Compressive Sensing Image Reconstruction Algorithm

This text introduces a custom compressive sensing image reconstruction algorithm designed for educational purposes. The algorithm operates through three distinct phases. First, it performs sparsification processing using transform domains (such as wavelet or DCT transforms) to reduce data dimensionality while preserving essential image information. Second, the algorithm handles observation coefficients through random measurement matrices (typically Gaussian or Bernoulli matrices) to capture compressed representations of the sparse signals. Finally, reconstruction is achieved using optimization methods like L1-norm minimization (implemented through basis pursuit or iterative thresholding algorithms) to recover the original image from the compressed measurements. This approach is particularly valuable for learning image processing fundamentals, as it demonstrates complete workflow from data compression to reconstruction while illustrating key concepts in sparse signal recovery. For those interested in computational imaging, this algorithm provides practical insights into implementing compressive sensing frameworks with proper mathematical foundations and coding techniques.