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

TL;DR

This paper introduces the partial sum of the tubal nuclear norm (PSTNN) within the tensor SVD framework, offering improved tensor recovery methods for completion and PCA with demonstrated superior performance.

Contribution

The paper proposes PSTNN as a new tensor rank surrogate and develops ADMM algorithms for tensor recovery, advancing tensor completion and PCA techniques.

Findings

PSTNN outperforms existing tensor norms in recovery tasks.

The proposed methods are effective on both synthetic and real-world data.

Experimental results show superior recovery accuracy.

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.