  The low rank tensor completion (LRTC) problem has attracted great attention
in computer vision and signal processing. How to acquire high quality image
recovery effect is still an urgent task to be solved at present. This paper
proposes a new tensor $L_{2,1}$ norm minimization model (TLNM) that integrates
sum nuclear norm (SNN) method, differing from the classical tensor nuclear norm
(TNN)-based tensor completion method, with $L_{2,1}$ norm and Qatar Riyal
decomposition for solving the LRTC problem. To improve the utilization rate of
the local prior information of the image, a total variation (TV) regularization
term is introduced, resulting in a new class of tensor $L_{2,1}$ norm
minimization with total variation model (TLNMTV). Both proposed models are
convex and therefore have global optimal solutions. Moreover, we adopt the
Alternating Direction Multiplier Method (ADMM) to obtain the closed-form
solution of each variable, thus ensuring the feasibility of the algorithm.
Numerical experiments show that the two proposed algorithms are convergent and
outperform compared methods. In particular, our method significantly
outperforms the contrastive methods when the sampling rate of hyperspectral
images is 2.5\%.
