When recovering a sparse signal from noisy compressive linear measurements, the
distribution of the signal's non-zero coefficients can have a profound effect on recovery
mean-squared error (MSE). If this distribution was a priori known, then one could use
computationally efficient approximate message passing (AMP) techniques for nearly
minimum MSE (MMSE) recovery. In practice, however, the distribution is unknown,
motivating the use of robust algorithms like LASSO-which is nearly minimax optimal-at the …

… Expectation-Maximization We use expectation-maximization (EM) to learn the signal and
noise prior parameters q … The following shows the Gaussian-mixture pdf learned by EM-GM-GAMP
when the true active-signal pdf was uniform (left) and ±1 (right): …