A survey on compressive sensing: classical results and recent advancements

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  time-consuming for  practitioners to quickly grasp its main ideas and classical algorithms, and further touch upon the recent advancements. In this survey, we overview vital classical  tools and algorithms in compressive sensing and describe its significant recent advancements. We conclude  by a numerical comparison of the performance of described approaches.