Orthogonal Tensor Recovery Based on Non-Convex Regularization and Rank Estimation

In this paper, a method for orthogonal tensor recovery based on non-convex regularization and rank estimation (OTRN-RE) is proposed, which aims to accurately recover the low-rank and sparse components of the tensor. Specifically, a new low-rank tensor decomposition algorithm is designed, which can efficiently establish the equivalence between the rank of a large tensor before decomposition and the rank of the coefficient tensor after decomposition. The large tensor is decomposed into a small standard orthogonal tensor and another coefficient tensor, and a generalized non-convex regularization is used to inscribe the low rank of the coefficient tensor. Meanwhile, a new rank estimation strategy is developed to dynamically adjust the size of small orthogonal tensors and coefficient tensors. Experimental results on image denoising and salient object detection tasks confirm the state-of-the-art performance of the proposed method in terms of denoising capability and computational speed.