Simulation Algorithm for Compressed Sensing

This document presents a compressed sensing simulation algorithm employing the SOMP (Simultaneous Orthogonal Matching Pursuit) recovery technique. Compressed sensing is a signal processing methodology that enables signal compression during sampling, thereby reducing storage and transmission costs. The implementation structure typically involves three key stages: sparse signal representation using appropriate bases (e.g., discrete cosine transform or wavelet transforms), measurement acquisition through random projection matrices (often implemented via Gaussian or Bernoulli matrices), and signal reconstruction using specialized algorithms. The SOMP recovery algorithm operates on the principle of sparse signal recovery, enabling reconstruction of complete signals from limited measurements through iterative orthogonal projection. Its core functionality includes atom selection from a dictionary matrix, residual updating, and simultaneous processing of multiple signal vectors. This algorithm demonstrates particular efficiency in handling multi-signal scenarios where common sparse support is assumed across measurements. Key advantages of this approach include computational efficiency, high reconstruction accuracy, and robustness to noise. The algorithm's implementation typically involves matrix operations for projection calculations and iterative loops for support set identification. Due to these characteristics, this compressed sensing simulation algorithm has gained extensive application and research attention across various domains including image processing, video coding, and wireless communications systems.