Compressed Sensing of Lena Image using Hadamard Measurement Matrix and OMP Reconstruction Algorithm

This article demonstrates how to implement compressed sensing for the Lena image using a Hadamard measurement matrix. The method significantly reduces data volume while maintaining image quality through sparse signal representation. The OMP reconstruction algorithm effectively recovers the original image with minimal information loss by iteratively selecting the most correlated atoms from the measurement matrix. We provide detailed explanations of both the Hadamard measurement matrix (a deterministic matrix with orthogonal properties ideal for hardware implementation) and the OMP algorithm (a greedy pursuit method that solves sparse approximation problems through residual minimization). The implementation includes code segments showing: - How to generate the Hadamard measurement matrix using Walsh-Hadamard transform functions - The OMP algorithm workflow with key steps: residual calculation, atom selection, and least-squares solution updates - Parameter tuning for sparsity levels and measurement rates The evaluation section covers performance metrics including PSNR calculations and visual quality assessment. We discuss advantages like computational efficiency and hardware-friendly measurements, while addressing limitations such as noise sensitivity. Practical implementation considerations include memory optimization for large-scale images and real-time application adaptations. The complete MATLAB/Python code structure demonstrates: 1. Image preprocessing and vectorization 2. Measurement matrix initialization and normalization 3. Sparse coefficient recovery using OMP with termination conditions 4. Image reconstruction from recovered coefficients 5. Quantitative and qualitative result analysis