# A Survey on Compressive Sensing: Classical Results and Recent Advancements

## TL;DR

This survey reviews classical tools and recent advancements in compressive sensing, highlighting its core algorithms, recent progress, and practical performance comparisons, to aid understanding and further research in sparse signal recovery.

## Contribution

It provides a comprehensive overview of classical compressive sensing methods and recent developments, making the field more accessible and highlighting future research directions.

## Key findings

- Classical algorithms are effective for sparse signal recovery.
- Recent advancements improve performance and applicability.
- Numerical comparisons demonstrate practical effectiveness.

## Abstract

Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications. Compressive sensing is the topic that studies the associated raised questions for the possibility of a successful recovery. This topic is well-nourished and numerous results are available in the literature. However, their dispersity makes it challenging and time-consuming for readers and practitioners to quickly grasp its main ideas and classical algorithms, and further touch upon the recent advancements in this surging field. Besides, the sparsity notion has already demonstrated its effectiveness in many contemporary fields. Thus, these results are useful and inspiring for further investigation of related questions in these emerging fields from new perspectives. In this survey, we gather and overview vital classical tools and algorithms in compressive sensing and describe significant recent advancements. We conclude this survey by a numerical comparison of the performance of described approaches on an interesting application.