CN114782242A - High-frequency ultrasonic image reconstruction method, storage medium and computer equipment - Google Patents

High-frequency ultrasonic image reconstruction method, storage medium and computer equipment Download PDF

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CN114782242A
CN114782242A CN202210289407.5A CN202210289407A CN114782242A CN 114782242 A CN114782242 A CN 114782242A CN 202210289407 A CN202210289407 A CN 202210289407A CN 114782242 A CN114782242 A CN 114782242A
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equation
image
ultrasonic image
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李昕泽
崔崤峣
焦阳
王宁浩
李家奇
李章剑
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Suzhou Institute of Biomedical Engineering and Technology of CAS
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Abstract

The invention discloses a high-frequency ultrasonic image reconstruction method, a storage medium and computer equipment, wherein the method comprises the following steps: 1) converting the high-frequency ultrasonic image reconstruction problem into a morbid state inverse problem, and simulating an imaging mechanism equation of an ultrasonic image; 2) introducing a point spread function to update an imaging mechanism equation of the ultrasonic image; 3) introducing a regular constraint term, and updating an imaging mechanism equation of the ultrasonic image by a maximum posterior estimation expression; 4) deriving an alternative direction multiplier equation by adopting an augmented Lagrange equation; 5) and carrying out iterative solution on the multiplier equation in the alternating direction to obtain a reconstruction result of the high-frequency ultrasonic image. The ultrahigh frequency ultrasonic fast reconstruction method provided by the invention grasps the characteristics of a high frequency ultrasonic imaging system, utilizes the characteristics and carries out reverse deduction according to the noise representation equation in the system, thereby recovering the information which is lost among the reconstructed ultrasonic image pixel points due to a plurality of reasons such as the size of an ultrasonic probe, the sampling frequency of the system and the like, and improving the resolution ratio of an ultrasonic image.

Description

High-frequency ultrasonic image reconstruction method, storage medium and computer equipment
Technical Field
The present invention relates to the field of image processing, and in particular, to a method for reconstructing a high-frequency ultrasound image, a storage medium, and a computer device.
Background
The working frequency of the high-frequency ultrasonic system exceeds 50MHz and even can reach 200-500 MHz. Higher operating frequencies mean higher image resolutions, and more detailed information can be obtained, and thus higher image resolutions are a constant goal pursued. According to the nyquist sampling law, in order to completely recover the sampled ultrasonic radio frequency signal, the sampling frequency of the ultrasonic radio frequency signal is required to be greater than 2 times the highest frequency of the signal. Therefore, a sampling frequency as high as 1GHz has very high requirements on a chip circuit, the cost of the chip circuit also increases exponentially, and the high-sensitivity sampling circuit is more susceptible to working environment images. Correspondingly, the problem of huge data transmission amount is also brought by high sampling rate, the working cost of the data transmission module is increased, and the working load of the signal image processing at the rear end is also increased. Furthermore, the higher working frequency also increases the difficulty in manufacturing the ultrasonic transducer, and increases the cost.
Therefore, on the basis of not improving the existing hardware condition, the detail information of the ultrasonic image is reconstructed through a back-end algorithm, and the reconstruction of the image with higher resolution under the high-frequency working condition is significant.
Referring to FIG. 6a, an image obtained by a conventional high frequency ultrasound system is represented, having a size (j, k); the ultrahigh frequency ultrasound image reconstruction aims to reconstruct the missing information between adjacent pixel points in fig. 6a, as shown by the blue region (i.e., "; fig. 6c shows the reconstructed high resolution image with dimensions (n × j, n × k). Fig. 6d is the result of fig. 6a directly enlarged to the size (n × j, n × k), where n represents a positive integer multiple. It can be seen from the figure that although the size is the same, the reconstructed image contains richer spatial information, thus the information content contained in the unit pixel space is really improved, and the resolution of the ultrahigh frequency ultrasonic image is improved.
Conventional methods for adding information in images include interpolation methods including nearest neighbor, bilinear interpolation, cubic interpolation, and other high-order interpolation. The basic principle is that interpolation is carried out by analyzing the characteristic relation of a pixel point to be interpolated in an image and a plurality of other pixels adjacent to or in the neighborhood in a space domain and even a frequency domain. The method has the obvious advantages that the application range is wide, only pixel point values in the image need to be considered, and the method can be used for natural images, medical images and the like. In practical application scenarios, images generated by different imaging systems have specificity, and for example, an electron microscope, an optical microscope and an ultrasonic microscope have specific styles due to differences of respective imaging modes. Therefore, the conventional method for increasing the image information amount exposes the disadvantage of purely depending on the pixel value and the gray scale value, and does not consider other factors such as signal acquisition and resolution possibly influencing in the signal conversion processing process.
Disclosure of Invention
The present invention provides a method, a storage medium and a computer device for reconstructing a high-frequency ultrasound image, which are directed to overcome the above-mentioned deficiencies in the prior art. In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a method of reconstructing a high frequency ultrasound image, comprising the steps of:
1) converting the high-frequency ultrasonic image reconstruction problem into a pathological inverse problem, and simulating an imaging mechanism equation of the ultrasonic image;
2) introducing a point spread function to update an imaging mechanism equation of the ultrasonic image;
3) introducing a regular constraint term, converting a ill-conditioned inverse problem into a constraint optimization problem, and updating an imaging mechanism equation of the ultrasonic image by using a maximum posterior estimation expression;
4) deriving an alternative direction multiplier equation by adopting an augmented Lagrange equation based on the result of the step 3);
5) and carrying out iterative solution on the multiplier equation in the alternating direction, and stopping iteration when convergence occurs to obtain a reconstruction result of the high-frequency ultrasonic image.
Preferably, an imaging mechanism equation of the ultrasound image simulated in step 1) is:
y＝Ax+n (1)；
where x represents the original image input, y represents the image ultimately output by the system, n represents noise, and a represents the linear or non-linear operation applied by the imaging system on the original image.
Preferably, the imaging mechanism equation updated in step 2) is:
y＝SHx+n (2)；
wherein x represents an input original image, y represents an image finally output by the system, n represents noise, H represents convolution operation of a point spread function and an input signal, and S represents down-sampling extraction operation.
Preferably, wherein the point spread function is a type of bessel equation or a variant thereof, the point spread function includes at least the following parameters: sound velocity, ultrasonic wavelength, center frequency, aperture of the probe.
Preferably, the imaging mechanism equation updated in step 3) is:
Figure BDA0003561069140000031
Figure BDA0003561069140000032
wherein,
Figure BDA0003561069140000033
representing output
Figure BDA0003561069140000034
And the data fidelity between the noise n, wherein y represents an image finally output by the system; phi (Ax) is a regular constraint term; lambda is a weight coefficient to balance the weight between the data fidelity and the regular constraint term; a represents different image properties of different imaging systems;
where the canonical constraint term φ (Ax) is/1Norm, l2Norm, total variation or non-convex penalty term.
Preferably, the alternating direction multiplier equation obtained in step 4) is:
Figure BDA0003561069140000035
equation (5) replaces Ax in equation (4) with v, which aims to decompose the constraint optimization problem into two separate parts:
Figure BDA0003561069140000036
and phi (v); so that both parts are solved iteratively at the same time using the alternating multiplier equations.
Preferably, the step 5) specifically includes:
5-1) rewriting equation (5) to the augmented Lagrangian equation:
Figure BDA0003561069140000037
satisfy the requirements of
Ax＝v(6)；
5-2) transcribe equation (6) into 3 equations:
Figure BDA0003561069140000038
wherein k represents the number of iterations, u is a Lagrangian multiplier, and η is a weight parameter;
5-3) rewriting formula (7) as:
Figure BDA0003561069140000039
Figure BDA00035610691400000310
the formula (8-2) is regarded as oneA de-noising operation, v being due to the action of a constraint term phi (v)k+1V is composed ofkDeducing that each iteration round updates the denoised image vk+1And the image v before denoisingkAnd (5) data fidelity among the data, stopping updating until convergence is reached, and obtaining a reconstruction result of the high-frequency ultrasonic image.
Preferably, the step of iterating in step 5-3) is:
s1, inputting a low-resolution image y containing noise, performing down-sampling (sampling) operation S, a system point spread function H, and constraining weight parameters lambda and eta;
based on (8-1) and xk＝vk-ukThe following equation (9) is obtained, and x is updated according to the following equation (9):
Figure BDA0003561069140000041
s2, based on (8-2) and xk＝vk-ukObtaining the following formula (10), and updating v according to the following formula (10):
Figure BDA0003561069140000042
s3, according to yk+1And xk+1Computing lagrange multiplier u:
uk+1＝uk+η(xk+1-vk+1) (11)
s4, when satisfying max { | | xk+1-xk||2，||vk+1-vk||2，||uk+1-uk||2Stopping iteration when the rate is less than or equal to gamma, and outputting:
Figure BDA0003561069140000043
the present invention also provides a storage medium having stored thereon a computer program for, when executed, implementing a method as described above.
The invention also provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method as described above when executing the computer program.
The beneficial effects of the invention are:
the ultrahigh frequency ultrasonic rapid reconstruction method provided by the invention grasps the characteristics of a high frequency ultrasonic imaging system, utilizes the characteristics and carries out reverse deduction according to the in-system noise characterization equation, can recover and reconstruct information which is lost among ultrasonic image pixel points due to a plurality of reasons such as the size of an ultrasonic probe, the sampling frequency of the system and the like, and improves the resolution ratio of an ultrasonic image.
The optimization cost of each part in the ultrahigh frequency ultrasound is very high, and the algorithm flow provided by the invention can obtain an ultrahigh frequency ultrasound image with higher quality on the basis of the existing hardware, so that the noise is reduced and the resolution is improved;
the framework adopted by the invention can be better suitable for systems with different working frequencies and different ultrasonic probes, and is used for improving the quality of one-dimensional signals and two-dimensional images;
the super-resolution ultrasonic image reconstruction method provided by the invention can restore twice or even higher data from less original data, thereby ensuring that the same or even better image quality can be obtained under the condition of smaller data transmission quantity, and being beneficial to realizing the high-efficiency remote processing function.
Drawings
FIG. 1 is a schematic view of an imaging process of an ultrasound image;
FIG. 2 is a schematic diagram of the effect of the point spread equation on imaging;
FIGS. 3-5 show the results of different solution methods in 3 examples;
fig. 6 is a schematic diagram of conventional high-frequency ultrasound image reconstruction.
Detailed Description
The present invention is further described in detail below with reference to examples so that those skilled in the art can practice the invention with reference to the description.
It will be understood that terms such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.
Example 1
The embodiment provides a method for reconstructing a high-frequency ultrasonic image, which comprises the following steps:
1) converting the high-frequency ultrasonic image reconstruction problem into a morbid state inverse problem, and simulating an imaging mechanism equation of an ultrasonic image; the method specifically comprises the following steps:
y＝Ax+n (1)；
wherein x represents an input original image, y represents an image finally output by the system, n represents accumulative noise introduced by units such as an ultrasonic transducer or a lens, and a represents a linear or nonlinear operation applied to the original image by the imaging system, and in most ultrasonic imaging systems, operation a includes down-sampling (decimation) and fuzzy aliasing, and fig. 1 is an imaging process of an ultrasonic image.
One of the key techniques of the present invention is to recover a lossless high resolution image data set x from a lossy image data set y using the systematic additive noise n and linear operation a. This process of inverting a more complete image from an incomplete dataset is generalized to the ill-posed inverse problem (ill-posed inverse schema). Regularization by using a cost function is an effective method for inverting the ill-conditioned inverse problem. By adding a regularization term into the cost function, the ill-posed inverse problem can be transformed into a constrained optimization problem.
2) An imaging mechanism equation for updating an ultrasonic image by introducing a point spread function is specifically as follows:
y＝SHx+n (2)；
where x represents the original image input, y represents the final output image of the system, n represents noise, H represents the convolution operation of the point spread function (point spread function) with the input signal, and S represents the down-sampling decimation operation.
With respect to the point spread function: in the actual ultrasonic imaging, according to the physical properties of the ultrasonic beam, the shape of the echo signal of the measured object captured finally may be different from the actual shape of the measured object, resulting in a slightly distorted final imaging result. When an acoustic beam is scattered or reflected by a target, its echo signal will produce an approximate impulse response. In order to characterize the response of the imaging system to the point target, the concept of point spread equation PSF is proposed. The characteristics of different ultrasound probes have a certain influence on the point spread equation of the system. Fig. 2 shows the effect of the point spread equation on the imaging, fig. 2 left one: actual point target, fig. 2: a point spread function; fig. 2 right: and (5) performing convolution to obtain a final result. The point spread equation is equivalent to a convolution process, and a distorted image is obtained after a real object is convolved by the point spread equation.
The point spread function is a Bessel equation or a variant thereof, and the point spread function at least comprises the following parameters: sound velocity, ultrasonic wavelength, center frequency, aperture of the probe, etc.
In this embodiment, a class of bessel equations is selected:
Figure BDA0003561069140000061
wherein α represents the order.
3) Introducing a regular constraint term, converting a morbid state inverse problem into a constraint optimization problem, and updating an imaging mechanism equation of an ultrasonic image by a Maximum posterior estimation (Maximum-a-posteriori) expression; the imaging mechanism equation obtained by updating is as follows:
Figure BDA0003561069140000062
Figure BDA0003561069140000063
wherein,
Figure BDA0003561069140000064
representing output
Figure BDA0003561069140000065
And the data fidelity between the noise n, wherein y represents an image finally output by the system; phi (Ax) is a regular constraint term, also called penaltyTerms to introduce sparsity; lambda is a weight coefficient to balance the weight between the data fidelity and the regular constraint term; a represents different image properties of different imaging systems;
where the canonical constraint term φ (Ax) is/1Norm, l2Norm, total variation or non-convex penalty term.
4) Deriving an alternative direction multiplier equation by adopting an augmented Lagrange equation based on the result of the step 3); there are several methods for solving the constraint optimization problem, and the solution of the augmented lagrangian equation is preferably adopted in the invention. The augmented lagrange equation can derive an Alternating direction multiplier equation (Alternating direction method of multipliers), and the specific Alternating direction multiplier equation is as follows:
Figure BDA0003561069140000066
equation (5) replaces Ax in equation (4) with v, which aims to decompose the constraint optimization problem into two separate parts:
Figure BDA0003561069140000071
and phi (v); so that both parts are solved iteratively at the same time using the alternating multiplier equations. After the k +1 iteration, for xkAnd vkUpdate to obtain xk+1，vk+1And stopping iteration until the result converges. Compared with direct deconvolution operation, the method has the advantages that the deconvolution problem is converted into the optimization problem, and the operation dimensionality and complexity are reduced.
5) Performing iterative solution on the multiplier equation in the alternating direction, stopping iteration when convergence occurs, and obtaining a reconstruction result of the high-frequency ultrasonic image, wherein the iterative solution specifically comprises the following steps:
5-1) rewriting equation (5) to the augmented Lagrangian equation:
Figure BDA0003561069140000072
satisfy the requirement of
Ax＝v(6)；
5-2) to find the saddle point at which equation (6) converges, equation (6) is transcribed into 3 equations:
Figure BDA0003561069140000073
wherein k represents the number of iterations, u is a Lagrangian multiplier, and η is a weight parameter;
5-3) rewriting formula (7) as:
Figure BDA0003561069140000074
Figure BDA0003561069140000075
equation (8-2) can be considered as a de-noising operation because v is subject to the constraint term φ (v)k+1V is composed ofkDeducing that each iteration round updates the denoised image vk+1And the image v before denoisingkAnd stopping updating until convergence is reached, wherein the updating means that image noise is removed as much as possible, and the reconstruction result of the high-frequency ultrasonic image is obtained.
The constraint term phi (v) in equation (8) can be regarded as a flexible denoising module, and the replacement of phi (v) does not affect the solution of the whole optimization function. Therefore, the problem of high-resolution reconstruction of images of various imaging systems can be conveniently realized by substituting different phi (v), and the choice of phi (v) can be determined according to the practical application requirements and the characteristics of the imaging systems.
In the alternative direction multiplier equation solution, the regular constraint term phi (Ax) can be selected as 11 norms, 12 norms, total variation or non-convex penalty terms and the like to be derived, and besides the constraint optimization problem is solved in a space domain or a frequency domain, the derivation can also be performed in a wavelet domain. The following example demonstrates the solving process of step 5-3) when the constraint term phi (v) takes 11 norms, and the specific iteration steps are as follows:
s1, inputting a low-resolution image y containing noise, performing down-sampling (sampling) operation S, a system point spread function H, and constraining weight parameters lambda and eta;
based on (8-1) and xk＝vk-ukTo obtain the following equation (9), x is updated according to the following equation (9):
Figure BDA0003561069140000081
s2, based on (8-2) and xk＝vk-ukObtaining the following formula (10), and updating v according to the following formula (10):
Figure BDA0003561069140000082
s3, according to vk+1And xk+1Computing lagrange multiplier u:
Figure BDA0003561069140000083
s4, when max { | | | x is satisfiedk+1-xk||2,||vk+1-vk||2，||uk+1-uk||2Stopping iteration when the rate is less than or equal to gamma, and outputting:
Figure BDA0003561069140000084
in this embodiment, the derivation process of other constraint terms in the wavelet domain and the frequency domain is not described in detail.
In the invention, the process of outputting images by the high-frequency ultrasonic imaging system is represented as the convolution of an input signal and a system function, and then random noise is superposed, so that the degradation process of an image signal is more visual and is convenient to solve.
According to the invention, according to the physical properties of ultrasonic imaging, the characteristic point spread function of a high-frequency ultrasonic system is taken as the focus of denoising and high-resolution reconstruction, so that the specificity of ultrasonic imaging is fully utilized, and the reconstruction result is more accurate compared with the traditional general method.
The image super-resolution reconstruction belongs to a morbid state inverse problem, and the method is characterized in that a regular constraint term is introduced and converted into a constraint optimization problem to be solved.
In the invention, the problem is converted into a plurality of sub-equations by using the multiplier equation in the alternating direction, so that the operation dimensionality is reduced, the simultaneous solution of a plurality of variables in each iteration is realized, the operation speed is improved, and the time from the iteration of an equation set to a convergence condition is shortened.
In the invention, in the solving process of the multiplier equation in the alternating direction, the substitution of the constraint term in one of the sub-equations can be approximately regarded as the denoising operation; and the constraint term can be flexibly replaced without influencing the whole operation framework, so that different denoising operators can be conveniently inserted to reconstruct the image. I.e. indicating the flexibility and robustness of the present architecture.
In the invention, the solution of the multiplier equation in the alternating direction can be carried out in the time domain, can also be finished in the time domain by carrying out Fourier transform, and can also be finished in the wavelet domain, thereby having high degree of freedom and being capable of selecting according to the characteristics of signals. The derivation process is not repeated herein.
In the invention, convex functions (such as l) are adopted for solving solutions of the alternative direction multiplier equation1Norm, l2Norm, total variation, etc.) as constraint terms to solve the convex optimization problem; because the convex optimization problem is convenient for iterative convergence, the optimal solution can be found. In fact, the solution of the ill-conditioned inverse problem can also adopt a non-convex constraint term to further introduce sparsity, thereby greatly shortening the computational complexity.
Referring to fig. 3, the results of different constraint terms and their solving methods in an example are sequentially a: a low-resolution noisy image output by the high-frequency ultrasonic imaging system; b: optimizing results of the traditional interpolation method; c: time domain of the invention1Optimizing results under norm constraint; d: the invention has the advantages that the optimization result under the total variation constraint in the time domain is obtained; e: under the wavelet domain of the invention1Norm-constrained optimization results, F: the invention optimizes the result of the non-convex constraint term. The signal-to-noise ratio SNR and the root mean square error RMSE of the method have the effect improved compared with the original image, and the specific parameters are shown in the following table 1:
TABLE 1
PSNR ISNR RMSE TIME/S
B 35.236 / 0.0371 /
C 37.513 2.362 0.0133 2.541
D 39.985 4.132 0.0103 2.999
E 35.635 0.923 0.0233 1.757
F 42.194 6.356 0.0071 4.971
Referring to fig. 4, another example is shown, which is the result of different solving methods, in order a: performing high-frequency ultrasonic original drawing; b: optimizing results of the traditional interpolation method; c: time domain of the invention1The result under the norm constraint; d: the invention is a result under the constraint of total variation in the time domain; e: in the frequency domain of the invention1The result under the norm constraint; f: the result of the invention is a non-convex constraint. The signal-to-noise ratio SNR and the root mean square error RMSE are shown in the following table 2:
TABLE 2
Figure BDA0003561069140000091
Figure BDA0003561069140000101
As can be seen, compared with the traditional interpolation method, the SNR of the signal-to-noise ratio in the method is improved from 26.75 to 33.66 by 10-15%; root mean square error is reduced from 0.0382 to 0.0216; meanwhile, the calculation speed is improved by 15-20%.
Referring to fig. 5, another example is shown, which is the result of different solving methods, in order a: high-frequency ultrasonic original drawing; b: optimizing results of the traditional interpolation method; c: time domain of the invention1The result under the norm constraint; d: the invention is the result under the constraint of total variation in the time domain; e: i in frequency domain of the invention1The result under the norm constraint; f: the result of the non-convex constraint term of the present invention. The signal-to-noise ratio SNR and the root mean square error RMSE are shown in the following table 3:
the signal-to-noise ratio SNR and the root mean square error RMSE are shown in the following table 1:
TABLE 3
PSNR ISNR RMSE TIME/S
B 28.595 / 0.0372 /
C 31.534 2.939 0.0265 0.327
D 29.631 1.036 0.0330 1.032
E 29.620 1.025 0.0341 2.757
F 33.923 5.328 0.0239 0.471
Similarly, the method of the invention has obvious effect of improving the SNR and the root mean square error.
Example 2
A storage medium having stored thereon a computer program which, when executed, is for implementing the method of embodiment 1.
Example 3
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method of embodiment 1 when executing the computer program.
The present embodiment also provides a cloud server having a computer program stored thereon, which when executed, is configured to implement the method of embodiment 1.
While embodiments of the invention have been disclosed above, it is not limited to the applications listed in the description and the embodiments, which are fully applicable in all kinds of fields of application of the invention, and further modifications may readily be effected by those skilled in the art, so that the invention is not limited to the specific details without departing from the general concept defined by the claims and the scope of equivalents.

Claims (10)

1. A high-frequency ultrasonic image reconstruction method is characterized by comprising the following steps:
1) converting the high-frequency ultrasonic image reconstruction problem into a morbid state inverse problem, and simulating an imaging mechanism equation of an ultrasonic image;
2) introducing a point spread function to update an imaging mechanism equation of the ultrasonic image;
3) introducing a regular constraint term, converting the ill-conditioned inverse problem into a constraint optimization problem, and updating an imaging mechanism equation of the ultrasonic image by a maximum posterior estimation expression;
4) deriving an alternative direction multiplier equation by adopting an augmented Lagrange equation based on the result of the step 3);
5) and carrying out iterative solution on the multiplier equation in the alternating direction, and stopping iteration when convergence occurs to obtain a reconstruction result of the high-frequency ultrasonic image.
2. The method for reconstructing high-frequency ultrasonic image according to claim 1, wherein the imaging mechanism equation of the ultrasonic image simulated in step 1) is:
y＝Ax+n (1)；
where x represents the input raw image, y represents the final output image of the system, n represents noise, and a represents the linear or non-linear operation applied by the imaging system on the raw image.
3. The method for reconstructing high-frequency ultrasonic images according to claim 2, wherein the imaging mechanism equation updated in the step 2) is:
y＝SHx+n (2)；
wherein x represents an input original image, y represents an image finally output by the system, n represents noise, H represents convolution operation of a point spread function and an input signal, and S represents down-sampling extraction operation.
4. A method for reconstructing a high frequency ultrasound image according to claim 3, wherein the point spread function is a class of bessel equations or variants thereof, the point spread function comprising at least the following parameters: sound velocity, ultrasonic wavelength, center frequency, aperture of the probe.
5. The method for reconstructing high-frequency ultrasonic images according to claim 4, wherein the imaging mechanism equation updated in step 3) is:
Figure FDA0003561069130000011
Figure FDA0003561069130000012
wherein,
Figure FDA0003561069130000021
representing output
Figure FDA0003561069130000022
And the data fidelity between the noise n, wherein y represents an image finally output by the system; phi (Ax) is a regular constraint term; lambda is a weight coefficient to balance the weight between the data fidelity and the regular constraint term; a represents different image properties of different imaging systems;
where the canonical constraint term φ (Ax) is/1Norm, l2Norm, total variation or non-convex penalty term.
6. The method for reconstructing high-frequency ultrasonic images according to claim 5, wherein the alternating direction multiplier equation obtained in the step 4) is:
Figure FDA0003561069130000023
ax ═ v (5) is satisfied;
equation (5) replaces Ax in equation (4) with v, which aims to decompose the constraint optimization problem into two separate parts:
Figure FDA0003561069130000024
and phi (v); so that both parts are solved iteratively at the same time using the alternating multiplier equations.
7. The method for reconstructing a high-frequency ultrasound image according to claim 6, wherein the step 5) specifically comprises:
5-1) rewrite equation (5) to augmented Lagrangian equation:
Figure FDA0003561069130000025
satisfies Ax-v (6);
5-2) transcribe equation (6) into 3 equations:
Figure FDA0003561069130000026
wherein k represents the number of iterations, u is a Lagrangian multiplier, and eta is a weight parameter;
5-3) rewriting formula (7) as:
Figure FDA0003561069130000027
Figure FDA0003561069130000028
equation (8-2) is considered as a denoising operation because v is subject to the constraint term φ (v)k+1By vkDeducing that each iteration round updates the denoised image vk+1And the image v before denoisingkAnd (5) data fidelity among the data, stopping updating until convergence is reached, and obtaining a reconstruction result of the high-frequency ultrasonic image.
8. The high-frequency ultrasonic image reconstruction method according to claim 7, wherein the step of iterating in step 5-3) is:
s1, inputting a low-resolution image y containing noise, performing down-sampling (sampling) operation S, a system point spread function H, and constraining weight parameters lambda and eta;
based on (8-1) and xk＝vk-ukThe following equation (9) is obtained, and x is updated according to the following equation (9):
Figure FDA0003561069130000031
s2, based on (8-2) and xk＝vk-ukObtaining the following formula (10), and updating v according to the following formula (10):
Figure FDA0003561069130000032
s3, according to vk+1And xk+1Computing lagrange multiplier u:
uk+1＝uk+η(xk+1-vk+1) (11)；
s4, satisfying max { | xk+1-xk‖2,‖vk+1-vk‖2,‖uk+1-uk‖2Stopping iteration when the rate is less than or equal to gamma, and outputting:
Figure FDA0003561069130000033
9. a storage medium on which a computer program is stored, characterized in that the program is adapted to carry out the method of any one of claims 1-8 when executed.
10. A computer arrangement comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method according to any of claims 1-8 when executing the computer program.
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CN117274094A (en) * 2023-09-22 2023-12-22 哈尔滨工业大学 Deconvolution reconstruction method for improving wearable ultrasonic imaging quality

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117274094A (en) * 2023-09-22 2023-12-22 哈尔滨工业大学 Deconvolution reconstruction method for improving wearable ultrasonic imaging quality
CN117274094B (en) * 2023-09-22 2024-05-28 哈尔滨工业大学 Deconvolution reconstruction method for improving wearable ultrasonic imaging quality

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