Image Denoising Based on Compressed Sensing

This article explores image denoising techniques utilizing compressed sensing methodology, applicable to various dimensional data including 2D images and higher-dimensional data such as 3D volumetric and 4D spatiotemporal images. The implementation typically involves sparse transformation using wavelets or discrete cosine transform (DCT) to represent images in sparse domains, followed by optimization algorithms like L1-minimization or iterative thresholding to reconstruct clean signals from noisy measurements. The compressed sensing framework enables effective noise removal while preserving critical image details through signal reconstruction from incomplete measurements. Key computational components include measurement matrix design using random sampling and reconstruction algorithms such as basis pursuit or matching pursuit. This methodology finds extensive applications across fields including medical imaging (MRI/CT reconstruction), wireless communications (signal recovery), and security surveillance systems, significantly enhancing image quality and interpretability through efficient sparse signal recovery mechanisms.