Wavelet Transform-Based Compressed Sensing Image Processing with Three Reconstruction Algorithms

This paper explores wavelet transform-based compressed sensing image processing and three reconstruction algorithms. Compressed sensing is a technique that reduces storage requirements while maintaining image quality through sparse signal representation. Wavelet transforms serve as mathematical tools that decompose signals or images into basis functions for enhanced analysis and processing. We detail three reconstruction algorithms that recover original images from wavelet coefficients: 1) L1-minimization using linear programming approaches 2) Iterative thresholding algorithms with convergence optimization 3) Greedy pursuit methods like Orthogonal Matching Pursuit (OMP) Each algorithm implementation typically involves matrix operations for sparse recovery, where key functions include wavelet decomposition (using libraries like PyWavelets or MATLAB's wavedec2), measurement matrix generation, and optimization solvers. Through code examples, we demonstrate how these methods balance reconstruction accuracy against computational complexity, enabling practitioners to select appropriate approaches based on application requirements. Readers will gain comprehensive understanding of wavelet-based compressed sensing framework and its practical implementation through algorithmic comparisons and performance metrics.