant progress has been made in improving the visual effect of image signals and improving the noise reduction accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flowchart of the denoising process of the traditional wavelet decomposition and reconstruction technology.

FIG2 is a flowchart of the noise reduction process of the fractional wavelet decomposition and reconstruction technology.

FIG3 is a comparison diagram of the effects of one-layer wavelet decomposition and reconstruction of an image applied in an example of the new invention. FIG3 (a) is the original image woman, FIG3 (b) is the noisy signal, FIG3 (c) is the effect diagram of the noisy image after denoising using the traditional wavelet decomposition and reconstruction technology, and FIG3 (d) is the effect diagram of the noisy image after denoising using the fractional wavelet decomposition and reconstruction technology.

FIG4 is a comparison diagram of the two-layer wavelet decomposition and reconstruction image effects of the new invention example application, wherein FIG4(a) is the original image woman, FIG4(b) is the noisy signal, FIG4(c) is the effect diagram of the noisy image after denoising using the traditional wavelet decomposition and reconstruction technology, and FIG4(d) is the effect diagram of the noisy image after denoising using the fractional wavelet decomposition and reconstruction technology.

FIG5 is a comparison diagram of the three-layer wavelet decomposition and reconstruction image effects of the new invention example application. FIG5 (a) is the original image woman, FIG5 (b) is the noisy signal, FIG5 (c) is the effect diagram of the noisy image after denoising using the traditional wavelet decomposition and reconstruction technology, and FIG5 (d) is the effect diagram of the noisy image after denoising using the fractional wavelet decomposition and reconstruction technology.

Detailed ways

The present invention is further described below in conjunction with the accompanying drawings and embodiments.

The traditional noise reduction steps using wavelet decomposition and reconstruction technology are shown in Figure 1. The boundary extension and interception of the vector are omitted in Figure 1, which is reflected in step 2, where Dh is the wavelet decomposition low-pass filter, Dg is the wavelet decomposition high-pass filter, Rh is the wavelet reconstruction low-pass filter, and Rg is the wavelet reconstruction high-pass filter. The specific steps are as follows:

Step 1: Call the noisy signal

This is the first step of using wavelet decomposition and reconstruction technology to reduce noise. The noisy signal can be called by reading it in Matlab or other platforms.

Step 2: Perform wavelet decomposition on the noisy signal to generate a wavelet coefficient matrix

The two-dimensional noisy signal is decomposed by wavelet filtering in the horizontal and vertical directions, and four sub-images are generated, as follows:

(a) LL subband

The two-dimensional noisy signal is convolved with a wavelet decomposition low-pass filter after horizontal boundary extension, and each row vector is downsampled. The two-dimensional noisy signal is convolved with a wavelet decomposition low-pass filter after vertical boundary extension, and each column vector is downsampled to obtain the approximate wavelet coefficient matrix CA of the image signal.

(b) HL subband

The two-dimensional noisy signal is convolved with a wavelet decomposition low-pass filter after horizontal boundary extension, and each row vector is downsampled. The two-dimensional noisy signal is convolved with a wavelet decomposition high-pass filter after vertical boundary extension, and each column vector is downsampled to obtain the wavelet coefficient matrix CH of the image signal.

(c) LH subband

The two-dimensional noisy signal is convolved with a wavelet decomposition high-pass filter after horizontal boundary extension, and each row vector is downsampled. The two-dimensional noisy signal is convolved with a wavelet decomposition low-pass filter after vertical boundary extension, and each column vector is downsampled to obtain the wavelet coefficient matrix CV of the image signal.

(d) HH subband

The two-dimensional noisy signal is processed by convolution with a wavelet decomposition high-pass filter after horizontal boundary extension, and each row vector is downsampled. The two-dimensional noisy signal is processed by convolution with a wavelet decomposition high-pass filter after vertical boundary extension, and each column vector is downsampled to obtain the wavelet coefficient matrix CD of the image signal.

Step 3: Threshold processing of high frequency coefficients in three directions

(a) Setting the scale vector and threshold vector

According to actual needs, the noisy signal is decomposed by wavelet one, two and three layers respectively. The scale vector setting is determined by the number of wavelet decomposition layers, and the threshold vector is set according to actual needs.

(b) Threshold filtering

The coefficient matrices CA, CH, CV and CD of the LL, HL, LH and HH subbands are respectively subjected to threshold filtering in three directions to generate new coefficient matrices NA, NH, NV and ND accordingly.

Step 4: Signal wavelet reconstruction

The specific process of signal wavelet reconstruction is:

(a) Approximate reconstruction coefficient matrix CA’

After upsampling and extending the boundaries of each column vector of the coefficient matrix NA of the image signal, it is convolved with a wavelet reconstruction low-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, it is convolved with a wavelet reconstruction low-pass filter and the row vector is intercepted, thus obtaining the approximate reconstruction coefficient matrix CA’ of the image signal.

(b) Reconstruction coefficient matrix CH’

After upsampling and extending the boundaries of each column vector of the coefficient matrix NH of the image signal, it is convolved with the wavelet reconstruction high-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, it is convolved with the wavelet reconstruction low-pass filter and the row vector is intercepted, thus obtaining the reconstructed coefficient matrix CH’ of the image signal.

(c) Reconstruction coefficient matrix CV’

After upsampling and extending the boundaries of each column vector of the coefficient matrix NV of the image signal, it is convolved with the wavelet reconstruction low-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, it is convolved with the wavelet reconstruction high-pass filter and the row vector is intercepted to obtain the reconstructed coefficient matrix CV’ of the image signal.

(d) Reconstruction coefficient matrix CD’

After upsampling and extending the boundaries of each column vector of the coefficient matrix ND of the image signal, it is convolved with the wavelet reconstruction high-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, it is convolved with the wavelet reconstruction high-pass filter and the row vector is intercepted, and the reconstructed coefficient matrix CD’ of the image signal is obtained.

Step 5: Signal restoration after noise reduction

The noise-reduced signal is obtained by adding the approximate reconstruction coefficient matrix obtained in step 4 to the reconstruction coefficient matrix, that is, X’=CA’+CH’+CV’+CD’.

The steps of the present invention using wavelet decomposition and reconstruction technology to reduce noise are shown in Figure 2. Since the boundary extension and interception of the vector do not change, they are omitted in Figure 2, where: Dh' is a fractional wavelet decomposition low-pass filter, Dg' is a fractional wavelet decomposition high-pass filter, Rh' is a fractional wavelet reconstruction low-pass filter, and Rg' is a fractional wavelet reconstruction high-pass filter. The specific steps of the technical solution adopted by the present invention to solve its technical problem are as follows:

Step 1: Call the noisy signal

In Matlab or other platforms, reading the noisy signal means calling the noisy signal.

Step 2: Perform fractional wavelet decomposition on the noisy signal to generate a new wavelet coefficient matrix;

First, the wavelet decomposition high-pass filter coefficients and low-pass filter coefficients are changed by fractional calculus, so that the filter form changes with the number of integration times of fractional calculus; secondly, the fractional wavelet decomposition high-pass filter coefficients and low-pass filter changed by fractional calculus are applied to the generation process of four sub-bands; the specific steps are as follows:

(a) LL sub-band;

After the two-dimensional noisy signal is extended in the horizontal direction, it is convolved with a fractional wavelet decomposition low-pass filter, and each row vector is downsampled. After the two-dimensional noisy signal is extended in the vertical direction, it is convolved with a fractional wavelet decomposition low-pass filter, and each column vector is downsampled to obtain the approximate wavelet coefficient matrix FCA of the image signal.

(b) HL subband

After the two-dimensional noisy signal is extended in the horizontal direction, it is convolved with a fractional wavelet decomposition low-pass filter, and each row vector is downsampled. After the vertical direction boundary is extended, it is convolved with a fractional wavelet decomposition high-pass filter, and each column vector is downsampled to obtain the wavelet coefficient matrix FCH of the image signal.

(c) LH subband

After the two-dimensional noisy signal is extended in the horizontal direction, it is convolved with a fractional wavelet decomposition high-pass filter, and each row vector is downsampled. After the vertical direction boundary is extended, it is convolved with a fractional wavelet decomposition low-pass filter, and each column vector is downsampled to obtain the wavelet coefficient matrix FCV of the image signal.

(d) HH subband

After the horizontal boundary extension, the two-dimensional noisy signal is processed by convolution with a fractional wavelet decomposition high-pass filter, and each row vector is downsampled. After the vertical boundary extension, the two-dimensional noisy signal is processed by convolution with a fractional wavelet decomposition high-pass filter, and each column vector is downsampled to obtain the wavelet coefficient matrix FCD of the image signal.

Step 3: Threshold processing is performed on the high-frequency coefficients in three directions;

Threshold processing is performed on the high-frequency coefficients in the horizontal, diagonal and vertical directions to generate new coefficient matrices FNA, FNH, FNV and FND;

Step 4: Signal wavelet reconstruction;

Firstly, the wavelet reconstruction high/low pass filter coefficients are transformed by fractional calculus to change the original fixed form, so that the filter form changes with the change of the number of integration times of fractional calculus; secondly, the wavelet reconstruction high/low pass filter after fractional calculus is applied to the generation process of four reconstruction coefficient matrices; the details are as follows:

(a) Approximate reconstruction coefficient matrix FCA’;

After upsampling and extending the boundaries of each column vector of the coefficient matrix FNA of the image signal, convolution is performed with the fractional wavelet reconstruction low-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, convolution is performed with the fractional wavelet reconstruction low-pass filter and the row vector is intercepted, and the approximate reconstruction coefficient matrix FCA' of the image signal is obtained.

(b) Reconstruction coefficient matrix FCH’

After upsampling and extending the boundaries of each column vector of the coefficient matrix FNH of the image signal, it is convolved with the fractional wavelet reconstruction high-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, it is convolved with the fractional wavelet reconstruction low-pass filter and the row vector is intercepted to obtain the reconstructed coefficient matrix FCH’ of the image signal.

(c) Reconstruction coefficient matrix FCV’

After upsampling and extending the boundaries of each column vector of the coefficient matrix FNV of the image signal, it is convolved with the fractional wavelet reconstruction low-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, it is convolved with the fractional wavelet reconstruction high-pass filter and the row vector is intercepted to obtain the reconstructed coefficient matrix FCV’ of the image signal.

(d) Reconstruction coefficient matrix FCD’

After upsampling and extending the boundaries of each column vector of the coefficient matrix FND of the image signal, convolution is performed with the fractional wavelet reconstruction high-pass filter and the column vector is intercepted. After upsampling and extending the boundaries of each row vector, convolution is performed with the fractional wavelet reconstruction high-pass filter and the row vector is intercepted, and the reconstruction coefficient matrix FCD' of the image signal is obtained.

Step 5: Signal restoration after noise reduction;

The approximate reconstruction coefficient matrix obtained in step 4 is added to the reconstruction coefficient matrix to obtain the denoised signal, that is: FX’=FCA’+FCH’+FCV’+FCD’, where FX’ is the final denoised signal.

The present invention adopts a soft threshold algorithm to perform fractional calculus changes, so that the existing soft threshold algorithm changes continuously with the change of the number of integration times of the fractional calculus, better adapts to the processed signal, and achieves a better threshold filtering effect; the adopted soft threshold algorithm performs fractional calculus changes; according to actual needs, the noisy signal is respectively subjected to wavelet one-layer wavelet decomposition, two-layer wavelet decomposition and three-layer wavelet decomposition, the scale vector setting is determined by the number of wavelet decomposition layers, and the threshold vector is set according to actual needs; the coefficient matrices FCA, FCH, FCV and FCD of the LL, HL, LH and HH subbands are respectively subjected to soft threshold filtering processing in three directions of horizontal, diagonal and vertical directions, and new coefficient matrices FNA, FNH, FNV and FND are correspondingly generated.

(3) Technical defects of using existing wavelet decomposition and reconstruction technology for noise reduction

At present, the defect of using wavelet decomposition and reconstruction technology for signal noise reduction is that the selected wavelet decomposition high/low pass filters and reconstruction high/low pass filters are single and fixed in form, and the threshold algorithm form is also limited, and cannot be flexibly adjusted according to the actual signal, so the noise reduction effect is also limited.

Let x = X + 40 * randn (size (X)) be the noisy signal, where X is the original image woman that comes with the Matlab system, and 40 * randn (size (X)) is the added white noise signal. The wavelet decomposition technology is used to decompose the noisy signal into one layer, two layers and three layers respectively, and the high-frequency component is filtered using a soft threshold, where the threshold vector is P, and the wavelet function name used is ‘sym5’, and then wavelet reconstruction is performed to complete the denoising of the noisy signal. The processing results are divided into two parts: one part is the image simulation effect diagram, and the other part is the maximum error value between the denoised image and the original image. The results are shown in Figures 3, 4, 5 and Table 2 respectively.

By comparing Table 2 with Table 1 and Figure 3, Figure 4, and Figure 5 (c) with (d), it can be seen that the noise reduction effect of fractional wavelet decomposition and reconstruction technology is significantly better than the existing technology. In addition, the values of Lo_D and Lo_R in Table 2 are temporarily set to zero, that is, the number of integrations of fractional calculus is zero. If other values are selected, the noise reduction effect can be improved.

Table 2 Comparison of the maximum error of the original image after fractional wavelet decomposition and reconstruction

Serial number N P Hi_D Lo_D Hi_R Lo_R V Err1 O 1 1 [34 50] 0.808 0 -0.2 0 0.25 121.63 16.9% 2 2 [87 87] 0.51 0 0.01 0 0.26 111.37 23.8% 3 3 [97 97] 0.10 0 0.11 0 0.01 117.37 20.3%

Where: N—number of wavelet decomposition layers

Hi_D—Decomposition of high-pass filter fractional calculus integration times

Lo_D—Decomposition of low-pass filter fractional calculus integration times

Hi_R—Reconstruction high-pass filter fractional calculus integration times

Lo_R—Reconstruction low-pass filter fractional calculus integration times

V—The number of integrations of the soft threshold algorithm fractional calculus

Err1—Noise reduction error value of fractional wavelet decomposition and reconstruction technology

O—Accuracy improvement rate after noise reduction using fractional wavelet decomposition and reconstruction technology (relative to the error in Table 1)

The present invention changes the theoretical algorithm of the threshold by fractional calculus, so that the algorithm form of the threshold changes with the number of integration times of the fractional calculus, which greatly increases the algorithm form of the threshold. In this way, the defects of the current threshold algorithm limited to soft threshold and hard threshold or several other fixed forms are overcome. In addition, in order to further improve the noise reduction effect, the traditional noise reduction process using wavelet decomposition and reconstruction technology is improved.

Claims (2)

1. The noise reduction method by utilizing fractional wavelet decomposition and reconstruction technology is characterized by comprising the following steps:

Step 1: invoking noisy signals

Reading the noise-containing signal under Matlab or other platforms, namely completing calling the noise-containing signal;

step 2: performing fractional wavelet decomposition on the noise-containing signal to generate a new wavelet coefficient matrix;

Firstly, fractional calculus changes are carried out on wavelet decomposition high-pass filter coefficients and low-pass filter coefficients, so that the filter form changes along with the change of the integral times of fractional calculus; secondly, the fractional wavelet decomposition high-pass filter coefficient and the low-pass filter after fractional calculus change are applied to the generation process of four sub-bands; the method comprises the following specific steps:

(a) LL subband;

after the boundary of the two-dimensional noise-containing signal in the horizontal direction is prolonged, carrying out convolution processing by using a fractional wavelet decomposition low-pass filter, carrying out downsampling on each row vector, after the boundary of the two-dimensional noise-containing signal in the vertical direction is prolonged, carrying out convolution processing by using the fractional wavelet decomposition low-pass filter, and carrying out downsampling on each column vector to obtain an approximate wavelet coefficient matrix FCA of the image signal;

(b) HL sub-band

After the two-dimensional noise-containing signal is prolonged at the boundary in the horizontal direction, performing convolution processing by using a fractional wavelet decomposition low-pass filter, performing downsampling on each row vector, and after the two-dimensional noise-containing signal is prolonged at the boundary in the vertical direction, performing convolution processing by using a fractional wavelet decomposition high-pass filter, performing downsampling on each column vector, and obtaining a wavelet coefficient matrix FCH of the image signal;

(c) LH sub-band

The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition low-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCV of the image signal;

(d) HH sub-band

The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCD of the image signal;

step 3: threshold processing is carried out on the high-frequency coefficients in three directions;

Thresholding the high frequency coefficients in the horizontal, diagonal, and vertical directions to generate new coefficient matrices FNA, FNH, FNV and FND;

Step 4: reconstructing signal wavelets;

Firstly, carrying out fractional calculus change on wavelet reconstruction high/low pass filter coefficients, changing the original fixed form, and enabling the filter form to change along with the change of the integral times of fractional calculus; secondly, a wavelet reconstruction high/low pass filter changed by a plurality of times of calculus is applied to the generation process of four reconstruction coefficient matrixes; the method comprises the following steps:

(a) Approximating the reconstruction coefficient matrix FCA';

After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNA of the image signal, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete column vector interception, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction low-pass filter to complete row vector interception, so that an approximate reconstruction coefficient matrix FCA' of the image signal is obtained;

(b) Reconstructing coefficient matrix FCH'

After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNH of the image signal, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCH' of the image signal is obtained;

(c) Reconstructing coefficient matrix FCV'

After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNV of the image signal, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCV' of the image signal is obtained;

(d) Reconstructing coefficient matrix FCD'

After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FND of the image signal, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCD' of the image signal is obtained;

step5: recovering after noise reduction of the signal;

Adding the approximate reconstruction coefficient matrix obtained in the step 4 to the reconstruction coefficient matrix to obtain a noise-reduced signal, namely: FX '=fca' +fch '+fcv' +fcd ', FX' is the resulting noise reduced signal.

2. The noise reduction method using fractional wavelet decomposition and reconstruction technique according to claim 1, wherein:

Step 3, adopting a soft threshold algorithm to perform fractional calculus change; the adopted soft threshold algorithm performs fractional calculus change; according to actual needs, carrying out wavelet first-layer wavelet decomposition, second-layer wavelet decomposition and three-layer wavelet decomposition on the noise-containing signal respectively, wherein the scale vector setting is determined by the number of wavelet decomposition layers, and the threshold vector is set according to actual needs; the coefficient matrices FCA, FCH, FCV and FCD of the LL, HL, LH, and HH subbands are respectively subjected to soft threshold filtering in the horizontal, diagonal, and vertical directions, to correspondingly generate new coefficient matrices FNA, FNH, FNV and FND.