Weighted t-Schatten-p Norm Minimization for Real Color Image Denoising

Min Liu,Lan Tang,Xinggan Zhang

doi:10.1109/access.2020.3016777

Min Liu, Lan Tang + Show 1 more

Open Access

https://doi.org/10.1109/access.2020.3016777

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Abstract

In this paper, to fully exploit the spatial and spectral correlation information, we present a new real color image denoising scheme using tensor Schatten-p norm (t-Schatten-p norm) minimization based on t-SVD to recover the underlying low-rank tensor. Similar to matrix Schatten-p norm, using non-convex t-Schatten-p (0 <; p <; 1) norm minimization could obtain better results than the tensor nuclear norm minimization which is a convex relaxation of the nonconvex tensor tubal rank. To avoid over-shrink the tensor tubal rank components, a flexible weighted t-Schatten-p norm model is proposed with weights assigned to different elements of tensor singular tubes. We adopt the generalized iterated shrinkage algorithm to solve the minimization problem efficiently. Extensive experiments on one synthetic and two realistic datasets demonstrate the effectiveness of our proposed method to remove noise both quantitatively and qualitatively.

Highlights

As a low-level image processing technique, image denoising is crucial to high-level computer vision tasks, for example, segmentation [32], [45], feature extraction, classification and so on
We treat a real color image as a third-order tensor with each color channel corresponding to a frontal slice, and introduce low tubal rank minimization to exploit the spatial and spectral information by utilizing the nonlocal self-similarity and DFT (Discrete Fourier Transformation) along the color channel of the image. we first search similar patches for each local patch to form the nonlocal patch group tensor (NPGT) Y
EXPERIMENTAL RESULTS we first evaluate the denoising performance of the proposed method on one synthetic and two public realistic image datasets, and we compare it with nine representative methods, including color blockmatching 3D filtering (CBM3D) [7], multi-channel weighted nuclear norm minimization (MCWNNM) [38], guided image denoisng (GID) [36], trilateral weighted sparse coding (TWSC) [37], multi-channel weighted Schatten-p norm minimization (MCWSNM) combining WSNM in [35] and MCWNNM in [38] for color images denoising, color multispectral tensor singular value decomposition (t-SVD) (CMSt-SVD) [18], denoising convolutional neural networks (DnCNN) [42], fast and flexible denoising network (FFDNet) [43] and weighted tensor nuclear norm minimization (WTNNM) [20]

Summary

INTRODUCTION

As a low-level image processing technique, image denoising is crucial to high-level computer vision tasks, for example, segmentation [32], [45], feature extraction, classification and so on. To recover low tubal rank tensor, the tensor nuclear norm (TNN) minimization has achieved competitive performance in [22], [44], since t-SVD based methods are better in exploiting the intrinsic structure and correlation information compared with the matricization operation of the Tucker model. We treat a real color image as a third-order tensor with each color channel corresponding to a frontal slice, and introduce low tubal rank minimization to exploit the spatial and spectral information by utilizing the nonlocal self-similarity and DFT (Discrete Fourier Transformation) along the color channel of the image. Our method employs the low tubal rank tensor prior to model the spatial nonlocal self-similarity and spectral correlation information of real color images.

NOTATIONS AND PRELIMINARIES

APPLYING T-Schatten-p NORM MINIMIZATION TO

EXPERIMENTAL RESULTS

EXPERIMENTAL RESULTS ON SYNTHETIC DATASET

CONCLUSION