Image Processing with Compressive Sensing

In modern digital image processing, compressive sensing-based techniques have emerged as a prominent research area. This methodology primarily achieves image compression and reconstruction through sparsifying transformations of image signals. Key sparsification approaches include 2D Discrete Cosine Transform (DCT), Fast Fourier Transform (FFT), and 1D Discrete Wavelet Transform (DWT). Following sparsification, the Orthogonal Matching Pursuit (OMP) algorithm is widely implemented for reconstruction, enabling efficient and accurate image recovery. The OMP algorithm operates iteratively by selecting the most correlated atoms from the measurement matrix and solving least-squares problems to approximate sparse coefficients. When implementing compressive sensing for image processing, comprehensive investigation and comparative analysis of different sparsification methods and reconstruction algorithms are essential to identify optimal processing strategies. Code implementation typically involves preprocessing steps like image blocking, transformation matrix generation, and parameter optimization for reconstruction quality metrics.