Typical Compressed Sensing Program Simulation with Wavelet Basis and OMP Reconstruction

This paper explores the implementation of a typical compressed sensing program simulation. The methodology employs wavelet basis functions for signal sparsification and Orthogonal Matching Pursuit (OMP) algorithm for signal reconstruction. The core implementation involves transforming signals into sparse representations using discrete wavelet transforms (e.g., MATLAB's wavedec function) and reconstructing them through OMP's iterative optimization process that sequentially selects the most correlated atoms from the measurement matrix. This approach enables significant reduction in data volume while preserving critical information, substantially minimizing storage and transmission requirements. Furthermore, we investigate scenario-specific optimizations through parameter tuning of sparsity levels and iteration counts to enhance performance. The advantages (e.g., computational efficiency with O(nk²) complexity) and limitations (e.g., sensitivity to measurement matrix coherence) of this methodology are thoroughly analyzed. This work aims to provide valuable reference for compressed sensing research, demonstrating practical implementation through MATLAB-based simulations with wavelet decomposition thresholds and greedy pursuit mechanisms.