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Sparse representation of medical images via compressed sensing using Gaussian Scale Mixtures

The increased high-resolution capabilities of modern medical image acquisition systems raise the crucial tasks of effectively storing and interacting with large databases of such data. The ease of image storage and query would be unfeasible without compression, which represents high-resolution images with a relatively small set of significant transform coefficients. Due to the specific content of medical images, compression often results in highly sparse representations in appropriate orthonormal bases. The inherent property of compressed sensing (CS) working simultaneously as a sensing and compression protocol using a small subset of random projection coefficients, enables a potentially significant reduction in storage requirements. In this paper, we introduce a Bayesian CS approach for obtaining highly sparse representations of medical images based on a set of noisy CS measurements, where the prior belief that the vector of transform coefficients should be sparse is exploited by modeling its probability distribution by means of a Gaussian Scale Mixture. The experimental results show that the proposed approach maintains the reconstruction performance of other state-of-the-art CS methods while achieving significantly sparser representations of medical images with distinct content.