Strongly Convex Programming for Principal Component Pursuit

TL;DR

This paper investigates strongly convex optimization methods for principal component pursuit, enabling exact recovery of low-rank and sparse matrices from limited measurements, with guidelines for parameter selection.

Contribution

It provides theoretical conditions for exact recovery using strongly convex programming and practical advice on parameter tuning.

Findings

Sufficient conditions for exact recovery established

Guidelines for parameter selection in algorithms provided

Effective recovery from reduced measurements demonstrated

Abstract

In this paper, we address strongly convex programming for princi- pal component pursuit with reduced linear measurements, which decomposes a superposition of a low-rank matrix and a sparse matrix from a small set of linear measurements. We first provide sufficient conditions under which the strongly convex models lead to the exact low-rank and sparse matrix recov- ery; Second, we also give suggestions on how to choose suitable parameters in practical algorithms.