Robust Low Transformed Multi-Rank Tensor Completion With Deep Prior Regularization for Multi-Dimensional Image Recovery

Abstract

In this paper, we study the robust tensor completion problem in three-dimensional image data, where only partial entries are available and the observed tensor is corrupted by Gaussian noise and sparse noise simultaneously. Compared with the existing tensor nuclear norm minimization for the low-rank component, we propose to use the transformed tensor nuclear norm to explore the global low-rankness of the underlying tensor. Moreover, the plug-and-play (PnP) deep prior denoiser is incorporated to preserve the local details of multi-dimensional images. Besides, the tensor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> norm is utilized to characterize the sparseness of the sparse noise. A symmetric Gauss-Seidel based alternating direction method of multipliers is designed to solve the resulting model under the PnP framework with deep prior denoiser. Extensive numerical experiments on hyperspectral and multispectral images, videos, color images, and magnetic resonance image datasets are conducted to demonstrate the superior performance of the proposed model in comparison with several state-of-the-art models.