Sample allocation for statistical multiresolution compressed sensing

We model the compressible signal with the two states Gaussian mixture distribution and consider the sample distortion function for the recently proposed Bayesian optimal AMP decoder. By leveraging the rigorous analysis of the AMP algorithm, we are able to derive the theoretical SD function and a sample allocation scheme for multi-resolution statistical image model. We then adopt the “turbo” message passing method to integrate the bandwise sample allocation with the exploitation of the hidden Markov tree structure of wavelet coefficients. Experiments on natural image show that the combination outperforms either of them working alone.