Abstract
Traditional image denoising algorithms obtain prior information from noisy images that are directly based on low rank matrix restoration, which pays little attention to the nonlocal self-similarity errors between clear images and noisy images. This paper proposes a new image denoising algorithm based on low rank matrix restoration in order to solve this problem. The proposed algorithm introduces the non-local self-similarity error between the clear image and noisy image into the weighted Schatten p-norm minimization model using the non-local self-similarity of the image. In addition, the low rank error is constrained by using Schatten p-norm to obtain a better low rank matrix in order to improve the performance of the image denoising algorithm. The results demonstrate that, on the classic data set, when comparing with block matching 3D filtering (BM3D), weighted nuclear norm minimization (WNNM), weighted Schatten p-norm minimization (WSNM), and FFDNet, the proposed algorithm achieves a higher peak signal-to-noise ratio, better denoising effect, and visual effects with improved robustness and generalization.
Highlights
In the past few decades, many effective image prior knowledge models have been developed, such as regularization methods that are based on total variation [3,4,5], sparse representation [6,7], low rank representation [8,9], nonlocal self-similarity [10,11], and deep learning [12], et al Recently, the image prior method based on nonlocal self-similarity [13,14] and low rank matrix approximating [15,16,17,18] can better preserve image edge details while denoising, which has achieved some success in image denoising [19,20]
In order to test the performance of the proposed weighted Schatten p-norm low rank error constraint (WSNLEC) in image denoising, we compare it with four representative algorithms: block matching three-dimensional (3D)
The peak signal-to-noise ratio (PSNR) values of WSNLEC are higher than other comparison algorithms at almost all noise levels, and the average PSNR
Summary
The purpose of image denoising is to restore a clean image X from the noise observation Y as accurately as possible while maintaining important detailed features (such as edges and textures). Image denoising is a typical ill-posed problem in mathematics, which can be solved using prior knowledge of an image [2]. In the past few decades, many effective image prior knowledge models have been developed, such as regularization methods that are based on total variation [3,4,5], sparse representation [6,7], low rank representation [8,9], nonlocal self-similarity [10,11], and deep learning [12], et al
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