Abstract
Color images can be seen as third-order tensors with column, row and color modes. Considering two inherent characteristics of a color image including the non-local self-similarity (NSS) and the cross-channel correlation, we extract non-local similar patch groups from a color image and treat these groups as tensors with each color channel corresponding to the frontal slice of the tensor to exploit the information within and cross channel correlation. Inspired by recently proposed tensor-tensor product (t-product), t-SVD, tensor tubal rank and rigorously deduced tensor nuclear norm, a novel t-product based weighted tensor nuclear norm minimization (WTNNM) is proposed to model the extracted non-local similar patch group tensor (NPGT). Considering the NPGT is of low tubal rank, we formulate real color image denoising as a low tubal rank tensor recovery problem and solve it with the weighted tensor nuclear norm minimization. Experiments on both simulated and realistic noisy images verify the effectiveness of our method.
Highlights
Image denoising is a fundamental and classical problem in image processing and computer vision, aiming to acquire the underlying clean image from a noisy observation
Inspired by the proposed tensor-tensor product (t-product) in [21] and a new tensor nuclear norm deduced by Lu et al [25] and [26], we propose a new color image denoising method using t-product based weighted tensor nuclear norm minimization (WTNNM), which exploits non-local self-similarity and cross-channel correlation simultaneously
EXPERIMENTAL RESULTS we validate the effectiveness of the proposed t-product based WTNNM method on both simulated and realistic image datasets and compare it with CBM3D [11], TNRD [9], NC [23], [24], MCWNNM [33], GID [31], TWSC [32] both quantitatively and qualitatively
Summary
Image denoising is a fundamental and classical problem in image processing and computer vision, aiming to acquire the underlying clean image from a noisy observation. Gu et al assigned different weights to different singular values of the matrix to better recover the underlying low rank matrix from its noisy observation [17] When it comes to real color images (sRGB), there were generally three ways to deal with color image denoising. M. Liu et al.: Real Color Image Denoising Using t-Product-Based Weighted Tensor Nuclear Norm Minimization satisfactory performance [5]. Inspired by the proposed tensor-tensor product (t-product) in [21] and a new tensor nuclear norm deduced by Lu et al [25] and [26], we propose a new color image denoising method using t-product based weighted tensor nuclear norm minimization (WTNNM), which exploits non-local self-similarity and cross-channel correlation simultaneously. We propose a new model for real color image denoising using t-product based weighted tensor nuclear norm minimization.
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