Robust compressed sensing in Gaussian noise environment by resampling with replacement

A reconstruction method using the ensemble of compressed measurement signals is proposed for reconstructing the image from the signal corrupted by Gaussian noise. The ensemble is created from one signal under the assumption that an image is highly redundant; hence, it is approximated as the mixture of a number of signals. The proposed method adopted the sampling with replacement in bootstrapping to extract L signals from the mixture. The extracted L signals from the ensemble of signals corrupted by Gaussian noise with the same mean and variance. The signals have different bases; thus, they he in different space. Orthogonal Matching Pursuit with Partially Known Support (OMP-PKS) is applied to reconstruct the L signals to the same sparse space. Gaussian noise is reduced by averaging the reconstructed signals. The performance of the proposed method was compared with Basis Pursuit Denoising (BPDN), OMP-PKS and Distributed Compressed Sensing using Simultaneously Orthogonal Matching Pursuit (DCS-SOMP). The experimental results of 10 standard test images showed that our method yielded higher Peak Signal-to-Noise Ratio (PSNR) and better visual quality at a high level of noise.