Shrinkage Function And Its Applications In Matrix Approximation

TL;DR

This paper provides an elementary derivation of the shrinkage function and demonstrates its applications in matrix approximation, compressive sensing, and statistical estimation, including a new result in matrix approximation.

Contribution

It introduces a simple derivation of the shrinkage function and applies it to various problems, offering a novel result in matrix approximation.

Findings

Elementary derivation of the shrinkage function

Applications in matrix approximation and compressive sensing

New result in matrix approximation

Abstract

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are demonstrated in solving several well-known problems, together with a new result in matrix approximation.