Generalised Approximate Message Passing for Non-I.I.D. Sparse Signals

Generalised approximate message passing (GAMP) is an approximate Bayesian estimation algorithm for signals observed through a linear transform with a possibly non-linear subsequent measurement model. By leveraging prior information about the observed signal, such as sparsity in a known dictionary, GAMP can for example reconstruct signals from under-determined measurements -- known as compressed sensing. In the sparse signal setting, most existing signal priors for GAMP assume the input signal to have i.i.d. entries. Here we present sparse signal priors for GAMP to estimate non-i.d.d. signals through a non-uniform weighting of the input prior, for example allowing GAMP to support model-based compressed sensing.