Compressive Sensing: Wavelet-Based Sparsification with OMP Algorithm for Reconstruction and Recovery

This article introduces an emerging discipline—compressive sensing. Compressive sensing represents a signal processing methodology that enables signal compression and reconstruction without compromising signal quality. Within compressive sensing frameworks, wavelet sparsification serves as a fundamental technique that transforms signals into sets of sparse coefficients. The Orthogonal Matching Pursuit (OMP) algorithm functions as a crucial reconstruction algorithm that recovers original signals from these sparse coefficients through iterative greedy selection of the most correlated basis vectors. This methodology finds broad applications across signal processing, image processing, speech recognition, and related domains, garnering significant attention in both academic research and industrial applications. Notably, the classic simplified framework provided by Hong Kong University's Sha Wei offers exceptional reference material and an accessible entry point for beginners studying compressive sensing, demonstrating practical implementation through clear algorithmic steps and coefficient thresholding mechanisms.