CN102652680A - Ultrasound computed tomography method on basis of non uniform fast Fourier transform (NUFFT) - Google Patents
Ultrasound computed tomography method on basis of non uniform fast Fourier transform (NUFFT) Download PDFInfo
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Abstract
The invention discloses an ultrasound CT (computed tomography) method on the basis of non uniform fast Fourier transform (NUFFT). According to the ultrasound CT method, the imaging result of ultrasound CT obtained by a gridding method serves as an initial value of an iteration method, so that iterations approaching a truth value are reduced, and the amount of computation is decreased. Regularization factors are introduced and are optimized and analyzed by virtue of an improved conjugate gradient (CG) method, so that the convergence of the iteration method is ensured, and the iterations can approach the truth value of an image step by step. According to the method, air domain and frequency domain methods are combined with information of UTCT (Ultrasound Treatment Computed Tomography) and URCT (Ultrasound Reflection Computed Tomography), wherein the UTCT contains the information of the low frequency part of the image, the URCT contains the information of the relatively high band pass part of the image, the URCT can be used for restoring part of edge information lost by the UTCT, and the information is increased by virtue of the combination of the UTCT and UCRT, so that the effect of the restored image is better than that of the image formed by virtue of the independent UTCT or UCRT, and the better imaging effect is achieved.
Description
Technical field:
The present invention be more particularly directed to a kind of method of improved ultrasound computed tomography image reconstruction, belong to the medical imaging field.
Technical background:
Traditional ultrasonic imaging technique is that the interior of articles medium that arrives according to the object collected outside is to hyperacoustic scattered information; The constructed object internal structure; But the supersonic imaging apparatus that is applied to medical domain of success mostly is based on echo at present; And its imaging according to the information of ultrasonic scattering ripple, generates the structure chart of inside of human body also just qualitatively quantitatively.It is the fresh target that applications of ultrasound Study on Technology person pursues.
Tomography (Computed Tomography, be called for short CT) technology be meant through from the object external detection to data rebuild the technology of interior of articles information, also make computed assisted tomography technological.If the energy waves of diagnosis usefulness is hyperacoustic, be called as ultrasound computed tomography (Ultrasound CT).Ultrasonic CT imaging can obtain the quantitative image of the velocity of sound, acoustic attenuation coefficient and non-linear parameter etc. by X-CT imaging amplification with this formation method.The ultrasound tomography technology is widely used in fields such as medical science, industrial detection.Aspect biomedical engineering, the variation of the data for projection that causes unusually of the acoustic characteristic of biological tissue can be finally inversed by the pathological characters of biological tissue.Ultrasound computed tomography comprises ultrasonic projection tomography technology (UTCT:Ultrasound Transmission-mode Computed Tomography) and ultrasonic reflection tomography technology (URCT:UltrasoundReflection-mode Comoputed Tomography) again.The ultrasonic transmitter of porjection type CT and receptor are positioned at the both sides of measured medium, obtain the information of medium according to the ultrasound wave of accepting transmission.And the ultrasonic transmitter of reflection-type CT and receptor are positioned at the same side of measured medium, the information of rebuilding medium through the ultrasonic echo that receives reflection.
Early stage research hypothesis ultrasound wave at interior of articles with straightline propagation; Utilize emitter to time delay between the receptor or re-reading decay; Rebuild the parameters such as the velocity of sound, absorption characteristic of interior of articles, but ultrasonicly have an obvious diffraction characteristic, on the interface, have significant refraction, diffraction; Thereby propagation path is complicated, and this makes the theoretical research of U-CT and x-ray imaging (X-CT) different.Ultrasound tomography domestic and international research method is roughly following three kinds at present:
1. filtering anti-spread method.Utilization is similar to stack and the back projection that the method for the FBP algorithm of X-CT realizes the dependent projections data of impact point.Algorithm is simple, but computing is time-consuming, need on computational complexity, improve.
2. frequency domain Gridding method.The theoretical basis of ultrasound tomography is Fourier's scatter projection theorem, i.e. the value of the Fourier transformation correspondence of the projection of a certain angle on a curve of the two-dimensional Fourier transform of original image.The uneven projection value of known multi-angle can obtain the frequency domain value of corresponding original image through methods such as interpolation.Can obtain the distribution of the spatial domain of original image through two-dimensional Fourier transform.But can introduce multiple-error, image quality is not good.
3.UTCT utilize transmitted field and mirror field data reconstruction interface image respectively with URCT, the former lacks high-frequency information, profile and details imperfection, and the latter lacks low frequency information, can only obtain the outside marginal information, and imaging effect remains to be improved.
Summary of the invention
Technical problem: to the problem that occurs in the above ultrasonoscopy reconstruction; The present invention provides a kind of new ultrasound tomography method based on ultrasonic scattering projection theorem and non-homogeneous Fourier transformation (NUFFT); When improving image quality; Reduce computational complexity, reached reasonable effect.
Technical scheme: the ultrasound tomography method based on non-homogeneous Fourier transformation provided by the present invention; Adopt the method combination transmission of frequency domain and spatial domain and the information that reflectance data is comprised, based on the iterative image reconstruction algorithm reconstructed image of non-homogeneous fast Fourier transform.The method is utilized the scattered field data, is the non-homogeneous Fourier inverse transformation of a 2D problem with image reconstruction problem definition.Because direct non-homogeneous Fourier inverse transformation is difficult for realizing, so adopt the non-homogeneous quick Fourier direct transform of optimizing criterion based on min-max, realizes effectively calculating fast of non-homogeneous Fourier inverse transformation through alternative manner.Specific as follows:
1. modelling research, because actual data are difficult to obtain, we adopt the method for experiment simulation to obtain experimental data in the research of algorithm.The Shepp-Logan model of selection standard is convenient to the excellent summary of analysis result and comparison algorithm.
2. the utilization mathematical method solves practical problem.The inverting of ultrasonic scattering field belongs to the category of inverse problem on mathematics, this problem is introduced mathematical computational methods such as iteration method etc., the result that expectation can be optimized.
3. introduce advanced now non-homogeneous Fourier transform method and fast algorithm thereof, and its parameter is improved.
4. combine the pluses and minuses of UTCT and URCT, improve image quality.Imaging effect for UTCT and URCT is analyzed, and can find that at frequency domain the two is the relation that complements each other.Adopt frequency domain or spatial domain method to realize the stack of quantity of information.
The present invention also has some technical characterictics following:
1. used diffraction chromatography method for imaging, it is based upon on the basis of Fourier's diffraction theorem, has set up the one dimension Fourier transform of data for projection and the relation between the transform frequency domain, shown in the following formula:
FT
1D{P
ψ(ξ)}(k
ξ)＝FT
2D{f(x，y)}(k
x，k
y)
P wherein
w(ξ) representing angle of incidence is the projection value of ψ, and (x is former transform y) to f, and the one-dimensional Fourier transform that data for projection is described is corresponding to the value on the semicircle of the two-dimensional Fourier transform frequency domain of transform (Ewald circle).
2. introduce non-homogeneous Fourier transform method, adopted alternative manner to level off to the actual value of image, definition NUDFT operator
F＝Ψf?Ψ∈C
M×N
F is Non-uniform DFT value in the formula, and Ψ is the complex-exponential function matrix of full rank, and f is a sampled signal.Directly calculate the NUDFT value, computation complexity is too big, and its approximation method is the Fourier base space Φ ∈ C that f was mapped to uniform sampling through the FFT computing
CN * N, more non-homogeneous sampling point is carried out interpolation calculation.The approximate NUFFT operator Γ of definition:
F≈Γf＝U
pΦf
C is an oversample factor in the formula, U
pBe interpolation operator.For non-homogeneous sampling point z
k, choose its most contiguous p element and carry out interpolation arithmetic.The formula of asking for f is:
f＝Ψ+F
Also can pass through least squares formalism
When iteration progressively makes g (f) when reaching minima, f levels off to actual value, and the transform of reconstruction levels off to optimum.
Experimental procedure is following:
Calculate UTCT and URCT respectively, obtain transmission-type back projection image and reflection-type back projection image, and adopt image interfusion method to carry out the figure image intensifying in the spatial domain.
1. adopt the Shepp-Logan model of standard to carry out the emulated data that projection obtains transmission-type and reflection-type ultrasonic scattering field.
2. transmission-type and reflection-type scattered field data are superposeed in frequency domain.Adopt the gridding method to calculate to add and the reconstructed image of data initial value as alternative manner.
3. calculate the Grad of the cost function g (f) that uses in the iterative step of non-homogeneous Fourier transformation.
4. iterative computation levels off to optimal value gradually.
5. calculate UTCT and URCT respectively, obtain transmission-type back projection image and reflection-type back projection image, and adopt image interfusion method to carry out the figure image intensifying with contrast experiment's effect in the spatial domain.
With respect to scheme of the prior art, advantage of the present invention is:
1. adopted the initial value of the imaging results of the ultrasound computed tomography that the frequency domain interpolation method obtains, reduced leveling off to the iterations of true value, reduced amount of calculation as alternative manner.
2. utilize improved conjugate gradient (CG) method, introduce the regularization factor, and it is optimized analysis, the convergence of iterative method is guaranteed, can progressively level off to the actual value of image.
3. the information that combines UTCT and URCT with spatial domain and two kinds of methods of frequency domain.UTCT has comprised the information of image low frequency part, and URCT has comprised the information of the logical part of image higher band.URCT recovers a part of marginal information that UTCT loses, and both increase by bonded quantity of information, and the effect of the image that recovers is better than a kind of quality that forms images of independent application.
Description of drawings
Below in conjunction with accompanying drawing the present invention is further described:
Fig. 1 ultrasonic scattering theorem is for the sketch map of the ultrasound computed tomography of reflective-mode.
Fig. 2 ultrasonic scattering theorem is for the sketch map of the ultrasound computed tomography of transmission mode.
The frequency-domain information of Fig. 3 transmission mode ultrasound tomography combines with reflective-mode ultrasound tomography frequency-domain information.
Fig. 4 imaging effect.Wherein a is an original image, and b is the transmission mode imaging, and c is that UTCT and URCT combine imaging effect, and d is the reflective-mode imaging effect.
Claims (5)
1. ultrasound tomography method based on non-homogeneous Fourier transformation; It is characterized in that combining the information of transmission and reflective-mode ultrasound tomography; Through calculate the optimal value of original image based on the alternative manner of non-homogeneous Fourier transformation; And adopt the initial value of the result of Gridding method acquisition as iteration, to reduce iterations and amount of calculation.
2. the ultrasound tomography method based on non-homogeneous Fourier transformation according to claim 1, its image-forming step is following:
A. adopt the Shepp-Logan model of standard to carry out the emulated data that projection obtains transmission-type and reflection-type ultrasonic scattering field.
B. transmission-type and reflection-type scattered field data are superposeed in frequency domain.Adopt the gridding method to calculate to add and the reconstructed image of data initial value as alternative manner.
C. calculate the Grad of the cost function g (f) that uses in the iterative step of non-homogeneous Fourier transformation.
D. iterative computation levels off to optimal value gradually.
E. calculate UTCT and URCT respectively, obtain transmission-type back projection image and reflection-type back projection image, and adopt image interfusion method to carry out the figure image intensifying with contrast experiment's effect in the spatial domain.
3. the method for the Shepp-Logan model of the described selection standard of step a according to claim 2 utilizes its analytic value can obtain the amplitude of frequency domain corresponding point, and numerical value is accurate, does not have the error of introducing, and is convenient to the excellent summary of comparison algorithm.
4. the described initial value that utilizes the method for frequency domain interpolation as alternative manner of step b according to claim 2 has been saved iterations, has reduced computational complexity.
5. the information that has combined transmission and reflective-mode ultrasound tomography increases the quantity of information of back projection, and image quality is more excellent.
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| CN104462017A (en) * | 2014-11-21 | 2015-03-25 | 电子科技大学 | I/O number-unequal quick non-uniform discrete Fourier transform method and system |
| CN108519351A (en) * | 2018-04-09 | 2018-09-11 | 西安工业大学 | The three-dimensional refractive index of wavelength magnitude non-uniformity phase object quantifies reconstructing method |
| CN108761752A (en) * | 2012-10-30 | 2018-11-06 | 加州理工学院 | Fourier overlapping associations imaging system, device and method |
| CN109884183A (en) * | 2019-01-05 | 2019-06-14 | 天津大学 | Ultrasound tomography method for transmission reflection modality fusion |
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| CN108761752A (en) * | 2012-10-30 | 2018-11-06 | 加州理工学院 | Fourier overlapping associations imaging system, device and method |
| US12237094B2 (en) | 2012-10-30 | 2025-02-25 | California Institute Of Technology | Fourier ptychographic imaging systems, devices, and methods |
| US11468557B2 (en) | 2014-03-13 | 2022-10-11 | California Institute Of Technology | Free orientation fourier camera |
| CN104462017A (en) * | 2014-11-21 | 2015-03-25 | 电子科技大学 | I/O number-unequal quick non-uniform discrete Fourier transform method and system |
| CN104462017B (en) * | 2014-11-21 | 2017-03-29 | 电子科技大学 | The unequal Fast Inhomogeneous discrete Fourier transform method and system of I/O numbers |
| US10718934B2 (en) | 2014-12-22 | 2020-07-21 | California Institute Of Technology | Epi-illumination Fourier ptychographic imaging for thick samples |
| US11092795B2 (en) | 2016-06-10 | 2021-08-17 | California Institute Of Technology | Systems and methods for coded-aperture-based correction of aberration obtained from Fourier ptychography |
| CN108519351A (en) * | 2018-04-09 | 2018-09-11 | 西安工业大学 | The three-dimensional refractive index of wavelength magnitude non-uniformity phase object quantifies reconstructing method |
| CN109884183A (en) * | 2019-01-05 | 2019-06-14 | 天津大学 | Ultrasound tomography method for transmission reflection modality fusion |
| CN109884183B (en) * | 2019-01-05 | 2021-07-09 | 天津大学 | Ultrasound tomography method for transmission reflection modality fusion |
| CN112914611A (en) * | 2021-01-29 | 2021-06-08 | 大连东软教育科技集团有限公司 | Ultrasonic microvascular imaging method based on random singular value decomposition and weighted L1 norm |
| CN112914611B (en) * | 2021-01-29 | 2024-05-31 | 东软教育科技集团有限公司 | Ultrasound microvascular imaging method based on randomized singular value decomposition and weighted L1 norm |
| US12198300B2 (en) | 2021-02-25 | 2025-01-14 | California Institute Of Technology | Computational refocusing-assisted deep learning |
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