MATLAB Implementation of Image Compressive Sensing with FFT/DWT Sparsity Bases and OMP Reconstruction

This article presents an image compressive sensing methodology implemented in MATLAB. The approach employs two distinct sparsity bases: FFT (Fast Fourier Transform) and DWT (Discrete Wavelet Transform). In implementation, FFT constructs an orthogonal transformation matrix for signal representation, while DWT specifically targets high-frequency coefficient measurements to capture essential image features. The reconstruction process utilizes the Orthogonal Matching Pursuit (OMP) algorithm, which iteratively selects the most correlated atoms from the measurement matrix to approximate the original signal. The core principle involves balancing image quality preservation with significant size reduction during compression. Through strategic use of sparsity bases and the OMP reconstruction algorithm, this method maintains high-quality visual output while achieving substantial compression ratios. The implementation typically involves: - Constructing measurement matrices using FFT orthonormal bases or DWT thresholding operations - Applying sparse sampling techniques to capture essential image information - Implementing OMP algorithm with stopping criteria based on residual thresholds or sparsity levels This approach proves particularly valuable for applications requiring efficient transmission of large image datasets, such as medical imaging systems, satellite communication, and real-time video streaming platforms, where bandwidth optimization without quality degradation is critical. The MATLAB implementation would involve key functions like fft2() for Fourier transforms, wavedec2() for wavelet decomposition, and custom OMP optimization routines using matrix operations and greedy atom selection.