CN115956944B - Cauchy-RPCA-based random space downsampling ultrasonic micro-blood flow imaging method - Google Patents
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Abstract
The invention provides a random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA, which comprises the following steps: step S1, continuously acquiring a group of original signal data N x×Nz×Nt with high frame rate; step S2, reconstructing the original signal data N x×Nz×Nt into a two-dimensional matrix D with a size of N s×Nt, where the specific expression of N s is: n s＝Nx×Nz; step S3, performing position calibration on the two-dimensional matrix D by adopting a motion correction method based on phase correlation to obtain a calibrated matrix D'; s4, randomly decomposing the calibrated matrix D' into a plurality of non-overlapping ultrasonic data submatrices X by adopting a random space downsampling method; step S5, extracting each ultrasonic data submatrix X by using a Cauchy-RPCA method to obtain a low-rank matrix L containing tissue signals and a sparse matrix S containing blood flow signals; and S6, combining the blood flow signal components extracted from each ultrasonic data submatrix, and obtaining an ultrasonic Doppler blood flow image by calculating the signal intensity.
Description
Technical Field
The invention relates to a random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA.
Background
The scattered echo of the micro blood flow is weak and is easily interfered by tissue back scattered ultrasonic signal clutter, so that the related clutter extraction method is important to micro blood flow ultrasonic imaging.
In recent years, scholars have proposed several methods to solve the clutter filtering problem in ultrasound imaging, such as filtering ultrasound signals with finite impulse response filters or infinite impulse response filters to extract blood flow signals (see literature ：L.Thomas and A.Hall,"An improved wall filter for flow imaging of low velocity flow,"in Ultrasonics Symposium,1994.Proceedings.,1994IEEE,vol.3.IEEE,1994,pp.1701–1704.), but where clutter signals overlap the blood flow signal spectrum and lose useful information).
The current mainstream method is still a clutter removal method for performing matrix singular value decomposition on a three-dimensional ultrasonic signal sampled in time-space by utilizing the spatial characteristics of tissue signals (a threshold value of a blood flow signal space, a clutter signal space and a noise space is required to be determined by a reference ：C.Demene,T.Deffieux,M.Pernot,B.F.Osmanski.,V.Biran,S.Franqui,and M.Tanter,"Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases doppler and fultrasound sensitivity,"IEEE Transactions on Medical Imaging,vol.34,pp.2271–2285,2015.). singular value decomposition filter so as to realize component separation of the tissue clutter signal, the blood flow signal and the noise signal).
Disclosure of Invention
In order to solve the problems, the invention provides a random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA, which adopts the following technical scheme:
The invention provides a random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA, which comprises the following steps: step S1, continuously acquiring a group of original signal data N x×Nz×Nt with high frame rate; step S2, reconstructing the original signal data N x×Nz×Nt into a two-dimensional matrix D with a size of N s×Nt, where the specific expression of N s is: n s＝Nx×Nz; step S3, performing position calibration on the two-dimensional matrix D by adopting a motion correction method based on phase correlation to obtain a calibrated matrix D'; s4, randomly decomposing the calibrated matrix D' into a plurality of non-overlapping ultrasonic data submatrices X by adopting a random space downsampling method; step S5, extracting each ultrasonic data submatrix X by using a Cauchy-RPCA method to obtain a low-rank matrix L containing tissue signals and a sparse matrix S containing blood flow signals, and solving by adopting an alternate direction multiplier method in the extraction process to obtain blood flow signal components; and S6, combining the blood flow signal components extracted from each ultrasonic data submatrix, and obtaining an ultrasonic Doppler blood flow image by calculating the signal intensity.
The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA provided by the invention can also have the technical characteristics that the step S3 further comprises the following steps: step S3 further comprises the steps of: s3-1, dividing all images into N t/N image blocks by taking N frames as one block; s3-2, extracting a tissue signal by adopting a space-time clutter filter based on singular value decomposition, wherein the highest singular value comprises tissue information and general motion information; in step S3-3, in each image block containing n frames of images, selecting an intermediate frame of image as a reference image I 1 (x, z), correcting other images by taking the reference image as a standard, and for the image I 2 (x, z) to be corrected, the specific expression is: i 2(x,z)＝I1 (x+Deltax, z+Deltaz), wherein Deltax is the axial displacement between two frames, deltaz is the lateral displacement between two frames, and can be solved by the cross-correlation function of the two frames of images, and the expression is: In the method, in the process of the invention, Is the fourier transform of I 1 (x, z),Is the fourier transform of I 2 (x, z),Is thatIs used to determine the complex number of the conjugate,Representing phase; and step S3-4, correlating the reference frame of each image block with the reference frame of the first image block to obtain the displacement between the image blocks, and realizing the motion correction between the image blocks.
The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA provided by the invention can also have the technical characteristics that the step S5 further comprises the following steps: in the step S5-1, the Cauchy-RPCA method utilizes the low rank property of tissue signals and the sparsity of blood flow signals in the ultrasonic data submatrix X to represent the tissue clutter and additive noise removal algorithm as the following optimization problem: min L+X＝X‖σ(L)‖c+λ‖S‖c, wherein II c is the Cauchy norm of the matrix, sigma (L) is the singular value vector of the low-rank matrix L, lambda is a hyper-parameter to be adjusted for balancing sparsity of blood flow and low rank of tissue, and lambda >0; step S5-2, because the expression of the Cauchy norm as a penalty function is: in the formula, z' is a function variable, sigma c is a parameter for adjusting the sharpness of the Cauchy norm, and the adjustment of the sparse penalty term can be realized, so that the optimization problem of the decomposition matrix of the Cauchy-RPCA method is converted into: Wherein σ j represents the j-th singular value of the matrix L, S ij represents the element of S, L is less than or equal to min { m, n }, m represents a row of the matrix, and n represents a column of the matrix; step S5-3, introducing a Lagrangian multiplier Y to construct an augmented Lagrangian function The specific expression is: Where < Y, X-L-S > represents the standard inner product of Lagrangian multiplier Y and X-L-S, μ is a penalty parameter for controlling convergence speed, Represents the Frobenius norm of X-L-S; and S5-4, iteratively solving an optimization problem by using an alternate direction multiplier method to obtain a blood flow signal component.
The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA provided by the invention can also have the technical characteristics that the step S5-4 further comprises the following steps: step S5-4-1, S k is a sparse matrix after k iterations, Y k is a Lagrangian multiplier after k iterations, L k+1 is a low rank matrix after k+1 iterations, S k and Y k are fixed first, a formula minimized L k+1 is calculated, and the lambda initial value is M and n are the size of the input matrix, mu is 10X lambda, X is the initial value of L k+1, all 0 matrices are the initial values of S k and Y k, v k is the weight variable of the low rank matrix L k, w k is the weight variable of the S k matrix, and all 1 matrices I are the initial values of v k and w k. Wherein; In the method, in the process of the invention, Is the j-th singular value of L k+1, v k+1 is the weight variable of the low-rank matrix L k+1,Is the j-th value of v k+1,The singular value contraction operator taking v k*μ-1 as a threshold value is represented by the following specific expression: Wherein U and V T are orthogonal matrices obtained after singular value decomposition of a variable matrix E, Σ is a diagonal matrix containing singular values obtained after singular value decomposition of E, The soft threshold operator with v k*μ-1 as a threshold is expressed as follows: step S5-4-2: fixing L k+1 and Y k, and solving a sparse matrix S k+1 for minimizing a formula, wherein the specific expression is as follows: In the method, in the process of the invention, The elements of the matrix of S k+1 are represented,The soft threshold operator with w k x lambda/mu as the threshold is represented by the following specific expression: Step S5-4-3, updating Y with S k+1 and L k+1, Y k+1＝Yk+μ(X-Lk+1-Sk+1); and step S5-4-4, iterating the step S5-4-1 to the step S5-4-3, and outputting the iterated low-rank matrix L and sparse matrix S when the stopping condition is met, so as to realize the separation of clutter and blood flow signals.
The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA provided by the invention can also have the technical characteristics that the stopping condition is any one of the following conditions: the value of II X-L k+1-Sk +1‖F/‖X‖F is less than a given value and the number of iterations is equal to the given number.
The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA provided by the invention can also have the technical characteristics that the random space downsampling method does not repeatedly randomly sample the calibrated matrix D', each element is randomly extracted once, and meanwhile, the extracted element combination has contingency.
The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA provided by the invention can also have the technical characteristics that errors generated in the matrix decomposition process are propagated in an incoherent mode in the whole image space by utilizing the random space downsampling method, so that a high-quality blood flow image with low artifacts is obtained.
The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA provided by the invention can also have the technical characteristics that the original signal data comprises echo signals of static tissues, echo signals of blood flow and noise.
The actions and effects of the invention
According to the random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA, each ultrasonic data submatrix X is firstly extracted by using Cauchy-RPCA to obtain a low-rank matrix L containing tissue signals and a sparse matrix S containing blood flow signals, so that separation of tissue clutter signals, blood flow signals and noise signals is realized, the recovery capacity of the sparse signals is enhanced through Cauchy norms, and related components of low-rank tissue motion can be better removed, so that a blood flow component matrix which is close to a full rank and has space and frequency spectrum sparse characteristics is obtained.
And secondly, the invention adopts a random space downsampling method to decompose the original data matrix into a plurality of non-overlapping submatrices to accelerate calculation, thereby improving the signal extraction efficiency. Meanwhile, the Cauchy-RPCA is optimized by adopting an alternate direction multiplier method, and the combination of the Cauchy-RPCA and random space downsampling is very suitable for a multithread architecture and can be independently and parallelly calculated, so that the running speed is further improved.
Finally, in the matrix decomposition process by utilizing the random space downsampling method, errors generated by random sampling are spread in an incoherent mode in the whole image space, so that a high-quality blood flow image with low artifacts can be obtained.
Drawings
FIG. 1 is a flow chart of a Cauchy-RPCA based random spatial downsampling ultrasound micro-blood flow imaging method in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of a method for random spatial downsampling in accordance with an embodiment of the present invention;
FIG. 3 is a dynamic blood flow chart isolated by the Cauchy-RPCA method in an embodiment of the invention;
FIG. 4 is a static tissue map isolated by the Cauchy-RPCA method in an embodiment of the invention;
FIG. 5 is a power Doppler blood flow graph obtained by imaging a rat brain using the Cauchy-RPCA method in an embodiment of the present invention;
FIG. 6 is a partial enlarged view of a blood flow map and a region of interest extracted by two methods, cauchy-RPCA and singular value decomposition, in an embodiment of the present invention;
FIG. 7 is a graph comparing the resolution of two methods, cauchy-RPCA and singular value decomposition, in an embodiment of the invention.
Detailed Description
In order to make the technical means, creation characteristics, achievement purposes and effects of the method easy to understand, the method for random space downsampling ultrasonic micro-blood flow imaging based on Cauchy-RPCA is specifically described below with reference to the embodiment and the accompanying drawings.
< Example >
The embodiment uses a Cauchy-RPCA-based random space downsampling ultrasonic micro-blood flow imaging method to image the brain of the rat.
FIG. 1 is a flow chart of a Cauchy-RPCA based random spatial downsampling ultrasound micro-blood flow imaging method in accordance with an embodiment of the present invention.
As shown in fig. 1, in step S1, a great amount of high-frame-rate and high-quality rat brain ultrasound data is acquired by using an ultra-fast ultrasonic plane wave imaging technique. The ultrasound data includes echo signals of static tissue, echo signals of blood flow, and noise. And (3) performing image processing on the rat brain ultrasonic data by a beam synthesis method to finally obtain a data matrix of continuous 200 frames of composite images with the size of 960 multiplied by 128.
And S2, reconstructing the data matrix to obtain a two-dimensional matrix D with the size of 122880 multiplied by 200.
In step S3, since the position is shifted due to the factors such as the heartbeat and the respiration, the position calibration between the multi-frame images is performed. In this embodiment, a method based on phase correlation and rigid motion correction is used to calibrate the position of the matrix D, so as to obtain a calibrated matrix D'. Step S3 comprises the following sub-steps:
in step S3-1, in this embodiment, all images are divided into 2 image blocks by taking 100 frames as one block.
And S3-2, extracting a tissue signal by adopting a space-time clutter filter based on singular value decomposition, wherein the highest singular value comprises tissue information and general motion information.
In the embodiment, a singular value decomposition filtering method is adopted, and only two singular values with highest intensity are collected, so that a tissue signal can be extracted.
In step S3-3, in each image block containing 100 frames of images, selecting an intermediate frame of image as a reference image I 1 (x, z), and correcting other images by taking the reference image as a standard. For the image I 2 (x, z) to be corrected, the specific expression is:
I2(x,z)＝I1(x+Δx,z+Δz)
wherein Δx is the axial displacement between two frames, Δz is the lateral displacement between two frames, and the expression is as follows:
In the method, in the process of the invention, Is the fourier transform of I 1 (x, z),Is the fourier transform of I 2 (x, z),Is thatIs used to determine the complex number of the conjugate,Representing the phase.
And performing two-dimensional Fourier inverse transformation to obtain dirac peaks in deltax and deltaz. The motion correction of the original data can be achieved by displacement.
And step S3-4, correlating the reference frame of each image block with the reference frame of the first image block to obtain the displacement between the image blocks, and realizing the motion correction between the image blocks.
And S4, randomly decomposing the calibrated matrix D' into a plurality of non-overlapping ultrasonic data submatrices X by adopting a random space downsampling method. In this embodiment, the number of parallel threads is 8, so the number of submatrices for random spatial downsampling, n=8.
Fig. 2 is a schematic diagram of a method for random spatial downsampling in accordance with an embodiment of the present invention.
As shown in fig. 2, the random spatial downsampling method performs non-repeated random sampling on the calibrated matrix D', and ensures that each element is randomly decimated once, while the decimated element combinations have contingency.
And S5, extracting each ultrasonic data submatrix X by using a Cauchy-RPCA method to obtain a low-rank matrix L containing tissue signals and a sparse matrix S containing blood flow signals, wherein an alternate direction multiplier method is adopted in the extraction process, and the blood flow signal components are obtained by solving the gradient property of a function.
In step S5-1, the submatrix X includes a matrix L containing tissue signals and a matrix S containing blood flow signals. The matrix L containing tissue signals has high space-time coherence and thus has the characteristic of low rank, while the matrix S containing blood flow signals has sparsity in space morphology. Noise components are neither low rank nor sparse. The method of Cauchy-RPCA is used to decompose the ultrasound data submatrix into a low rank matrix L and a sparse matrix S, and the tissue clutter and additive noise removal algorithm is expressed as the following optimization problem:
minL+S＝X‖σ(L)‖c+λ‖S‖c
Wherein II is c is the Cauchy norm of the matrix, sigma (L) is the singular value vector of the low rank matrix L, lambda is the hyper-parameter to be adjusted to balance the sparsity of blood flow and the low rank of tissue and lambda >0.
Step S5-2, because the expression of the Cauchy norm as a penalty function is:
Wherein z' is a function variable, sigma c is a parameter for adjusting the sharpness of the Cauchy norm, and the adjustment of the sparse penalty term can be realized.
The optimization problem of the Cauchy-RPCA method decomposition matrix is translated into:
Where σ j represents the jth singular value of the matrix L, S ij represents the element of S, l.ltoreq.min { m, n }, m representing the row of the matrix and n representing the column of the matrix.
Step S5-3, introducing a Lagrangian multiplier Y to construct an augmented Lagrangian functionThe specific expression is:
where < Y, X-L-S > represents the standard inner product of the Lagrangian multiplier Y and X-L-S, μ is a penalty parameter for controlling convergence speed, The Frobenius norm of X-L-S is represented.
The minimization problem can be solved by using the gradient properties of the function, for which the gradient in z 'is equal to the Cauchy norm function g (z')Σ c is a parameter for adjusting the sharpness of the Cauchy norm, and can realize the adjustment of the sparse penalty term, in this embodiment, σ c takes a value of 0.1.
And S5-4, iteratively solving the optimization problem by using an alternate direction multiplier method to obtain the blood flow signal component. Step S5-4 further comprises the steps of:
Step S5-4-1, fixing S k and Y k, solving a sparse matrix with the formula minimized L k+1 and v k+1.Sk after k iterations, Y k being Lagrangian multiplier after k iterations, L k+1 being low rank matrix after k+1 iterations, and lambda initial value being M and n are the sizes of input matrices, mu initial value is 10X lambda, X is the initial value of L k+1, all 0 matrix O is the initial value of S k and Y k, v k is the weight variable of low rank matrix L k, w k is the weight variable of S k matrix, and all 1 matrix I is the initial value of v k and w k.
The expression of L k+1 is:
v k+1 has the expression:
In the method, in the process of the invention, Is the j-th singular value of the L k+1, v k+1 is the weight variable of the low-rank matrix L k+1,Is the j-th value of v k+1.
Wherein,The singular value contraction operator taking v k*μ-1 as a threshold value is represented by the following specific expression:
wherein U and V T are orthogonal matrices obtained after the singular value decomposition of the variable matrix E, and Sigma is a diagonal matrix containing singular values obtained after the singular value decomposition of the variable matrix E.
The soft threshold operator with v k*μ-1 as a threshold is expressed as follows:
step S5-4-2: fixing L k+1 and Y k, and solving a sparse matrix S k+1 for minimizing a formula, wherein the specific expression is as follows:
In the method, in the process of the invention, The elements representing the matrix of S k+1,
The soft threshold operator with w k x lambda/mu as the threshold is represented by the following specific expression:
Step S5-4-3, updating Y k with said S k+1 and said L k+1, then
Yk+1＝Yk+μ(X-Lk+1-Sk+1)
And step S5-4-4, iterating the step S5-4-1 to the step S5-4-3, and when a stop condition II X-L k+1-Sk+1‖F/‖X‖F＝10-6 is met or the iteration number reaches 1000, stopping iteration, outputting an iterated low-rank matrix L and a iterated sparse matrix S, so as to realize the separation of clutter and blood flow signals.
FIG. 3 is a dynamic blood flow chart separated by the Cauchy-RPCA method in an embodiment of the invention, and FIG. 4 is a static tissue chart separated by the Cauchy-RPCA method in an embodiment of the invention.
And according to the low-rank matrix L and the sparse matrix S after the output iteration, the obtained dynamic organization chart and static blood flow chart are shown in fig. 3 and 4.
Fig. 5 is a power doppler blood flow graph of a rat brain imaged by the Cauchy-RPCA method in an embodiment of the invention.
Further processing the dynamic blood flow map, calculating the signal power at each pixel: The obtained power Doppler image is shown in FIG. 5, from which the rat brain microvascular structure can be obtained. Then, a region of interest is selected in the power Doppler image, and the contrast resolution of the result is analyzed.
Fig. 6 is a partial enlarged view of a blood flow chart and a region of interest extracted by two methods of Cauchy-RPCA and singular value decomposition in an embodiment of the present invention, and fig. 7 is a comparison curve comparing resolutions of the two methods of Cauchy-RPCA and singular value decomposition in an embodiment of the present invention.
Fig. 6 (a) is a partial enlarged view of the imaging result of the Cauchy-RPCA method and the region of interest, and fig. 6 (b) is a partial enlarged view of the imaging result of the singular value decomposition method and the region of interest, as shown in fig. 6, the Cauchy-RPCA method can better distinguish two adjacent microvasculature compared to the singular value decomposition. Meanwhile, as can be seen from the normalized amplitude curves of the Cauchy-RPCA method and the singular value decomposition method shown in fig. 7, the Cauchy-RPCA method has higher resolution than the singular value decomposition method.
Example operation and Effect
According to the random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA, each ultrasonic data submatrix is firstly extracted by using Cauchy-RPCA to obtain a low-rank matrix L containing tissue signals and a sparse matrix S containing blood flow signals, so that separation of the tissue clutter signals, the blood flow signals and noise signals is realized, the recovery capacity of the sparse signals is enhanced through the Cauchy norm, and tissue motion related components of the low rank can be better removed, so that a blood flow component matrix which is close to the whole rank and has space and frequency spectrum sparse characteristics is obtained.
In the embodiment, a random space downsampling method is adopted to decompose an original data matrix into a plurality of non-overlapping submatrices to accelerate calculation, so that the signal extraction efficiency can be improved. Meanwhile, the Cauchy-RPCA is optimized by adopting an alternate direction multiplier method, and the combination of the Cauchy-RPCA and random space downsampling is very suitable for a multithread architecture and can be independently and parallelly calculated, so that the running speed is further improved.
Finally, in the matrix decomposition process by using the random space downsampling method in the embodiment, errors generated by random sampling propagate in an incoherent manner in the whole image space, so that a high-quality blood flow image with low artifacts can be obtained.
The above examples are only for illustrating the specific embodiments of the present invention, and the present invention is not limited to the description scope of the above examples.
Claims (5)
1. The random space downsampling ultrasonic micro-blood flow imaging method based on Cauchy-RPCA is characterized by comprising the following steps of:
step S1, acquiring a large amount of high-frame-rate and high-quality original signal data N x×Nz×Nt by using an ultrafast ultrasonic plane wave imaging technology, wherein the original signal data comprises echo signals of static tissues, echo signals of blood flow and noise, and performing image processing on the original signal data by using a beam synthesis method to finally obtain a data matrix of continuous 200-frame composite images with the size of 960 multiplied by 128;
Step S2, reconstructing the data matrix into a two-dimensional matrix D with a size of N s×Nt, where the specific expression of N s is:
Ns＝Nx×Nz；
Step S3, performing position calibration on the two-dimensional matrix D by adopting a motion correction method based on phase correlation to obtain a calibrated matrix D';
s4, randomly decomposing the calibrated matrix D' into a plurality of non-overlapping ultrasonic data submatrices X by adopting a random space downsampling method;
Step S5, extracting each ultrasonic data submatrix X by using a Cauchy-RPCA method to obtain a low-rank matrix L containing tissue signals and a sparse matrix S containing blood flow signals, and solving by adopting an alternate direction multiplier method in the extraction process to obtain blood flow signal components;
Step S6, combining the blood flow signal components extracted by each ultrasonic data submatrix, obtaining an ultrasonic Doppler blood flow image by calculating signal intensity,
Wherein the original signal data comprises echo signals of static tissues, echo signals of blood flow and noise,
The step S5 further includes the steps of:
step S5-1, the Cauchy-RPCA method utilizes the low rank property of tissue signals and the sparsity of blood flow signals in the ultrasonic data submatrix X to represent the tissue clutter and additive noise removal algorithm as the following optimization problem:
minL+S＝X‖σ(L)‖c+λ‖S‖c
Wherein, II is c is the Cauchy norm of the matrix, sigma (L) is the singular value vector of the low-rank matrix L, lambda is the super-parameter to be adjusted, and is used for balancing the sparsity of blood flow and the low rank of tissue, and lambda >0;
step S5-2, because the expression of the Cauchy norm as a penalty function is:
wherein z' is a function variable, sigma c is a parameter for adjusting the sharpness of the Cauchy norm, the adjustment of the sparse penalty term can be realized,
The optimization problem of the Cauchy-RPCA method decomposition matrix is translated into:
Wherein σ j represents the j-th singular value of the matrix L, S ij represents the element of S, l.ltoreq.min { m, n }, m representing the row of the matrix, n representing the column of the matrix;
Step S5-3, introducing a Lagrangian multiplier Y to construct an augmented Lagrangian function The specific expression is:
where < Y, X-L-S > represents the standard inner product of the Lagrangian multiplier Y and X-L-S, μ is a penalty parameter for controlling convergence speed, Represents the Frobenius norm of X-L-S;
And S5-4, iteratively solving the optimization problem by using an alternate direction multiplier method to obtain the blood flow signal component.
Step S5-4 further comprises the steps of:
Step S5-4-1, S k is a sparse matrix after k iterations, Y k is a Lagrangian multiplier after k iterations, L k+1 is a low rank matrix after k+1 iterations, S k and Y k are fixed first, a formula minimized L k+1 is calculated, and the lambda initial value is M, n are the size of the input matrix, mu initial value is 10X lambda, X is the initial value of L k+1, all 0 matrix O is the initial value of S k and Y k, v k is the weight variable of low rank matrix L k, w k is the weight variable of S k matrix, all 1 matrix I is the initial value of v k and w k,
Wherein,
In the method, in the process of the invention,Is the j-th singular value of the L k+1, v k+1 is the weight variable of the low-rank matrix L k+1,Is the j-th value of v k+1,
The singular value contraction operator taking v k*μ-1 as a threshold value is represented by the following specific expression:
Wherein U and V T are orthogonal matrices obtained after singular value decomposition of a variable matrix E, and Sigma is a diagonal matrix containing singular values obtained after singular value decomposition of E,
The soft threshold operator with v k*μ-1 as a threshold is expressed as follows:
Step S5-4-2, fixing the L k+1 and the Y k, and solving a sparse matrix S k+1 for minimizing a formula, wherein the specific expression is as follows:
In the method, in the process of the invention, The elements representing the matrix of S k+1,
The soft threshold operator with w k x lambda/mu as the threshold is represented by the following specific expression:
Step S5-4-3, updating Y k with said S k+1 and said L k+1, then
Yk+1＝Yk+μ(X-Lk+1-Sk+1)
And step S5-4-4, iterating the step S5-4-1 to the step S5-4-3, and outputting the iterated low-rank matrix L and sparse matrix S when the stopping condition is met, so as to realize the separation of clutter and blood flow signals.
2. The Cauchy-RPCA based random space downsampling ultrasound micro-blood flow imaging method of claim 1, wherein:
wherein, the step S3 further comprises the following steps:
S3-1, dividing all images into N t/N image blocks by taking N frames as one block;
S3-2, extracting a tissue signal by adopting a space-time clutter filter based on singular value decomposition, wherein the highest singular value comprises tissue information and general motion information;
Step S3-3, selecting an intermediate image as a reference image I 1 (x, z) in each image block containing n frames of images, correcting other images by taking the reference image as a standard, and for the image I 2 (x, z) needing correction, the specific expression is as follows:
I2(x,z)＝I1(x+Δx，z+Δz)
wherein Δx is the axial displacement between two frames, Δz is the lateral displacement between two frames, and the expression is as follows:
In the method, in the process of the invention, Is the fourier transform of I 1 (x, z),Is the fourier transform of I 2 (x, z),Is thatIs used to determine the complex number of the conjugate,Representing phase;
And step S3-4, correlating the reference frame of each image block with the reference frame of the first image block to obtain the displacement between the image blocks, and realizing the motion correction between the image blocks.
3. The Cauchy-RPCA based random space downsampling ultrasound micro-blood flow imaging method of claim 1, wherein:
Wherein the stop condition is any one of the following conditions: the value of X-L k+1-Sk+1||F/‖X‖F is less than a given value and the number of iterations is equal to the given number.
4. The Cauchy-RPCA based random space downsampling ultrasound micro-blood flow imaging method of claim 1, wherein:
The random space downsampling method performs non-repeated random sampling on the calibrated matrix D', and ensures that each element is randomly extracted once, and meanwhile, the extracted element combination has accidental.
5. The Cauchy-RPCA based random space downsampling ultrasound micro-blood flow imaging method of claim 4, wherein the steps of:
The random space downsampling method is used for enabling errors generated in the matrix decomposition process to be spread in an incoherent mode in the whole image space, and a high-quality blood flow image with low artifacts is obtained.
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