Tensor nonconvex unified prior for tensor recovery

Abstract

Tensor data, such as hyperspectral images and multi-frame videos, have gained significant attention in practical applications. However, the inherent degradation phenomena during data acquisition, including noise and missing pixels, give rise to a series of ill-posed inverse problems that need to be addressed. Currently, the rational exploration of prior knowledge for tensor recovery, including global low-rankness and local smoothness, has emerged as a common concern. Inspired by recent notable works, this paper proposes a novel tensor non-convex unified prior term, which employs weighted tensor Schatten p-norm as a rank surrogate function in the gradient domain. The new prior can yield a regularizer that effectively captures low-rankness and smoothness, and is applied to tensor completion and tensor robust principal component analysis models. An efficient algorithm is developed by using the alternating direction method of multipliers and its convergence analysis is also provided. Extensive experimental results demonstrate that the proposed method outperforms the state-of-the-art methods, particularly in cases of high missing rates and strong noise levels.