Expectation maximization hard thresholding methods for sparse signal reconstruction

摘要: Reconstructing a high dimensional sparse signal from low linear measurements has been an important problem in various research disciplines including statistics, machining learning, data mining and processing. In this dissertation, we develop probabilistic framework for reconstruction propose several novel algorithms computing the maximum likelihood (ML) estimates under framework. We first consider underdetermined model where regression-coefficient vector is sum of unknown deterministic component zero-mean white Gaussian with variance. Our schemes are based on expectation-conditional maximization either (ECME) iteration that aims at maximizing function respect to parameters given sparsity level. double overrelaxation (DORE) thresholding scheme accelerating ECME prove that, certain conditions, DORE iterations converge local maxima achieve near-optimal or perfect recovery approximately signals, respectively. If level unknown, introduce unconstrained selection (USS) criterion tuning-free automatic (ADORE) method employs USS estimate applications such as tomographic imaging, interest nonnegative. modify our algorithm incorporate additional nonnegativity constraint. The step modified approximated by difference map iteration. compare proposed existing methods using simulated real-data imaging experiments. Finally, generalized expectation-maximization (GEM)