Block compressive sensing-based image denoising framework using optimized sensing matrix and split Bregman algorithm

Compressive Sensing (CS) has revolutionized signal and image acquisition by enabling high-fidelity reconstruction with significantly fewer measurements. This advantage makes CS invaluable for applications where data collection is expensive or time-intensive, such as medical imaging and remote sensing. However, the presence of noise and the improper selection of sensing matrices can severely degrade reconstruction quality, leading to artifacts and loss of fine structural details. To overcome these challenges, we propose a novel three-stage Block Compressive Sensing-Based Image Denoising Framework that enhances reconstruction accuracy while effectively suppressing noise. In the first stage, the Discrete Wavelet Transform (DWT) is applied to image blocks, and the resulting coefficient matrices are reordered using zigzag scanning, ensuring an efficient compression ratio by prioritizing low-frequency components. The second stage employs an optimized sensing matrix within each block to maximize the quality of compressed measurements, mitigating information loss. Finally, the Split Bregman algorithm is integrated to remove residual noise and enhance image clarity. We validate our framework through extensive experiments on natural and medical images, evaluating performance at sampling ratios of 20% - 50% and Signal-to-Noise Ratios (SNRs) from 10 dB to 25 dB. The results consistently demonstrate superior denoising and reconstruction performance, as reflected in Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Root Mean Square Error (RMSE).