Rectified Sparse Bayesian Learning
The goal of this work is to solve the sparse non-negative least squares problem
$$ \text{argmin} \Vert y - \Phi x \Vert_2^2 \; \; \text{subject to} \; \; x \geq 0, \Vert x \Vert_0 \leq L $$
We extend the Sparse Bayesian Learning (SBL) framework used in Bayesian sparse signal recovery to non-negative signals. We investigate rectified Gaussian (RG) scale mixtures as a viable sparsity enforicing prior and develop efficient inference techniques.