MATLAB-Based Compressed Sensing Video Coding Implementation with DCVS Framework

This MATLAB-based compressed sensing video coding program implements a Distributed Compressed Video Sensing (DCVS) framework. The implementation employs Binary Walsh-Hadamard Transform (BWHT) as the sparse basis matrix and utilizes Gradient Projection for Sparse Reconstruction (GPSR) algorithm for signal recovery, achieving high-quality video compression and reconstruction at significantly reduced sampling rates. Compressed sensing technology enables original signal recovery through optimization algorithms at sampling rates far below Nyquist theorem requirements. In video coding applications, this approach is particularly effective for handling highly redundant video data, substantially reducing storage and transmission overhead. The program's selection of BWHT matrix as the sparse basis leverages its excellent orthogonality properties and computational efficiency, which is implemented through fast Hadamard transform operations requiring only O(n log n) computations for effective signal sparsification. The reconstruction phase incorporates GPSR algorithm, a gradient projection-based optimization method specifically designed for large-scale sparse signal recovery problems. The MATLAB implementation uses iterative thresholding and projection operations to solve the l1-minimization problem, balancing reconstruction quality with computational complexity. Key functions include gradient descent steps with Barzilai-Borwein line search and efficient handling of non-negativity constraints through projection onto the non-negative orthant. The program architecture focuses on optimizing the trade-off between compression ratio and reconstruction fidelity while maintaining practical computational requirements for potential real-time applications. The implementation includes separate modules for video frame preprocessing, compressive measurements acquisition using random sampling matrices, and iterative reconstruction with convergence monitoring. This implementation demonstrates the significant potential of compressed sensing in video coding applications, particularly in resource-constrained environments such as wireless video surveillance systems and mobile video transmission platforms, where it can substantially reduce bandwidth requirements while maintaining acceptable visual quality.