Noisy Low Rank Column-wise Sensing

TL;DR

This paper analyzes the AltGDmin algorithm for noisy low rank column-wise sensing, providing improved sample complexity guarantees and a comprehensive comparison of related work in the field.

Contribution

It offers the first improved sample complexity bounds for AltGDmin in LRCS and clarifies the relationships among various studies on the same problem.

Findings

Sample complexity improved by a factor of rac{rac{r, \, \, \\log(1/\\epsilon)}{r}

Provides detailed comparison of guarantees across related works

Enhances understanding of theoretical bounds in LRCS

Abstract

This letter studies the AltGDmin algorithm for solving the noisy low rank column-wise sensing (LRCS) problem. Our sample complexity guarantee improves upon the best existing one by a factor $\max(r, \log(1/\epsilon))/r$ where $r$ is the rank of the unknown matrix and $\epsilon$ is the final desired accuracy. A second contribution of this work is a detailed comparison of guarantees from all work that studies the exact same mathematical problem as LRCS, but refers to it by different names.