Comparison of compressed sensing based algorithms for sparse signal reconstruction

Compressed sensing theory shows that any signal which is defined as sparse in a given domain can be reconstructed using fewer linear projections instead of using all Nyquist-rate samples. In this paper, we investigate basis pursuit, matching pursuit, orthogonal matching pursuit and compressive sampling matching pursuit algorithms, which are basic compressed sensing based algorithms, and present performance curves in terms of mean squared error for various parameters including signal-to-noise ratio, sparsity and number of measurements with regard to mean squared error. In addition, accuracy of estimation performances has been supported with theoretical lower bounds (Cramer-Rao lower bound and deterministic lower mean squared error). Considering estimation performances, compressive sampling matching pursuit yields the best results unless the signal has a non-sparse structure.