Bayesian Compressed Sensing Imaging using a Gaussian Scale Mixture

The ease of image storage and transmission in modern applications would be unfeasible without compression, which converts highresolution images into a relatively small set of significant transform coefficients. Due to the specific content of many real-world images they are highly sparse in an appropriate orthonormal basis. The inherent property of compressed sensing (CS) theory working simultaneously as a sensing and compression protocol, using a small subset of random incoherent projection coefficients, enables a potentially significant reduction in the sampling and computation costs of images favoring its use in real-time applications which do not require an excellent reconstruction performance. In this paper, we develop a Bayesian CS (BCS) approach for obtaining highly sparse representations of images based on a set of noisy CS measurements, where the prior belief that the vector of projection coefficients should be sparse is enforced by fitting directly its prior probability distribution by means of a Gaussian Scale Mixture (GSM). The experimental results show that our proposed method, when compared with norm-based constrained optimization algorithms, maintains the reconstruction performance, in terms of the reconstruction error and the PSNR, while achieving an increased sparsity using much less basis functions. 1