MATLAB Compressive Sensing Reconstruction Algorithm Implementations

This documentation presents a collection of MATLAB implementations for compressive sensing reconstruction algorithms. The codebase includes several key algorithm categories: greedy pursuit methods such as Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), and Subspace Pursuit (SP); convex optimization approaches including Basis Pursuit (BP) and Linear Programming (LP) formulations; and iterative hard thresholding algorithms like Iterative Hard Thresholding (IHT), Total Variation minimization with quadratic constraints (TVq), and its constrained variant TVqc. These algorithms are widely applied in computer science and engineering, particularly in the field of compressive sensing where they enable efficient processing of large datasets. Each implementation includes optimized MATLAB code with appropriate parameter tuning and algorithm-specific optimizations. For instance, the OMP implementation features efficient matrix operations using QR decomposition for orthogonal projection, while the BP algorithm utilizes linear programming solvers with proper constraint handling. To evaluate algorithm performance, we provide a standardized testing framework using image data. The evaluation process involves measuring reconstruction quality through metrics like PSNR and SSIM, comparing computational efficiency, and analyzing convergence behavior across different sparsity levels. This image-based verification approach demonstrates how each algorithm performs with various data types and noise conditions, helping users select appropriate methods for specific applications. Through understanding these algorithm implementations and their MATLAB code structures, researchers and engineers can effectively apply them to solve practical problems in signal processing, image reconstruction, and data compression, thereby improving workflow efficiency and solution quality. The code includes detailed comments explaining key computational steps, parameter selection guidelines, and performance optimization techniques.