CN111340699B - Magnetic resonance image denoising method and device based on non-local prior and sparse representation - Google Patents
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Abstract
The invention discloses a magnetic resonance image denoising method and device based on non-local prior and sparse representation, which can adaptively filter non-Gaussian noise which destroys a magnetic resonance image, including Rician or non-central chi-square distributed noise which is spatially stable and spatially variable. Firstly, the variance stabilizing transformation technology is used for correcting the deviation caused by non-Gaussian noise, and then non-local prior information in the image is captured on the basis, namely non-local similar image blocks in the image are extracted. Noise intensity in the magnetic resonance image is then estimated to be adaptive to spatially varying Rician or non-central chi-square distributed noise. And finally, sparsifying the non-local similar image blocks by combining with improved weighted nuclear norm minimization so as to eliminate the noise in the magnetic resonance image. Besides, the invention also obtains the final unbiased estimation of the magnetic resonance image by using the inverse variance transformation on the basis of the operation.
Description
Technical Field
The invention relates to a magnetic resonance image denoising method and device, in particular to a magnetic resonance image denoising method and device based on non-local prior and sparse representation.
Background
Magnetic resonance imaging is a widely used medical imaging modality that enables the detection of structural and functional characteristics of internal organs of the human body by non-invasive techniques. Magnetic resonance imaging enables the delineation and differentiation of anatomical tissues based on their physical and biochemical properties, which offers unique advantages for clinical diagnosis and surgical treatment. However, due to the imaging mechanism of the magnetic resonance image (number of coils, multi-coil reconstruction, acceleration, etc.), the tissue signals acquired in the magnetic resonance imaging are susceptible to interference of random noise, so that the finally obtained image is corrupted by Rician noise or non-central chi-square distributed noise. In addition, in the imaging process, the noise level is constantly changed in space due to physiological factors such as blood flow and the like and due to inhomogeneity of the magnetic field, so that the noise characteristics are more complicated. To summarize, the types of noise in magnetic resonance images are mainly classified into spatially stable and spatially varying Rician or non-central chi-square distributed noise.
The visual quality of magnetic resonance images plays a crucial role in the accuracy of clinical diagnosis. The existence of noise affects the identification of detail information of the magnetic resonance image by a doctor in the medical diagnosis process, and the unreliability of the final quantitative analysis is caused, thereby preventing the doctor from effectively diagnosing diseases. The image denoising is a basic image post-processing technology, can be used for restoring the magnetic resonance image, and can effectively improve the reliability and robustness of subsequent analysis by denoising the magnetic resonance image. There are a number of processing methods for noise in magnetic resonance images, but these are mainly classified into two types. The first is to effectively reduce the noise level in the magnetic resonance image by averaging the multiple acquired signals directly in the scanner, but this approach has significant time loss and is therefore not common in clinical settings. And the second method is to process the magnetic resonance image containing noise by using post-processing technology such as filtering, and the like, so that the noise can be effectively removed on the basis of not increasing the acquisition time, and the method has great application value. At present, researchers have proposed a large number of magnetic resonance image denoising algorithms, such as a classical spatial filter, an algorithm based on anisotropic diffusion filtering, an algorithm based on non-local mean, an algorithm based on sparse representation, an algorithm based on wavelet transform, and the like. Although these methods can remove noise in the magnetic resonance image, artifacts are inevitably introduced during the noise processing, and certain edge blurring is also caused.
Disclosure of Invention
The invention aims to provide a magnetic resonance image denoising method and device based on non-local prior and sparse representation, which are used for solving the problems of low robustness caused by edge blurring, detail loss and artifact introduction in the magnetic resonance image denoising method and device in the prior art.
In order to realize the task, the invention adopts the following technical scheme:
a magnetic resonance image denoising method based on non-local prior and sparse representation is performed according to the following steps:
step 1, acquiring a magnetic resonance image to be denoised; performing non-Gaussian noise deviation correction on the magnetic resonance image to be denoised to obtain a corrected image;
step 2, selecting image blocks from the corrected image by adopting a sliding window to obtain a plurality of first image blocks;
extracting non-local similar features of each first image block to obtain a plurality of feature matrixes;
step 3, obtaining a residual image of the corrected image, wherein the size of the residual image is the same as that of the magnetic resonance image to be denoised;
selecting image blocks from the residual image by adopting a sliding window with the same size as that in the step 2 to obtain a plurality of second image blocks;
performing local noise estimation on each second image block to obtain a plurality of noise standard deviations; the plurality of noise standard deviations correspond to the plurality of feature matrixes one by one;
step 4, iterative solution is carried out on the formula I to obtain an estimated low-rank matrix corresponding to the ith feature matrix
Wherein ZiDenotes the ith feature matrix obtained in step 2, I is 1,2, …, I is a positive integer, δ (z)i) Representing the noise standard deviation, E, corresponding to the ith feature matrix obtained in step 3iTo representIth low rank matrix to be estimated, EiIs Z as an initial valuei，σj(Ei) Representing the j singular value, σ, of the i-th low-rank matrix to be estimatedj(Ei) Not less than 0, j is 1,2, …, n, n +1, n is positive integer, omegajRepresenting the weight corresponding to the jth singular value of the ith low-rank matrix to be estimated, and omega is more than or equal to 0j≤1；
Step 5, repeating the step 4 to obtain an estimated low-rank matrix corresponding to each feature matrix;
step 6, restoring all the estimated low-rank matrixes obtained in the step 5 into image blocks to obtain a plurality of denoised image blocks;
splicing the plurality of denoised image blocks to obtain a primarily denoised magnetic resonance image;
and processing the primarily denoised magnetic resonance image by a sampling inverse variance stable transformation method to obtain the denoised magnetic resonance image.
Further, when non-local similar feature extraction is performed on each first image block in step 2 to obtain a plurality of feature matrices, steps 2.1 to 2.3 are adopted to obtain the ith feature matrix:
step 2.1, searching a plurality of candidate image blocks with the same size as the ith first image block in a search window corresponding to the ith first image block;
the center of the search window is an ith first image block, the size of the search window is larger than that of the ith first image block, and the size of the search window is smaller than that of the corrected image;
step 2.2, selecting n candidate image blocks with highest similarity with the ith first image block from the plurality of candidate image blocks as similar image blocks to obtain n similar image blocks;
and 2.3, storing the ith first image block and the n similar image blocks into a matrix in a vector mode to obtain an ith characteristic matrix.
Further, when the n candidate image blocks with the highest similarity to the ith first image block are selected from the plurality of candidate image blocks as the similar image blocks in step 2.2, the similarity between the ith first image block and each candidate image block is calculated by using the euclidean distance.
Further, step 4 is described as step EiIs an initial value ZiWhen the temperature of the water is higher than the set temperature,
wherein
Representing the j-th singular value, σ, obtained by singular value decomposition of the i-th eigen matrixj(Zi)≥0。
A magnetic resonance image denoising device based on non-local prior and sparse representation comprises an image correction module, a characteristic matrix obtaining module, a noise standard deviation obtaining module, a low-rank matrix estimation module and a reconstruction denoising module;
the image correction module is used for acquiring a magnetic resonance image to be denoised; performing non-Gaussian noise deviation correction on the magnetic resonance image to be denoised to obtain a corrected image;
the characteristic matrix obtaining module is used for selecting image blocks from the corrected image by adopting a sliding window to obtain a plurality of first image blocks;
extracting non-local similar features of each first image block to obtain a plurality of feature matrixes;
the noise standard deviation obtaining module is used for obtaining a residual image of the corrected image, and the size of the residual image is the same as that of the magnetic resonance image to be denoised;
selecting image blocks from the residual image by adopting a sliding window with the same size as that of the characteristic matrix obtaining module to obtain a plurality of second image blocks;
performing local noise estimation on each second image block to obtain a plurality of noise standard deviations; the plurality of noise standard deviations correspond to the plurality of feature matrixes one by one;
the low rank matrix estimation module is used for the pair formulaI, iterative solution is carried out to obtain an estimated low-rank matrix corresponding to the ith feature matrix
Wherein ZiDenotes the ith feature matrix, I is 1,2, …, I is a positive integer, δ (z)i) Representing the noise standard deviation corresponding to the ith feature matrix, EiRepresenting the ith low rank matrix to be estimated, EiIs Z as an initial valuei，σj(Ei) Representing the j singular value, σ, of the i-th low-rank matrix to be estimatedj(Ei) Not less than 0, j is 1,2, …, n, n +1, n is positive integer, omegajRepresenting the weight corresponding to the jth singular value of the ith low-rank matrix to be estimated, and omega is more than or equal to 0j≤1；
Obtaining an estimated low-rank matrix corresponding to each feature matrix;
the reconstruction denoising module is used for restoring all the obtained estimated low-rank matrixes into image blocks to obtain a plurality of denoised image blocks;
splicing the plurality of denoised image blocks to obtain a primarily denoised magnetic resonance image;
and processing the primarily denoised magnetic resonance image by a sampling inverse variance stable transformation method to obtain the denoised magnetic resonance image.
Further, the characteristic matrix obtaining module comprises an image searching sub-module, a similar image block screening sub-module and a matrix obtaining sub-module;
the image searching sub-module is used for searching a plurality of candidate image blocks with the same size as the ith first image block in a searching window corresponding to the ith first image block;
the center of the search window is an area where the ith first image block is located, and the search window is larger than the size of the ith first image block and smaller than the size of the corrected image;
the similar image block screening submodule is used for selecting n candidate image blocks with highest similarity with the ith first image block from the plurality of candidate image blocks as similar image blocks to obtain n similar image blocks;
the matrix obtaining submodule is used for storing the ith first image block and the n similar image blocks into a matrix in a vector mode to obtain an ith characteristic matrix.
Further, when the similar image block screening sub-module selects n candidate image blocks with the highest similarity to the ith first image block from the plurality of candidate image blocks as similar image blocks, the similarity between the ith first image block and each candidate image block is calculated by using the euclidean distance.
Further, the low rank matrix estimation module is called EiIs an initial value ZiWhen the temperature of the water is higher than the set temperature,
wherein
Representing the j-th singular value, σ, obtained by singular value decomposition of the i-th eigen matrixj(Zi)≥0。
Compared with the prior art, the invention has the following technical effects:
1. the magnetic resonance image denoising method and device based on non-local prior and sparse representation provided by the invention make full use of non-local prior information in a three-dimensional magnetic resonance image, combine non-local prior characteristics with low-rank characteristics of the image, and can perform sparse representation on the image better, and in the process of removing noise, the method can better retain image edge and detail information, and meanwhile, artifacts are hardly introduced into the denoised magnetic resonance image, so that the robustness of the denoising method and device is improved;
2. according to the magnetic resonance image denoising method and device based on non-local prior and sparse representation, the weighted nuclear norm minimization is popularized and applied to three-dimensional magnetic resonance image denoising, and is improved to enable the method to be well adaptive to the noise type of complex change in a magnetic resonance image, specifically embodied in noise adaptive processing, namely, the local noise intensity in the noise magnetic resonance image is automatically estimated firstly, then the local noise intensity information is integrated into the optimization target of the weighted nuclear norm minimization, and the noise type of spatial change can be processed in a self-adaptive mode by means of the local noise intensity information, so that the robustness of the denoising method and device is improved;
3. the magnetic resonance image denoising method and device based on non-local prior and sparse representation fully consider the complex noise type in the magnetic resonance image, such as Rician or non-central chi-square distributed noise with stable space and space change; the non-Gaussian characteristic of the noise type is fully considered in the denoising process, and corresponding deviation correction is carried out according to the characteristic, so that the non-Gaussian noise in the magnetic resonance image can be better filtered, and the robustness of the denoising method and the denoising device is improved.
Drawings
FIG. 1 is a structural diagram of a magnetic resonance image denoising method provided by the present invention;
FIG. 2 is a schematic diagram of a searching process of a non-local similar image block according to the present invention;
FIG. 3(a) is a partial detail view of a clean magnetic resonance image provided in an embodiment of the present invention;
FIG. 3(b) is a partial detail view of an image contaminated with spatially stabilized Rician noise (noise intensity of 10%) provided in an embodiment of the present invention
FIG. 3(c) is a graph illustrating the denoising effect of the method provided by the present invention on FIG. 3(b) according to an embodiment of the present invention;
figure 4(a) is a three-dimensional partial detail view of a clean magnetic resonance image provided in an embodiment of the invention;
FIG. 4(b) is a three-dimensional local detail graph contaminated by spatially stabilized Rician noise (noise intensity of 10%) provided in an embodiment of the present invention;
FIG. 4(c) is a diagram of the three-dimensional denoising effect of FIG. 4(b) according to the method of the present invention;
figure 5(a) is a clean magnetic resonance image provided in an embodiment of the present invention;
fig. 5(b) is a magnetic resonance image contaminated by spatially varying Rician noise (noise intensity of 7% -21%) provided in an embodiment of the present invention;
FIG. 5(c) is a diagram of the denoising effect of FIG. 5(b) according to the method of the present invention;
figure 6(a) is a partial detail view of a clean magnetic resonance image provided in an embodiment of the present invention;
FIG. 6(b) is a partial detail view of the noise pollution by the spatially stabilized non-centric chi-square distribution provided in one embodiment of the present invention (noise intensity is 10%);
FIG. 6(c) is a diagram of the denoising effect of FIG. 6(b) according to the method of the present invention;
figure 7(a) is a clean magnetic resonance image provided in an embodiment of the present invention;
FIG. 7(b) is an image contaminated by spatially varying non-centric chi-square distribution noise (noise intensity 7% -21%) provided in an embodiment of the present invention;
fig. 7(c) is a diagram of the denoising effect of fig. 7(b) by the method provided by the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples. So that those skilled in the art can better understand the present invention. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
The following definitions or conceptual connotations relating to the present invention are provided for illustration:
non-gaussian noise bias correction: the mean value of non-Gaussian noise such as Rician or non-central chi-square distribution is generally larger than 0, and has deviation with common Gaussian noise. In addition, due to inhomogeneity of the magnetic field, these non-gaussian noises exhibit spatially varying characteristics, i.e., noise variance varies in size from image to image. In order to weaken the negative influence of non-gaussian noise, bias correction needs to be carried out on the non-gaussian noise, namely, the non-gaussian noise is converted into homovariance noise close to zero mean value by using a correction technology, and the corrected noise distribution is similar to gaussian noise.
Sliding the window: image processing common operations. That is, in a three-dimensional image with a size of M × N × S, a window (M > > l, N > > w, S > > h) of l × w × h is moved according to a specified step length S, and specified operation is performed on pixels in the window. And after the current operation is finished, the window moves to the right or downwards for s steps until the whole image is traversed.
Non-locally similar features: images have a redundant character and thus there are non-local image blocks with similar features on the image. These similar features are referred to as non-locally similar features.
Residual image: and obtaining an image by performing difference operation on the original noise image and the filtered image. I.e. residual image-filtered image.
Local noise estimation: and (3) carrying out a noise intensity estimation process on a certain local noise image block, wherein the noise intensity is characterized by a noise standard deviation value.
Restoring an image block: in the invention, a plurality of image blocks are required to be respectively expressed as column vectors according to a certain rule, then the column vectors are stored in a two-dimensional matrix, and the matrix is subjected to sparse representation to remove noise components. And obtaining a low-rank matrix without a noise component after sparse representation. Each column vector in the low-rank matrix is a vector representation form of the denoised image block. And restoring the column vectors into the image blocks according to the corresponding rule, wherein the process is called restoring the image blocks.
And (3) inverse variance stabilizing transformation: an unbiased estimation method. And obtaining a corresponding maximum likelihood result through the inverse variance stable transformation.
Example one
In this embodiment, a magnetic resonance image denoising method based on non-local prior and sparse representation is provided, which is used for processing spatially stable and spatially varying Rician or non-central chi-square distributed noise in a magnetic resonance image. The method comprises the steps of obtaining similar information in a magnetic resonance image by using non-local prior information, then estimating a noise standard deviation in a noise magnetic resonance image, and finally performing sparse representation on the noise magnetic resonance image by combining with weighted nuclear norm minimization. The method effectively solves the problems of edge blurring, detail loss, artifact introduction and the like in the conventional magnetic resonance image denoising, thereby improving the robustness of the magnetic resonance image denoising method.
As shown in fig. 1, the method is performed according to the following steps:
step 1, acquiring a magnetic resonance image to be denoised; carrying out non-Gaussian noise deviation correction on the magnetic resonance image to be denoised to obtain a corrected image;
in this step, due to the special imaging mechanism, the noise in the magnetic resonance image (MR image) generally follows Rician or non-central chi-square distribution, which is generated because the real and imaginary signals acquired during the imaging process are corrupted by additive gaussian noise. In addition to this, the imaging process is also easily affected by inhomogeneities of the magnetic field, etc., so that the noise distribution has heteroscedasticity, i.e. the noise variance has different values at different positions in the image. These complex non-gaussian noises are prone to bias and are therefore difficult to handle. To correct for this bias, the present invention applies a forward stable variance transform to convert the stable and varying Rician or non-centric chi-square distribution noise into a homovariance noise that is similar to gaussian noise, and then performs all subsequent processing steps on the VST transform-based image.
Step 2, selecting image blocks from the corrected image in a sliding window mode to obtain a plurality of first image blocks;
extracting non-local similar features of each first image block to obtain a plurality of feature matrixes;
in the step, the three-dimensional noise magnetic resonance image z is traversed by using a sliding window to the noise three-dimensional magnetic resonance image z after the deviation correction, and a three-dimensional magnetic resonance image block z is obtainedi. The step size of the sliding window is 1 and the size of the sliding window is 3 × 3 × 3. Assuming each three-dimensional magnetic fieldThe shake image has S slices, and each slice has a size of M × N. Then M × N × S three-dimensional magnetic resonance image blocks of size 3 × 3 × 3 can be obtained by sliding the window.
Optionally, when non-local similar feature extraction is performed on each first image block in step 2 to obtain a plurality of feature matrices, the ith feature matrix is obtained by using steps 2.1 to 2.3:
step 2.1, searching a plurality of candidate image blocks with the same size as the ith first image block in a search window corresponding to the ith first image block;
the center of the search window is an area where the ith first image block is located, and the search window is larger than the size of the ith first image block and smaller than the size of the corrected image;
step 2.2, selecting n candidate image blocks with highest similarity with the ith first image block from the plurality of candidate image blocks as similar image blocks to obtain n similar image blocks;
and 2.3, storing the ith first image block and the n similar image blocks into a matrix in a vector form to obtain an ith characteristic matrix.
In steps 2.1 to 2.3, each target three-dimensional magnetic resonance image block z is imagediContinue to use sliding window to search for z in its search windowiCandidate three-dimensional image blocks z' of the same size. The search window is an area centered on the target three-dimensional image block. If the radius of the search window is denoted as wr, the size of the search window is (wr +1)3. The larger the search window, the better the denoising effect, but the increased search time. Considering the balance between algorithm processing time and denoising effect, set 8<wr<20, wr is set to 10 in this embodiment.
Fig. 2 shows a schematic diagram of a searching process of a non-local image block. The relationship between the target three-dimensional image block, the candidate three-dimensional image block, and the search window can be clearly seen from the figure.
Optionally, when n candidate image blocks with the highest similarity to the ith first image block are selected from the plurality of candidate image blocks as the similar image blocks in step 2.2, the similarity between the ith first image block and each candidate image block is calculated by using the euclidean distance.
In this step, after obtaining a plurality of candidate three-dimensional image blocks z', the target three-dimensional magnetic resonance image block z needs to be measurediAnd the degree of similarity between the candidate three-dimensional image block z'. The Euclidean distance is adopted for measuring the similarity of the images, and the specific measurement mode is shown as the following formula:
in the above formula, r is the side length of the three-dimensional image block. d (z)iZ') represents a three-dimensional magnetic resonance image block z of the objectiDegree of similarity with the candidate three-dimensional image block z', d (z)iZ') is higher, and vice versa, it represents a low degree of similarity.
Sorting the Euclidean distances calculated in the step 2.2 from small to large, and selecting the candidate three-dimensional image block with the Euclidean distance sorted as the top n as the target three-dimensional magnetic resonance image block z according to the sorting resultiSimilar image blocks.
Step 2.3, target three-dimensional image block ziStoring the selected n similar image blocks into a matrix Z in a vector modeiIn (1). At this time matrix ZiI.e. a redundant matrix containing a large number of non-locally similar features. The specific process is shown as the following formula:
in the above formula, { z'j1,z′j2,…,z′jm1,2, …, n is a vector representation of similar image blocks, n denotes the number of similar image blocks, and m denotes the number of pixels in an image block. In the present invention, when the size of a three-dimensional image block is 3 × 3 × 3, m is 27.
After step 2 is completed, a plurality of feature matrices are obtained, and singular value decomposition is further required for each feature matrix, for one momentIn the array, the size of the singular value represents the importance degree of the image feature, and the main feature in the image is reserved and the noise in the image is abandoned in the subsequent step through the relevant processing of the singular value. Therefore, in this step, the present invention combines the matrix Z obtained in step twoiSingular value decomposition is performed to obtain a matrix ZiSingular value of
The specific process is shown as the following formula:
[U,Σ,V]＝SVD(Zi)
in the above formula, U and V are both unit orthogonal matrices, U is a left singular matrix, and V is a right singular matrix.
For a diagonal matrix, only the values on the diagonal are singular values, and the remaining values are 0.
Step 3, obtaining a residual image of the corrected image, wherein the size of the residual image is the same as that of the magnetic resonance image to be denoised;
selecting image blocks from the residual image in the same sliding window manner as in the step 2 to obtain a plurality of second image blocks;
local noise estimation is carried out on each second image block to obtain a plurality of noise standard deviations; the noise standard deviations correspond to the characteristic matrixes one by one;
in this embodiment, step 3 specifically includes:
and 3.1, processing the noise magnetic resonance image z by using low-pass filtering to obtain a filtered image.
Step 3.2, in noisy images, the noise tends to correspond to high frequency parts. Therefore, this step calculates the difference between the noise magnetic resonance image z and the low-pass filtered image, thereby obtaining a residual image containing noise.
And 3.3, traversing the residual image by using a sliding window in the step so as to obtain each three-dimensional residual image block. The setting of the sliding window is the same as in step 2.
And 3.4, obtaining the residual image through low-pass filtering, wherein the residual image contains a large amount of noise information, such as the intensity degree of noise and the space change condition. The local noise situation can be estimated from each residual image block. And estimating the noise standard deviation of each image block from the residual image blocks, wherein the noise standard deviation represents the intensity degree of the noise. The process of noise estimation is shown by the following equation:
δ(zi)＝std(zi-Filter(zi))
in the above formula, δ (z)i) Representing a three-dimensional noisy image block ziCorresponding noise standard deviation. Filter (. cndot.) represents a low-pass filtering process. std (. circle.) represents the calculation of the standard deviation.
Step 4, iterative solution is carried out on the formula I to obtain an estimated low-rank matrix corresponding to the ith feature matrix
Wherein ZiDenotes the ith feature matrix obtained in step 2, I is 1,2, …, I is a positive integer, δ (z)i) Representing the noise standard deviation, E, corresponding to the ith feature matrix obtained in step 3iRepresenting the ith low rank matrix to be estimated, EiIs Z as an initial valuei，σj(Ei) Representing the j singular value, σ, of the i-th low-rank matrix to be estimatedj(Ei) Not less than 0, j is 1,2, …, n, n +1, n is positive integer, omegajRepresenting the weight corresponding to the jth singular value of the ith low-rank matrix to be estimated, and omega is more than or equal to 0j≤1；
In this embodiment, in a magnetic resonance image, the larger singular values in the image matrix usually correspond to the subspace of more important features in the image, and the smaller singular values usually correspond to noise information in the image. That is, high singular values of the image matrix mostly correspond to important edge structure and texture detail information in the image, while the main part of image denoisingThe goal is to remove noise from noisy images while recovering as much of the image detail as possible. The weighted kernel norm minimization can treat singular values with different sizes differently, so that main features in the image can be reserved while noise is removed. More specifically, the weighted kernel norm minimization assigns a smaller weight to a larger singular value and a larger weight to a smaller singular value in the optimization process of the objective function, so that the compression of high singular values is realized as less as possible, and the optimization target of the function can be met. In the present invention, the subsequent optimization process of the objective function involves singular values. The method mainly comprises the step of initializing a singular value sigma in a target function by using the obtained singular valuej(Zi)。
The initialization procedure is as follows:
in the above formula, the first and second carbon atoms are,
is ZiThe j-th singular value of (a), which is obtained by singular value decomposition, in a non-decreasing order. n denotes the number of similar image blocks searched. Delta (z)i) The estimated noise standard deviation is used.
The weight is an important index for measuring singular values in the optimization process of the objective function, wherein large singular values correspond to small weights, and small singular values correspond to large weights. Therefore, the large singular values representing the important features of the image can be compressed as little as possible in the optimization process of the objective function, and the small singular values representing the noise information can be compressed as large as possible. The step mainly calculates singular value sigmaj(Zi) Corresponding weight wj. Weight wjThe calculation of (a) is shown as follows:
in the above equation, τ is a constant and ε is a very small number to avoid the case where the divisor is 0.
The strength of the local noise, i.e. the standard deviation of the noise, has been estimated before. In this step, the estimated local noise is merged with the weighted nuclear norm minimization method, and the estimated noise standard deviation is used to adaptively cope with the variable noise situation in the magnetic resonance image, such as the spatial variation of the noise. Similar features in the image are extracted in step 2 and this information is stored in the matrix ZiIn (1). Due to noise pollution, matrix ZiThe state of high rank is exhibited, however, the matrix Z is due to the redundant characteristic of the imageiCan be expressed sparsely, and further can remove noise in the image and recover image information. The invention uses a weighted kernel norm minimization pair matrix ZiThe sparse representation is performed so as to obtain a low rank matrix which is the result after filtering out the noise. The optimization objective function for weighted kernel norm minimization is shown as follows:
in the above formula, EiIs the low rank matrix to be estimated, initial Ei＝Zi，
Is the final estimation result.
Optionally, when E in step 4iIs an initial value ZiWhen the temperature of the water is higher than the set temperature,
wherein
Representing the j-th singular value, σ, obtained by singular value decomposition of the i-th eigen matrixj(Zi)≥0。
Objective of weighted kernel norm minimizationThe function is needed to be solved by iterative optimization, and is stopped when the iteration times or the iteration target is reached. At iteration 1
At the t-th iteration
The value of (A) is shown by the following formula:
in the above formula, the first and second carbon atoms are,
for adjusting the parameters, the degree of noise filtering after each iteration is determined, which is generally set
Step 5, repeating the step 4 to obtain an estimated low-rank matrix corresponding to each feature matrix;
step 6, restoring all the estimated low-rank matrixes obtained in the step 5 into a plurality of denoised image blocks;
splicing the plurality of denoised image blocks to obtain a primarily denoised magnetic resonance image;
and processing the primarily denoised magnetic resonance image by a sampling inverse variance stable transformation method to obtain the denoised magnetic resonance image.
In this embodiment, step 6 includes:
step 6.1, the low rank matrix can be obtained through the steps 1-5
Each column vector in the matrix is a pixel in an image block, and the matrix needs to be divided into two or more rows in this step
All ofThe vectors are restored to the original three-dimensional image block.
And 6.2, splicing all the image blocks obtained in the step 6.1 into a complete image so as to obtain the denoised magnetic resonance image. Specifically, each denoised image block is placed at the original position according to the moving sequence (splitting sequence) of the sliding window in step 2. Different image blocks obtained by using the sliding window with the step size of 1 have the condition of pixel coincidence, that is, pixels corresponding to the same position of an image may exist in a plurality of different image blocks. Therefore, the pixel values at the corresponding positions need to be added and summed and averaged. The specific process is shown as the following formula:
in the above formula, e (p) represents the gray value of the pixel point p in the denoised image e, eq(p) representing image Block eqGrey value of middle pixel point p, image block eqIncluding pixel point p. count (e)q) Which refers to the total number of all image blocks containing the pixel point p.
Step 6.3, through the above steps, most of the noise in the magnetic resonance image has been removed, but the current processing results are not optimal. Therefore, in the step, the inverse variance stable transformation method is applied to the primarily denoised magnetic resonance image, and then the maximum likelihood estimation result of the noise-free magnetic resonance image is returned to obtain the final denoising result.
In order to verify the effectiveness of the method, the invention selects a public data set to carry out experimental verification:
the T1 data in Brainweb was used in experiments to verify the validity of the algorithm. Rician or non-central chi-square distributed noise is added into the T1 data, and noise variance is artificially controlled to generate spatially-varying noise, so that noise with spatially-stable and spatially-varying characteristics is obtained.
As shown in table 1, the PSNR value comparison results of the method provided by the present invention and other magnetic resonance image denoising methods are shown. For spatially stable noise (including Rician noise and non-centered chi-square distributed noise), the results in the table are averages for 4%, 6%, 8%, 10% noise intensity. For spatially varying noise (including Rician noise and non-central chi-square distributed noise), the results in the table are averages for noise intensities of 4% -12%, 5% -15%, 6% -18%, 7% -21%. The data in table 1 show that the method of the invention achieves optimal results compared to other methods.
Fig. 3-7 show the results of the processing of the method of the present invention for four noise cases, spatially stable and spatially varying Rician or non-central chi-square distributions. As can be seen from the figure, the method provided by the invention can well remove noise and can recover the edge and detail information of the image as much as possible. In addition, the method does not introduce artifacts into the image in the denoising process.
Table 1 PSNR value comparison of the method of the present invention with other methods
Example two
The embodiment provides a magnetic resonance image denoising device based on non-local prior and sparse representation, which comprises an image correction module, a characteristic matrix obtaining module, a noise standard deviation obtaining module, a low-rank matrix estimation module and a reconstruction denoising module;
the image correction module is used for acquiring a magnetic resonance image to be denoised; carrying out non-Gaussian noise deviation correction on the magnetic resonance image to be denoised to obtain a corrected image;
the characteristic matrix obtaining module is used for selecting the corrected image by adopting a sliding window to obtain a plurality of first image blocks;
extracting non-local similar features of each first image block to obtain a plurality of feature matrixes;
the noise standard deviation obtaining module is used for obtaining a residual image of the corrected image, and the size of the residual image is the same as that of the magnetic resonance image to be denoised;
selecting a sliding window in a characteristic matrix obtaining module for the residual image to obtain a plurality of second image blocks;
local noise estimation is carried out on each second image block to obtain a plurality of noise standard deviations; the noise standard deviations correspond to the characteristic matrixes one by one;
the low-rank matrix estimation module is used for carrying out iterative solution on the formula I to obtain an estimated low-rank matrix corresponding to the ith feature matrix
Wherein ZiDenotes the ith feature matrix, I is 1,2, …, I is a positive integer, δ (z)i) Representing the noise standard deviation corresponding to the ith feature matrix, EiRepresenting the ith low rank matrix to be estimated, EiIs Z as an initial valuei，σj(Ei) Representing the j singular value, σ, of the i-th low-rank matrix to be estimatedj(Ei) Not less than 0, j is 1,2, …, n, n +1, n is positive integer, omegajRepresenting the weight corresponding to the jth singular value of the ith low-rank matrix to be estimated;
obtaining an estimated low-rank matrix corresponding to each feature matrix;
the reconstruction denoising module is used for restoring all the obtained estimated low-rank matrixes into a plurality of denoised image blocks;
splicing the plurality of denoised image blocks to obtain a primarily denoised magnetic resonance image;
and processing the primarily denoised magnetic resonance image by a sampling inverse variance stable transformation method to obtain the denoised magnetic resonance image.
Optionally, the feature matrix obtaining module includes an image searching sub-module, a similar image block screening sub-module, and a matrix obtaining sub-module;
the image searching sub-module is used for searching a plurality of candidate image blocks with the same size as the ith first image block in a searching window corresponding to the ith first image block;
the center of the search window is an area where the ith first image block is located, and the search window is larger than the size of the ith first image block and smaller than the size of the corrected image;
the similar image block screening submodule is used for selecting n candidate image blocks with highest similarity with the ith first image block from the plurality of candidate image blocks as similar image blocks to obtain n similar image blocks;
the matrix obtaining submodule is used for storing the ith first image block and the n similar image blocks into the matrix in a vector mode to obtain the ith characteristic matrix.
Optionally, when the similar image block screening sub-module selects n candidate image blocks with the highest similarity to the ith first image block from the plurality of candidate image blocks as the similar image blocks, the euclidean distance is used to calculate the similarity between the ith first image block and each candidate image block.
Optionally, when E in the low rank matrix estimation moduleiIs an initial value ZiWhen the temperature of the water is higher than the set temperature,
wherein
Representing the j-th singular value, σ, obtained by singular value decomposition of the i-th eigen matrixj(Zi)≥0。
Through the above description of the embodiments, those skilled in the art will clearly understand that the present invention may be implemented by software plus necessary general hardware, and certainly may also be implemented by hardware, but in many cases, the former is a better embodiment. Based on such understanding, the technical solutions of the present invention may be substantially implemented or a part of the technical solutions contributing to the prior art may be embodied in the form of a software product, where the computer software product is stored in a readable storage medium, such as a floppy disk, a hard disk, or an optical disk of a computer, and includes several instructions for enabling a computer device (which may be a personal computer, a server, or a network device) to execute the method according to the embodiments of the present invention.
Claims (8)
1. A magnetic resonance image denoising method based on non-local prior and sparse representation is characterized by comprising the following steps:
step 1, acquiring a magnetic resonance image to be denoised; performing non-Gaussian noise deviation correction on the magnetic resonance image to be denoised to obtain a corrected image;
step 2, selecting image blocks from the corrected image by adopting a sliding window to obtain a plurality of first image blocks;
extracting non-local similar features of each first image block to obtain a plurality of feature matrixes;
step 3, obtaining a residual image of the corrected image, wherein the size of the residual image is the same as that of the magnetic resonance image to be denoised; the residual image is the difference between the noise magnetic resonance image and the image after low-pass filtering processing;
selecting image blocks from the residual image by adopting a sliding window with the same size as that in the step 2 to obtain a plurality of second image blocks;
local noise estimation is carried out on each second image block to obtain a plurality of noise standard deviations; the plurality of noise standard deviations correspond to the plurality of feature matrixes one by one;
step 4, iterative solution is carried out on the formula I to obtain an estimated low-rank matrix corresponding to the ith feature matrix
Wherein ZiDenotes the ith feature matrix obtained in step 2, I is 1,2, …, I is a positive integer, δ (z)i) Representing the noise standard deviation, E, corresponding to the ith feature matrix obtained in step 3iRepresenting the ith low rank matrix to be estimated, EiIs Z as an initial valuei，σj(Ei) Representing the j singular value, σ, of the i-th low-rank matrix to be estimatedj(Ei) Not less than 0, j is 1,2, …, n, n +1, n is positive integer, omegajRepresenting the weight corresponding to the jth singular value of the ith low-rank matrix to be estimated, and omega is more than or equal to 0j≤1；
Step 5, repeating the step 4 to obtain an estimated low-rank matrix corresponding to each feature matrix;
step 6, restoring all the estimated low-rank matrixes obtained in the step 5 into image blocks to obtain a plurality of denoised image blocks;
splicing the plurality of denoised image blocks to obtain a primarily denoised magnetic resonance image;
and processing the primarily denoised magnetic resonance image by a sampling inverse variance stable transformation method to obtain the denoised magnetic resonance image.
2. The method for denoising a magnetic resonance image based on non-local prior and sparse representation as claimed in claim 1, wherein in the step 2, when extracting non-local similar features for each first image block to obtain a plurality of feature matrices, obtaining the ith feature matrix by using the steps 2.1 to 2.3:
step 2.1, searching a plurality of candidate image blocks with the same size as the ith first image block in a search window corresponding to the ith first image block;
the center of the search window is an ith first image block, the size of the search window is larger than that of the ith first image block, and the size of the search window is smaller than that of the corrected image;
step 2.2, selecting n candidate image blocks with highest similarity with the ith first image block from the plurality of candidate image blocks as similar image blocks to obtain n similar image blocks;
and 2.3, storing the ith first image block and the n similar image blocks into a matrix in a vector mode to obtain an ith characteristic matrix.
3. The method for denoising a magnetic resonance image based on non-local prior and sparse representation as claimed in claim 2, wherein the similarity between the ith first image block and each candidate image block is calculated by using euclidean distance when selecting n candidate image blocks with highest similarity to the ith first image block from the plurality of candidate image blocks as the similar image blocks in step 2.2.
4. The method as claimed in claim 3, wherein step 4 is performed when E is equal to EiIs an initial value ZiWhen the temperature of the water is higher than the set temperature,
wherein
Representing the j-th singular value, σ, obtained by singular value decomposition of the i-th eigen matrixj(Zi)≥0。
5. A magnetic resonance image denoising device based on non-local prior and sparse representation is characterized by comprising an image correction module, a characteristic matrix obtaining module, a noise standard deviation obtaining module, a low-rank matrix estimation module and a reconstruction denoising module;
the image correction module is used for acquiring a magnetic resonance image to be denoised; performing non-Gaussian noise deviation correction on the magnetic resonance image to be denoised to obtain a corrected image;
the characteristic matrix obtaining module is used for selecting image blocks from the corrected image by adopting a sliding window to obtain a plurality of first image blocks;
extracting non-local similar features of each first image block to obtain a plurality of feature matrixes;
the noise standard deviation obtaining module is used for obtaining a residual image of the corrected image, and the size of the residual image is the same as that of the magnetic resonance image to be denoised; the residual image is the difference between the noise magnetic resonance image and the image after low-pass filtering processing;
selecting image blocks from the residual image by adopting a sliding window with the same size as that of the characteristic matrix obtaining module to obtain a plurality of second image blocks;
local noise estimation is carried out on each second image block to obtain a plurality of noise standard deviations; the plurality of noise standard deviations correspond to the plurality of feature matrixes one by one;
the low-rank matrix estimation module is used for carrying out iterative solution on the formula I to obtain an estimated low-rank matrix corresponding to the ith feature matrix
Wherein ZiDenotes the ith feature matrix, I is 1,2, …, I is a positive integer, δ (z)i) Representing the noise standard deviation corresponding to the ith feature matrix, EiRepresenting the ith low rank matrix to be estimated, EiIs Z as an initial valuei，σj(Ei) Representing the j singular value, σ, of the i-th low-rank matrix to be estimatedj(Ei) Not less than 0, j is 1,2, …, n, n +1, n is positive integer, omegajRepresenting the weight corresponding to the jth singular value of the ith low-rank matrix to be estimated, and omega is more than or equal to 0j≤1；
Obtaining an estimated low-rank matrix corresponding to each feature matrix;
the reconstruction denoising module is used for restoring all the obtained estimated low-rank matrixes into image blocks to obtain a plurality of denoised image blocks;
splicing the plurality of denoised image blocks to obtain a primarily denoised magnetic resonance image;
and processing the primarily denoised magnetic resonance image by a sampling inverse variance stable transformation method to obtain the denoised magnetic resonance image.
6. The apparatus for denoising magnetic resonance image based on non-local prior and sparse representation as claimed in claim 5, wherein the feature matrix obtaining module comprises an image searching sub-module, a similar image block screening sub-module and a matrix obtaining sub-module;
the image searching sub-module is used for searching a plurality of candidate image blocks with the same size as the ith first image block in a searching window corresponding to the ith first image block;
the center of the search window is an area where the ith first image block is located, and the search window is larger than the size of the ith first image block and smaller than the size of the corrected image;
the similar image block screening submodule is used for selecting n candidate image blocks with highest similarity with the ith first image block from the plurality of candidate image blocks as similar image blocks to obtain n similar image blocks;
the matrix obtaining submodule is used for storing the ith first image block and the n similar image blocks into a matrix in a vector mode to obtain an ith characteristic matrix.
7. The apparatus for denoising magnetic resonance image based on non-local prior and sparse representation as claimed in claim 6, wherein when the similar image block filtering sub-module selects n candidate image blocks with highest similarity to the ith first image block from the plurality of candidate image blocks as the similar image block, the euclidean distance is used to calculate the similarity between the ith first image block and each candidate image block.
8. The apparatus for denoising magnetic resonance image based on non-local prior and sparse representation as claimed in claim 7, wherein the low rank matrix estimation module is characterized by EiIs an initial valueZiWhen the temperature of the water is higher than the set temperature,
wherein
Representing the j-th singular value, σ, obtained by singular value decomposition of the i-th eigen matrixj(Zi)≥0。
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