Survey on compressed sensing over the past two decades

Abstract

Compressed Sensing (CS) is a novel data acquisition theorem exploiting the signals sparsity differing from traditional Nyquist theorem in the ability of obtaining all information of such signal in fewer samples. CS can enable full use of sparsity, where the sparse signal can be reconstructed using fewer measurements. Over the past decade, several papers have investigated the feasibility of deploying CS in current applications. A lot of developments are performed in this area in order to enhance the performance and re-usability. The CS algorithm involves many phases at the transmitter side, including: transformation, compression, encoding, encryption, and modulation. Meanwhile the receiver involves: demodulation, decryption, decoding, and reconstruction. This work assembles most of the published papers in the CS area, listing the important details and showing their contributions. Each building block of the CS system is studied solely and compared with its reference in the literature. A comparative study is performed reviewing the work in the literature with respect to compression metrics, deployed reconstruction algorithm, system complexity. Tabulated results are studied with respect to hardware and memory computation complexity. Recommendations and conclusions are illustrated at the end of our work.

Keywords

• Compressed Sensing (CS)
• Measurement matrix
• Mutual coherence
• Restricted isometry property