Convex recovery of tensors using nuclear norm penalization

TL;DR

This paper extends matrix convex recovery techniques to tensors, proposing a nuclear norm penalization approach for low-rank tensor recovery from linear measurements, with potential applications in signal processing and statistics.

Contribution

It introduces a convex optimization framework for tensor recovery based on nuclear norm penalization, extending existing matrix results to tensors.

Findings

Theoretical extension of nuclear norm methods to tensors.

Analysis of recovery guarantees for low-rank tensors.

Potential applications demonstrated in signal processing and statistics.

Abstract

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining much interest due to its potential applications to signal processing, statistics and engineering. The goal of this paper is to present an applications to the problem of low rank tensor recovery based on linear random measurement by extending the results of Tropp to the tensors setting.