CN107644406B - Image denoising method based on improved orthogonal matching pursuit - Google Patents
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Abstract
The invention discloses an image denoising method based on improved orthogonal matching pursuit. The method comprises the following steps: firstly, carrying out digital processing on an image, and regarding each pixel in the image as an atom; then calculating correlation coefficient by the absolute value of inner product between residual r and each atom in measurement matrix phi to select L values, and storing the index values of the L values in index matrix AmAnd updating the measurement matrix phi until the residual error is small enough when the condition is met, and the finally obtained residual error is smaller than the last residual error, and reconstructing an image according to the obtained residual error to realize denoising. The invention carries out sparse coding of the signals while carrying out signal sampling, realizes sparse decomposition and reconstruction of the signals by utilizing the self sparsity of the signals, reserves the detail characteristics of the images and improves the denoising precision.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image denoising method based on improved orthogonal matching pursuit.
Background
Image noise is useless information in an image, the image quality can be reduced, and the noise is often a main obstacle factor in the process of image acquisition and transmission, so that the integrity of the image is damaged, and the use value of the image is greatly influenced. Therefore, extracting useful signals to inhibit noise, improving image quality, preparing for subsequent higher-level processing, and performing denoising processing on images is an indispensable important link. The image denoising is to retain useful information in an image and eliminate or reduce interference and noise in the image.
At present, the more mature image denoising methods can be classified into the following categories:
(1) spatial domain and transform domain processing method
The spatial domain processing is to directly perform data operation on the original image, for example, directly perform data operation on the gray value of the image, and median filtering, wiener filtering and the like belong to the processing methods. The transform domain image denoising, also called frequency domain image denoising, is a very effective image denoising method based on image transform domain processing. The core idea of the method is that after certain transformation, the transformation of the domain range of the processed image from the space domain to the transformation domain is realized, and the operation of a related formula is further applied to the transformation coefficient in the transformation domain, so that the transformation coefficient is restored from the current transformation domain to the original space domain again, and the purpose of denoising is achieved.
For example, in 2013, the 'comparison and research of three spatial domain image denoising methods' of eastern Lin, studied the spatial domain image denoising method; in 2013, the research on a transform domain image denoising method is carried out by the unstable image denoising algorithm research based on the transform domain. They have in common that each point of the sampled signal, which is uniform based on the nyquist sampling theorem, is processed for each pixel in the image, resulting in redundancy of adjacent samples, with a significant waste of resources. And the same thinking and method are used, the data operation is directly carried out on the original image, and the characteristics of the image pixels are ignored. It is not difficult to understand why such methods usually accompany the more severe blurring phenomenon when denoising.
(2) Image denoising method based on orthogonal matching pursuit
The image is sparsely represented, namely, an image is considered to be an image or the image can be transformed into only a limited number of non-zero elements, most of the elements are close to zero, and the limited number of non-zero elements represent most of information of the image, so that the image can reconstruct a reconstructed image with small difference from the original image through the limited number of non-zero elements. The orthogonal matching pursuit algorithm is to use the sparse representation theory to orthogonalize the measurement matrix by an orthogonalization method, then to perform sparse approximation on the projection of the signal on the space formed by the orthogonal atoms to obtain the component and residual component of the signal on each selected atom, then to decompose the residual component by the same method, and to re-describe the signal by the finally obtained elements.
For example, in 2012, the "sparsity-based image denoising overview" of guo de pan and yanghu rain studies the orthogonal matching pursuit algorithm based on sparse representation and its early algorithm; in 2014, the fast implementation of the orthogonal matching pursuit algorithm was researched by the 'segmented regularized orthogonal matching pursuit algorithm' of Wudi, Quinumin and the like. The method realizes the orthogonal matching tracking algorithm, but does not strictly judge the matching tracking process, and excessive phenomenon can be generated in the iterative updating process of the residual error r, so that the edge in the image is unclear.
Disclosure of Invention
The invention aims to provide an image denoising method based on improved orthogonal matching pursuit, so that noise in an image is effectively removed.
The technical solution for realizing the purpose of the invention is as follows: an image denoising method based on improved orthogonal matching pursuit comprises the following steps:
step 4, residual error r is obtainedm-1And the measurement matrix phim-1Calculating the correlation coefficient by the absolute value of the inner product between each atom, selecting L values, and storing the corresponding index value into AmIn (A)mSelecting an index set for m times;
the pass residual rm-1And the measurement matrix phim-1The absolute value of the inner product between each atom in the equation (a) to calculate the correlation coefficient u, the equation is as follows:
in the above formula, u is a correlation coefficient, ukFor the correlation coefficient of the residual with the k-th column of the measurement matrix,
is the kth column of the measurement matrix;
calculating a correlation coefficient u through an expression (1), searching index values corresponding to L maximum values from u, and storing the index values into AmPerforming the following steps;
step 5, recording the matrix corresponding to the m index value found
Updating a set of measurement matrices
Wherein phimFor m updated measurement matrices, phim-1The measurement matrix is updated m-1 times;
step 6, obtaining from least squares
Updating the mth residual rmAnd approximation of target signal x m
The formula is as follows:
in the above formula, the first and second carbon atoms are,
the mth approximation of the target signal x is carried out;
and 7, judging whether the new residual meets the conditions: if | rm‖2If the value is greater than epsilon, wherein epsilon is a threshold value, and m is equal to m +1, turning to the step 4;
if | rm‖2| < epsilon > and | < r >m‖2＞‖rm-1‖2Wherein r ism-1Residual error of m-1 time; then the step length is changed to s ═ s/2, and the support set A is formedmIs increased to L ═ L + s, and m ═ m +1, go to step 4;
if | rm‖2| < epsilon > and | < r >m‖2≤‖rm-1‖2(ii) a And stopping iteration, and performing final signal reconstruction by using the obtained atoms to obtain a denoised image.
Compared with the prior art, the invention has the following remarkable advantages: (1) based on sparse representation of the image, namely, an image is considered to be changed into only a limited number of non-zero elements after being transformed, most of the elements are close to zero, and the limited number of non-zero elements represent most of information of the image, so that the image can reconstruct a reconstructed image with small difference from an original image through the limited number of non-zero elements, information needing to be reserved is greatly reduced, and resources can be effectively utilized; (2) sparse coding is carried out on the signals while signal sampling is carried out, sparse decomposition and reconstruction of the signals are realized by using the self sparsity of the signals, the neglect of the self characteristics of each pixel is avoided, and the detail characteristics of the image are reserved; (3) the method improves the phenomenon that the residual error r of the existing orthogonal matching pursuit algorithm possibly generates transition in the iterative updating process, and firstly, a support set is increased when the optimal residual error is close to the residual error, so that the precision is improved; and secondly, residual error iteration ending judgment conditions are added to avoid excess.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flowchart of an image denoising method based on improved orthogonal matching pursuit according to the present invention.
Fig. 2 is an original diagram adopted by the present invention, in which (a) is an original infrared image 1, (b) is an original infrared image 2, (c) is an original visible light image 1, and (d) is an original visible light image 2.
FIG. 3 is a graph showing comparison of denoising effects of a conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on an infrared image 1 having a noise variance of 30, where (a) is the noise infrared image 1, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
FIG. 4 is a graph showing comparison of denoising effects of a conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on an infrared image 1 having a noise variance of 45, where (a) is the noise infrared image 1, (b) is the b-mean filtering denoising result, (c) is the orthogonal matching algorithm result graph, and (d) is the denoising result graph of the method of the present invention.
Fig. 5 is a graph showing comparison of the denoising effects of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on an infrared image 1 having a noise variance of 60, where (a) is the noise infrared image 1, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 6 is a graph showing comparison of the denoising effects of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on an infrared image 2 having a noise variance of 30, where (a) is the noise infrared image 2, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 7 is a graph showing comparison of the denoising effects of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on an infrared image 2 having a noise variance of 45, where (a) is the noise infrared image 2, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 8 is a graph showing comparison of the denoising effects of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on an infrared image 2 having a noise variance of 60, where (a) is the noise infrared image 2, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 9 is a graph showing comparison of denoising effects of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on a visible light image 1 having a noise variance of 30, where (a) is the noise visible light image 1, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 10 is a graph showing comparison of the denoising effects of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on a visible light image 1 having a noise variance of 45, where (a) is the noise visible light image 1, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 11 is a graph showing comparison of the denoising effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on a visible light image 1 having a noise variance of 60, where (a) is the noise visible light image 1, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 12 is a graph showing comparison of the denoising effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on the visible light image 2 having a noise variance of 30, where (a) is the noise visible light image 2, (b) is the mean filtering denoising result, (c) is the orthogonal matching algorithm result graph, and (d) is the denoising result graph of the method of the present invention.
Fig. 13 is a graph showing comparison of the denoising effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on a visible light image 2 having a noise variance of 45, where (a) is the noise visible light image 2, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Fig. 14 is a graph showing comparison of denoising effects of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention performed on a visible light image 2 having a noise variance of 60, where (a) is the noise visible light image 2, (b) is a mean filtering denoising result graph, (c) is an orthogonal matching algorithm result graph, and (d) is a denoising result graph of the method of the present invention.
Detailed Description
With reference to fig. 1, the image denoising method based on the improved orthogonal matching pursuit of the present invention includes the following steps:
step 4, residual error r is obtainedm-1And the measurement matrix phim-1Calculating the correlation coefficient by the absolute value of the inner product between each atom, selecting L values, and storing the corresponding index value into AmIn (A)mSelecting an index set for m times;
the pass residual rm-1And the measurement matrix phim-1The absolute value of the inner product between each atom in the equation (a) to calculate the correlation coefficient u, the equation is as follows:
in the above formula, u is a correlation coefficient, ukFor the correlation coefficient of the residual with the k-th column of the measurement matrix,
is the kth column of the measurement matrix;
calculating a correlation coefficient u through an expression (1), searching index values corresponding to L maximum values from u, and storing the index values into AmPerforming the following steps;
step 5, recording the foundmatrix corresponding to index values of m times
Updating a set of measurement matrices
Wherein phimFor m updated measurement matrices, phim-1The measurement matrix is updated m-1 times;
step 6, obtaining from least squares
Updating the mth residual rmAnd approximation of target signal x m
The formula is as follows:
in the above formula, the first and second carbon atoms are,
the mth approximation of the target signal x is carried out;
and 7, judging whether the new residual meets the conditions: if | rm‖2If the value is greater than epsilon, wherein epsilon is a threshold value, and m is equal to m +1, turning to the step 4;
if | rm‖2| < epsilon > and | < r >m‖2＞‖rm-1‖2Wherein r ism-1Residual error of m-1 time; then the step length is changed to s ═ s/2, and the support set A is formedmIs increased to L ═ L + s, and m ═ m +1, go to step 4;
if | rm‖2| < epsilon > and | < r >m‖2≤‖rm-1‖2(ii) a And stopping iteration, and performing final signal reconstruction by using the obtained atoms to obtain a denoised image.
1) If | rm‖2If the residual error is larger than epsilon, the residual error is still larger, and the image cannot be well reconstructed.
2) If | rm‖2| < epsilon > and | < r >m‖2＞‖rm-1‖2Then change the step length to s ═ s/2 support set AmIs increased to L-L + s, and m-m +1 goes to step 1. Condition | rm‖2Epsilon is less than or equal to ensure that the finally obtained residual error is small enough; condition | rm‖2≥‖rm-1‖2And (4) explaining that the obtained residual error is worse than the previous effect, increasing the support set, and returning to the step (4) to obtain the residual error again.
3) If | rm‖2| < epsilon > and | < r >m‖2≤‖rm-1‖2Stopping iteration, and performing final signal reconstruction by using the obtained atoms, or performing the next step. Condition | rm‖2Epsilon is less than or equal to ensure that the finally obtained residual error is small enough, and epsilon is a small enough quantity; condition | rm‖2≤‖rm-1‖2And better values are ensured to be obtained continuously in the calculation process, and excessive calculation caused by overlarge step length and other reasons is avoided.
The invention is further described below in connection with simulated embodiments of the invention.
Example 1
Firstly, collecting infrared and visible light images by using an infrared focal plane and a control module thereof or a visible light CCD (charge coupled device), and inputting the images into a computer to obtain the infrared and visible light images; to evaluate the effectiveness of the improved orthogonal matching pursuit algorithm, simulation experiments were performed. The experiment is based on MATLAB R2014b software, and the PC is configured to be CPU 2.4GHz and memory 4G.
To denoise the infrared image and the visible image, 2 sets of experiments were performed. The original images are fig. 2(a) - (d), and the pixel sizes are all 320 × 240.
FIGS. 3(a) - (d) are graphs comparing denoising effects of a conventional mean filtering and orthogonal matching algorithm and an algorithm of the present invention for an infrared image 1 with a noise variance of 30; FIGS. 4(a) - (d) are graphs comparing denoising effects of an infrared image 1 containing a noise variance of 45, a conventional mean filtering and orthogonal matching algorithm, and an algorithm of the present invention; fig. 5(a) - (d) are graphs comparing denoising effects of the infrared image 1 containing the noise variance of 60, the conventional mean filtering and orthogonal matching algorithm, and the algorithm of the present invention.
FIGS. 6(a) - (d) are graphs comparing the denoising effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention for the infrared image 2 with the noise variance of 30; FIGS. 7(a) - (d) are graphs comparing the denoising effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention for the infrared image 2 with a noise variance of 45; fig. 8(a) - (d) are graphs comparing the denoising effect of the infrared image 2 containing the noise variance of 60, the conventional mean filtering and orthogonal matching algorithm, and the algorithm of the present invention.
FIGS. 9(a) - (d) are graphs comparing denoising effects of a visible light image 1 containing a noise variance of 30, a conventional mean filtering and orthogonal matching algorithm, and an algorithm of the present invention; FIGS. 10(a) - (d) are graphs comparing denoising effects of a visible light image 1 containing a noise variance of 45, a conventional mean filtering and orthogonal matching algorithm, and an algorithm of the present invention; FIGS. 11(a) - (d) are graphs comparing the noise removal effect of a visible light image 1 with a noise variance of 60, a conventional mean filtering and orthogonal matching algorithm, and an algorithm of the present invention
FIGS. 12(a) - (d) are graphs comparing the noise removal effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention for the visible light image 2 with the noise variance of 30; fig. 13(a) - (d) are graphs comparing the denoising effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention for the visible light image 2 with a noise variance of 45; fig. 14(a) to (d) are graphs showing comparison of the noise removal effect of the conventional mean filtering and orthogonal matching algorithm and the algorithm of the present invention, including the visible light image 2 with the noise variance of 60.
From the denoising results of fig. 3 to fig. 14, it can be found that: the 3 image denoising methods all achieve the purpose of image noise removal, except that an image processed by using the traditional spatial domain mean value filtering still contains more noise and can generate a fuzzy phenomenon, the image processed by using the orthogonal matching pursuit algorithm and the image processed by the algorithm have better effects than the mean value filtering, and the difference is that the image scene edge of the denoising effect image is clearer, such as the boundary between a person and a background, the boundary between the scene edge in the image processed by the algorithm is obvious and the definition is high.
Claims (1)
1. An image denoising method based on improved orthogonal matching pursuit is characterized by comprising the following steps:
step 1, collecting an image by using an infrared detector or a visible light camera, wherein the image contains noise;
step 2, if the RGB image is collected in the step 1, graying the RGB image; otherwise, performing step 3;
step 3, inputting a measurement matrix phi0Original signal y, sparsity M; initialization residual r0Initializing a support index set as y
Initial iteration m is 1, s is not equal to 0;
step 4, residual error r is obtainedm-1And the measurement matrix phim-1Calculating the correlation coefficient by the absolute value of the inner product between each atom, selecting L values, and storing the corresponding index value into AmIn (A)mSelecting an index set for m times;
the pass residual rm-1And the measurement matrix phim-1The absolute value of the inner product between each atom in the equation (a) to calculate the correlation coefficient u, the equation is as follows:
in the above formula, u is a correlation coefficient, ukFor the correlation of the residual with the kth column of the measurement matrixThe number of the first and second groups is,
is the kth column of the measurement matrix;
calculating a correlation coefficient u through an expression (1), searching index values corresponding to L maximum values from u, and storing the index values into AmPerforming the following steps;
step 5, recording the matrix corresponding to the m index value found
Updating a set of measurement matrices
Wherein phimFor m updated measurement matrices, phim-1The measurement matrix is updated m-1 times;
step 6, obtaining from least squares
Updating the mth residual rmAnd approximation of target signal x m
The formula is as follows:
in the above formula, the first and second carbon atoms are,
the mth approximation of the target signal x is carried out;
and 7, judging whether the new residual meets the conditions: if | rm‖2If the value is greater than epsilon, wherein epsilon is a threshold value, and m is equal to m +1, turning to the step 4;
if | rm‖2| < epsilon > and | < r >m‖2＞‖rm-1‖2Wherein r ism-1Residual error of m-1 time; then the step length is changed to s ═ s/2, and the support set A is formedmIs increased to L ═ L + s, and m ═ m +1, go to step 4;
if | rm‖2| < epsilon > and | < r >m‖2≤‖rm-1‖2(ii) a And stopping iteration, and performing final signal reconstruction by using the obtained atoms to obtain a denoised image.
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