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The low rank tensor completion (LRTC) problem has attracted great attentionin computer vision and signal processing. How to acquire high quality imagerecovery effect is still an urgent task to be solved at present. This paperproposes a new tensor $L_{2,1}$ norm minimization model (TLNM) that integratessum nuclear norm (SNN) method, differing from the classical tensor nuclear norm(TNN)-based tensor completion method, with $L_{2,1}$ norm and Qatar Riyaldecomposition for solving the LRTC problem. To improve the utilization rate ofthe local prior information of the image, a total variation (TV) regularizationterm is introduced, resulting in a new class of tensor $L_{2,1}$ normminimization with total variation model (TLNMTV). Both proposed models areconvex and therefore have global optimal solutions. Moreover, we adopt theAlternating Direction Multiplier Method (ADMM) to obtain the closed-formsolution of each variable, thus ensuring the feasibility of the algorithm.Numerical experiments show that the two proposed algorithms are convergent andoutperform compared methods. In particular, our method significantlyoutperforms the contrastive methods when the sampling rate of hyperspectralimages is 2.5\%.

Two New Low Rank Tensor Completion Methods Based on Sum Nuclear Norm