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An image and image matrix technology, applied in the field of image denoising, can solve the problems affecting the accuracy, sparseness, and unstable solutions of image restoration, and achieve the effects of improving accuracy, enhancing stability, and avoiding too sparse
Active Publication Date: 2018-12-21
NANJING UNIV OF POSTS & TELECOMM
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[0004] However, in the current low-rank image denoising method based on sparse representation, the most commonly used method is to use the kernel norm of the matrix instead of the ran...
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Embodiment 1
[0060] Such as figure 1 with image 3 As shown, the present invention provides a method for denoising a low-rank image, comprising the steps of:
[0061] 1) Input an image D containing noise;
[0062] 2) Firstly, the matrix D∈R to be restored m×n Perform singular value decomposition Get his left singular vector U=(u 1 , u 2 ,...,u m )∈R m×m , right singular vector V=(v 1 ,v 2 ,...,v m )∈R n×n and the singular value Σ r =diag(σ 1 ,σ 2 ,...,σ r );
[0063] 3) According to the definition of truncated nuclear norm Arrange the singular values from small to large, remove the largest r-t singular values, and take the left singular vector F=(u 1 , u 2 ,...,u t ) T and right singular vector G=(v 1 ,v 2 ,...,v t ) T ;
[0064] 4) According to the objective function and constraints, an image denoising model based on truncated kernel norm and Frobenius norm is established,
[0065]
[0066] Where A represents the original image; E represents noise, ||E|| ...
Embodiment 2
[0099] Such as figure 2 Shown, (a) is original image, and (b) is the noise-containing image of original image, utilizes NNR, NNF, TNNR and the method for embodiment 1 to carry out denoising process to noise-containing image (b) respectively, four kinds of methods The PSNRs are 25.3, 26.1, 27.5, and 28.4 respectively, and the denoised images (c), (d), (e) and (f) are obtained respectively. According to the comparison, the image (f) obtained by the method of Example 1 The closest to the original image (a), the best denoising effect.
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Abstract
The invention discloses a denoising method of a low-rank image, which is applied to the reconstruction of an image containing noise. By analyzing the correlation characteristics of the low-rank matrix, the denoising problem of the image is modeled as a non-linear constraint problem, and then the specific iterative steps are deduced by using an alternating direction multiplier method, thereby obtaining the image after denoising. The invention uses the truncated kernel norm to more accurately approximate the rank of the matrix and avoids the result deviation caused by the large singular value. In addition, the Frobenius norm is added to the model as a regular term, the Frobenius norm and the truncated kernel norm form an elastic network about the singular value, so that the final result is sparse and stable, so that better denoising effect can be achieved.
Description
technical field [0001] The invention belongs to the technical field of image denoising, and in particular relates to a low-rank image denoising method. Background technique [0002] Image is an important source of information, and image processing can help people understand the connotation of information. However, images are often disturbed and affected by various noises during the process of image generation and transmission, which degrades the image quality, which will have an adverse effect on subsequent image processing (such as segmentation, compression, and image understanding, etc.). There are many types of noise, such as: electrical noise, mechanical noise, channel noise and other noises. In order to suppress noise, improve image quality, and facilitate higher-level processing, image denoising preprocessing must be performed. [0003] After several years of research, there are many image denoising algorithms, but they cannot fully meet the growing application requi...
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