Theory and Applications of Compressed Sensing

TL;DR

Compressed sensing is a groundbreaking field that enables the recovery of high-dimensional sparse signals from limited measurements using efficient algorithms, impacting multiple scientific disciplines.

Contribution

This paper provides an introductory survey of compressed sensing, highlighting its theoretical foundations and broad applications across applied mathematics, computer science, and electrical engineering.

Findings

Sparse signals can be recovered from incomplete measurements.

Efficient algorithms enable practical signal reconstruction.

Compressed sensing has diverse applications across fields.

Abstract

Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that high-dimensional signals, which allow a sparse representation by a suitable basis or, more generally, a frame, can be recovered from what was previously considered highly incomplete linear measurements by using efficient algorithms. This article shall serve as an introduction to and a survey about compressed sensing.