MATLAB Implementation of Pseudo-Random Sampling for Compressive Sensing

This research presents a compressive sensing framework using pseudo-random sampling methodology for image acquisition. The implementation involves applying the 9/7 wavelet transform followed by iterative shrinkage thresholding algorithms to achieve effective signal compression and reconstruction. The MATLAB code employs pseudo-random measurement matrices that satisfy restricted isometry property (RIP) conditions, while the reconstruction algorithm utilizes soft-thresholding operations in the wavelet domain through iterative optimization. Experimental results demonstrate that this approach achieves superior reconstruction quality with computational efficiency. The method's simplicity stems from its straightforward implementation of wavelet decomposition and thresholding iterations, typically requiring only 20-50 iterations for convergence. Future research directions include comprehensive performance analysis comparing this method with other compressive sensing techniques and exploring applications in medical imaging, remote sensing, and signal processing domains. Key implementation aspects involve proper selection of shrinkage parameters and optimization of the random sampling matrix to maximize reconstruction accuracy.