Density evolution of sparse source signals

A sequential Bayesian approach to density evolution for sparse source reconstruction is proposed and analysed which alternatingly solves a generalized LASSO problem and its dual. Waves are observed by a sensor array. The waves are emitted by a spatially-sparse set of sources. A weighted Laplace-like prior is assumed for the sources such that the maximum a posteriori source estimate at the current time step is the solution to a generalized LASSO problem. The posterior Laplace-like density at step k is approximated by the corresponding dual solution. The posterior density at step k leads to the prior density at k+1 by applying a motion model. Thus, a sequence of generalized LASSO problems is solved for estimating the temporal evolution of a sparse source field.