Wavelet_OMP Compressive Sensing Algorithm

This document presents the Wavelet_OMP compressive sensing technique, which combines wavelet transformation with orthogonal matching pursuit for efficient signal compression. In implementation, the algorithm first applies wavelet decomposition (using functions like wavedec() in MATLAB) to break down signals into sparse wavelet components. The OMP algorithm then iteratively selects the most correlated wavelet coefficients through correlation calculations and least squares optimization, typically implemented via orthogonal projection matrices. This approach achieves significant data compression while preserving signal quality by leveraging sparse representations in wavelet domains. Key implementation considerations include setting appropriate sparsity constraints and termination criteria for the OMP iteration loop. Compressive sensing applications span image compression (handling 2D wavelet transforms), speech processing, and medical imaging systems where reduced storage and transmission bandwidth are critical. The Wavelet_OMP method represents a fundamental approach in modern signal processing worthy of comprehensive study.