Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm

Abstract

In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal multi-rank. We build two PSTNN-based minimization models for two typical tensor recovery problems, i.e., the tensor completion and the tensor principal component analysis. We give two algorithms based on the alternating direction method of multipliers (ADMM) to solve proposed PSTNN-based tensor recovery models. Experimental results on the synthetic data and real-world data reveal the superior of the proposed PSTNN.

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• Enhanced nonconvex low-rank approximation of tensor multi-modes for tensor completion
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• Multi-mode Core Tensor Factorization based Low-Rankness and Its Applications to Tensor Completion
• Quaternion tensor low rank Quaternion tensor low-rank approximation using a family of non-convex norms
• Non-convex approaches for low-rank tensor completion under tubal sampling
• Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recovery