CN107845081B - Magnetic resonance image denoising method - Google Patents
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Abstract
The invention discloses a magnetic resonance image denoising method, which comprises the following steps: tensor decomposition; splitting an image block; calculating similarity weight; estimating a pixel value; correcting deviation; the invention has the advantages that: the denoising effect of the magnetic resonance image is improved, more original image information can be stored, and the blur of the edge part of the image is reduced. The processing speed of the magnetic resonance image is improved. The method can be combined with other non-local mean denoising improvement algorithms to improve the speed of image processing and ensure the denoising effect.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a magnetic resonance image denoising method.
Background
Medical images are becoming more and more important with an increasing weight in clinical diagnosis and research. The noninvasive image acquisition system can provide complete accurate image information of relevant parts in the human body for doctors under the noninvasive condition, and provides very important reference basis for examination and diagnosis of the doctors. There are many techniques for imaging, including: x-ray, tomography, ultrasonic, nuclear imaging, magnetic resonance imaging and other technical means. Among them, Magnetic Resonance Imaging (MRI) technology is widely used in medical treatment because it can provide very clear images of organs and tissues of the human body. Due to the constraints of the conditions, the signal-to-noise ratio of the acquired magnetic resonance images is generally low. Furthermore, magnetic resonance images can be degraded by the effects of artifacts and noise. Establishing a proper denoising model is very important in magnetic resonance image processing. The research on modeling removal has been a very popular subject, and aims to remove noise and artifacts contained in an image, save details and edge information of the image, and improve the signal-to-noise ratio of the image.
There are many image denoising methods, which can be generally understood as denoising an image during the process of acquiring the image and denoising the image after the acquisition. Due to the technical condition limitation of magnetic resonance imaging, related denoising work is generally performed after acquisition is completed, and the commonly used denoising methods for magnetic resonance images can be roughly divided into two categories, namely a filtering method and a transform domain method. The filtering method can be subdivided into a linear filtering method and a nonlinear filtering method. The spatial filtering and the temporal filtering belong to linear filtering, anisotropic filtering, and non-local PCA and non-local mean filtering belong to nonlinear filtering methods. The denoising method based on the transform domain comprises wavelet transform, curvelet transform, Fourier transform, wave removing transform and contour wavelet transform. Non-local mean filtering and contour wavelet transformation are respectively the best denoising method of the two filtering methods. The method is improved by using a tensor decomposition method and an adjustment weight calculation method on the basis of non-local mean filtering, and is used for improving the denoising efficiency and the denoising effect of an algorithm.
The magnetic resonance image has high redundancy and large data volume, and the non-local mean filtering denoising method makes full use of the redundancy characteristic of the image, removes the noise contained in the image and recovers the image with higher signal-to-noise ratio. The basic method of non-local mean filtering is to divide an image into image blocks with the same size in the global scope, and then estimate the pixel value of a certain point by using all the image blocks, and the basic steps are as follows: and respectively calculating Euclidean distances between the image block where the current pixel point is located and other pixel blocks, wherein the number of the pixel points contained in the image block is the same because the size of each image block is the same, and the Euclidean distance can be calculated only according to the gray value of each pixel point. The euclidean distance is used for judging the similarity strength of the two image blocks, the greater the similarity strength of the two image blocks is, the higher the acquaintance degree of the central points of the two image blocks is, and when the value of the pixel point is estimated, the greater the similarity weight is, the greater the contribution to the point to be estimated is. By using the same method, values of all pixel points can be estimated by traversing all the pixel points in the whole image.
Tensor decomposition, which is used to distinguish flat regions, edges and corner portions of an image in an image. The calculation method comprises the steps of respectively calculating partial derivatives of the image in the direction X, Y, then calculating matrix lines K and traces H, and screening the lines K and the traces H through a threshold value to respectively obtain original image pixel values of a flat area, an edge part and a corner part. By the method, three images with the same size can be obtained, most of the structural information of the images is contained in the edge part, and the probability that random noise generated by the images is contained in the corner region is also higher. When calculating the similarity of images, it is possible to perform calculation using a portion in which the structure information contains more.
The original non-local mean filtering is applied to the magnetic resonance image denoising, the time complexity of the algorithm is high, the edge and detail information of the original image is not well reserved, and the denoising effect under the high-noise condition is poor.
The original non-local denoising method traverses all the pixel points in the global range, and the time complexity of calculation is increased. Meanwhile, the similarity weight of pixel points in the same image block is averaged, so that the edge and detail parts of the image are suppressed, and the structural information of the image is reduced.
Some improved methods have certain improvement on the denoising performance, but increase the running time of the algorithm.
Some researchers use random sampling, and the method of reducing image blocks reduces the running time of the program, with the consequence that the number of selected image blocks is limited, and compared with the original algorithm, the accuracy of the estimated pixel value is reduced, the running time is reduced, and the denoising effect is also lost.
Other improved methods have the advantage of improving the denoising speed, but sacrifice part of denoising effect.
Some researchers do much work on improving the denoising capability, and also obtain obvious effects. The improved method of the non-local mean algorithm by using the collaborative filtering of two or more algorithms improves the denoising performance and increases the processing complexity, thereby increasing the processing time.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a magnetic resonance image denoising method, which can effectively solve the problems in the prior art.
In order to realize the purpose, the technical scheme adopted by the invention is as follows:
a magnetic resonance image denoising method comprises the following steps:
step 1: tensor decomposition;
step 11: solving a tensor matrix of the noise image;
using the CP decomposition method in tensor decomposition, the partial derivatives Ix, Iy in the X, Y direction are calculated separately, and by the partial derivatives in the two directions:
Ix2=Ix.^2;
Iy2=Iy.^2;
Ixy=Ix.*Iy;
the three values constitute a tensor matrix ST of the noise image [ Ix2, Ixy; ixy, Iy2 ].
Step 12: extracting a high-frequency part in the image;
through traversing all pixel points, the determinant K and the trace H of the tensor matrix are calculated, and the noise image is split into three parts by dividing the values of different K and H: a flat portion, an edge portion, an angular point portion; the image of the edge portions and the corner portions is taken and is called a structural image.
Step 2: splitting an image block;
step 21: splitting a noise image; the method comprises the steps of splitting a noise image into image blocks with the same size, wherein each image block is used for estimating the value of one pixel point, and the image blocks are called as search windows.
Step 22: splitting the structural image;
and (3) splitting the structural image obtained in the step (12), wherein the split image blocks are called neighborhood windows, and the split neighborhood image blocks form a neighborhood matrix.
And step 3: calculating similarity weight;
step 31: using K-means clustering on the neighborhood matrix;
and (4) solving the clustering center of each neighborhood image block by using a k-means method for the neighborhood matrix in the step (22).
Step 32: calculating similarity weight between image blocks;
the cluster center through the previous step uses the formula:
wherein the content of the first and second substances,representing the weight of similarity between pixel points, Z (x)i) The normalization parameter is represented, e (xi) represents the cluster center of the image block centered at the point i, e (xj) represents the cluster center of the image block centered at the point j, and h is the filtering strength.
And calculating similarity weights among the neighborhood image blocks, wherein the similarity weights among the neighborhood image blocks are the similarity weights of the central pixel points, and estimating the values of the relevant pixel points by utilizing the similarity relation among the pixel points.
And 4, step 4: estimating a pixel value;
in each search window, estimating the value of the pixel point in the center of the search window according to the similarity weight of the pixel point calculated in step 32, wherein the estimation formula is as follows:
wherein W (-) is the similarity weight between the pixels estimated in the previous step, In(xj) The values of the pixels estimated for the observed values of the corresponding pixels, i (xi), are also true values. N represents the number of pixel points in the image block, xi represents the ith pixel point in the image block, and xj represents the jth pixel point in the image block.
The similarity weight of each pixel point corresponding to the pixel point to be estimated is the contribution of the point in the pixel value estimation, and the higher the similarity weight is, the larger the proportion of the point is.
And 5: correcting deviation;
the treatment method is as follows:
output result is sqrt (max (0, sum of denoising result/similarity weight-2 noise variance)).
Further, the size of the search window in step 21 uses an empirical value with a radius of 3.
Further, the radius of the neighborhood window in step 22 takes the empirical value of 2.
Compared with the prior art, the invention has the advantages that:
the denoising effect of the magnetic resonance image is improved, more original image information can be stored, and the blur of the edge part of the image is reduced.
The processing speed of the magnetic resonance image is improved.
The method can be combined with other non-local mean denoising improvement algorithms to improve the speed of image processing and ensure the denoising effect.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of tensor decomposition according to an embodiment of the present invention;
fig. 3 is a schematic diagram of splitting a noise image according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, a magnetic resonance image denoising method includes the following steps:
step 1: tensor decomposition;
step 11: solving a tensor matrix of the noise image;
using the CP decomposition method in tensor decomposition, the partial derivatives Ix, Iy in the X, Y direction are calculated separately, and by the partial derivatives in the two directions:
Ix2=Ix.^2;
Iy2=Iy.^2;
Ixy=Ix.*Iy;
the three values constitute a tensor matrix ST of the noise image [ Ix2, Ixy; ixy, Iy2 ]. The basic method of tensor decomposition is shown in fig. 2, which estimates the original image matrix with two smaller matrices, and main structural information can be saved occasionally.
Step 12: extracting a high-frequency part in the image;
through traversing all pixel points, the determinant K and the trace H of the tensor matrix are calculated, and the noise image is split into three parts by dividing the values of different K and H: flat portions, edge portions, corner portions. The structural information of the image is stored in the high-frequency structural part, so that the image of the edge part and the corner part is only selected, and the image is called as a structural image; the noisy image split is shown in fig. 3.
The low-frequency part and the high-frequency part are separated through an image after tensor decomposition, the high-frequency part stores structural information and edge information of the image, and the high-frequency part is selected mainly for calculating the similarity of the image. In addition, in the invention, tensor decomposition is carried out on the whole image, so that the calculation time can be reduced. More importantly, one of the main points of the invention is that only the structural part is selected for similarity comparison between image blocks, and the influence of the smooth part is eliminated.
Step 2: splitting an image block;
step 21: splitting a noise image;
the noise image is divided into image blocks with the same size, and each image block is used for estimating the value of one pixel point. The image block we call the search window, which is a size we use an empirical value with a radius of 3. The pixel points are estimated in only one search window without operating on the whole image, so that on one hand, the calculated amount can be reduced, on the other hand, the image smoothness caused by global averaging can be reduced, and more structural information is saved.
Step 22: splitting the structural image;
and (3) splitting the structural image obtained in the step (12), wherein the split image blocks are called neighborhood windows, the radius of each neighborhood window is also an empirical value of 2, and the split neighborhood image blocks form a neighborhood matrix. Each column of the neighborhood matrix stores values of all pixel points of a neighborhood window, so the number of the row pixel points of the matrix is the number of the image blocks.
And step 3: calculating similarity weight;
step 31: using K-means clustering on the neighborhood matrix;
and (4) solving the clustering center of each neighborhood image block by using a k-means method for the neighborhood matrix in the step (22). The method for clustering by using the k-means clustering method is one of core steps of the method, and all pixel points in each neighborhood window are clustered, so that the method has two advantages, namely, the number of the pixel points participating in weight calculation is reduced, and the running time of a program can be saved; secondly, the difference between the boundaries is increased in the same neighborhood window, so that the averaged edge part can be better stored; finally, the method differs from other denoising methods in that a clustering method is used inside the neighborhood window, rather than clustering between image blocks.
Step 32: calculating similarity weight between image blocks;
the cluster center through the previous step uses the formula:
and calculating similarity weights among the neighborhood image blocks, wherein the similarity weights among the neighborhood image blocks are the similarity weights of the central pixel point. The method for calculating the similarity weight is different from the traditional calculation method, the method uses the clustering center inside the image block to calculate the similarity weight, the clustering maximizes the distance between the classes, and the smoothness degree is reduced when averaging is carried out. Therefore, the blurring of the edge portion can be reduced, and more detailed information can be saved.
And 4, step 4: estimating a pixel value;
in each search window, estimating the value of the pixel point in the center of the search window according to the similarity weight of the pixel point calculated in step 32, wherein the estimation formula is as follows:
in the same search window, the pixel point to be estimated and each other pixel point have a similarity weight, and the value of the required pixel point, namely the value of the denoised image, can be obtained by weighting and averaging.
And 5: correcting deviation;
the magnetic resonance image is different from other images, the noise of the magnetic resonance image is mainly thermal noise, artifacts are generated after the image is obtained, and the noise type is understood as rice noise, so that the image is subjected to deviation correction after the noise removal. The general approach to processing is as follows:
the output result is sqrt (max (0, sum of denoising result/similarity weight-2 noise variance).
It will be appreciated by those of ordinary skill in the art that the examples described herein are intended to assist the reader in understanding the manner in which the invention is practiced, and it is to be understood that the scope of the invention is not limited to such specifically recited statements and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (3)
1. A magnetic resonance image denoising method is characterized by comprising the following steps:
step 1: tensor decomposition;
step 11: solving a tensor matrix of the noise image;
using the CP decomposition method in tensor decomposition, the partial derivatives Ix, Iy in the X, Y direction are calculated separately, and by the partial derivatives in the two directions:
Ix2=Ix.^2;
Iy2=Iy.^2;
Ixy=Ix.*Iy;
the three values constitute a tensor matrix ST of the noise image [ Ix2, Ixy; ixy, Iy2 ];
step 12: extracting a high-frequency part in the image;
calculating determinant K and trace H of a tensor matrix by traversing all pixel points, and splitting a noise image into three parts by dividing different values of K and H: a flat portion, an edge portion, an angular point portion; taking images of the edge part and the corner part, and calling the images as structural images;
step 2: splitting an image block;
step 21: splitting a noise image; the method comprises the steps of splitting a noise image into image blocks with the same size, wherein each image block is used for estimating the value of one pixel point and is called a search window;
step 22: splitting the structural image;
splitting the structural image obtained in the step 12, wherein the split image blocks are called neighborhood windows, and the split neighborhood image blocks form a neighborhood matrix;
and step 3: calculating similarity weight;
step 31: using K-means clustering on the neighborhood matrix;
calculating the clustering center of each neighborhood image block by using a k-means method for the neighborhood matrix in the step 22;
step 32: calculating similarity weight between image blocks;
the cluster center through the previous step uses the formula:
wherein the content of the first and second substances,representing the weight of similarity between pixel points, Z (x)i) Expressing normalization parameters, E (xi) expressing the clustering center of the image block taking the point i as the center, E (xj) expressing the clustering center of the image block taking the point j as the center, and h expressing the filtering strength;
calculating similarity weights among the neighborhood image blocks, wherein the similarity weights among the neighborhood image blocks are the similarity weights of the central pixel points, and estimating values of the relevant pixel points by utilizing the similarity relation among the pixel points;
and 4, step 4: estimating a pixel value;
in each search window, estimating the value of the pixel point in the center of the search window according to the similarity weight of the pixel point calculated in step 32, wherein the estimation formula is as follows:
wherein W (-) is the similarity weight between the pixels estimated in the previous step, In(xj) Estimating the value of the pixel point for the observed value of the corresponding pixel point, i (xi); n represents the number of pixel points in the image block, xi represents the ith pixel point in the image block, and xj represents the jth pixel point in the image block;
the similarity weight of each pixel point corresponding to a pixel point to be estimated is the contribution of the point in pixel value estimation, and the higher the similarity weight is, the larger the proportion of the point is;
and 5: correcting deviation;
the treatment method is as follows:
output result is sqrt (max (0, sum of denoising result/similarity weight-2 noise variance)).
2. The method of claim 1, wherein the method further comprises: the size of the search window in step 21 uses an empirical value with a radius of 3.
3. The method of claim 1, wherein the method further comprises: the radius of the neighborhood window in step 22 takes the empirical value of 2.
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