Compressed sensing using a Gaussian Scale Mixtures model in wavelet domain

Abstract

Compressed Sensing (CS) theory has gained attention recently as an alternative to the current paradigm of sampling followed by compression. Early CS recovery techniques operated under the implicit assumption that the transform coefficients in the sparsity domain are independently distributed. Recent works, however, demonstrated that exploiting the statistical dependencies between transform coefficients can further improve the recovery performance of CS. In this paper, we propose the use of a Gaussian Scale Mixtures (GSM) model in CS. This model can efficiently exploit the statistical dependencies between wavelet coefficients during CS recovery. The proposed model is incorporated into several recent CS techniques including Reweighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization (RL1), Iteratively Reweighted Least Squares (IRLS), and Iterative Hard Thresholding (IHT). Experimental results show that the proposed method improves reconstruction quality for a given number of measurements or requires fewer measurements for a desired reconstruction quality.