Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem - 2018


In this Project, we develop a Bayesian evidence maximization framework to unravel the sparse non-negative least squares (S-NNLS) problem. We tend to introduce a family of chance densities called the rectified Gaussian scale mixture (R-GSM) to model the sparsity imposing previous distribution for the answer. The R-GSM prior encompasses a selection of heavy-tailed densities like the rectified Laplacian and rectified Student's t-distributions with a proper choice of the blending density. We have a tendency to utilize the hierarchical illustration induced by the R-GSM previous and develop an proof maximization framework based mostly on the expectation-maximization (EM) algorithm. Using the EM based methodology, we estimate the hyper-parameters and acquire a purpose estimate for the answer. We confer with the proposed method as rectified sparse Bayesian learning (R-SBL). We tend to provide four R-SBL variants that provide a range of choices for computational complexity and the standard of the E-step computation. These strategies embrace the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing, and a diagonal approximation. Using numerical experiments, we have a tendency to show that the proposed R-SBL technique outperforms existing S-NNLS solvers in terms of each signal and support recovery performance, and is also terribly robust against the structure of the design matrix.

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