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 measurement model.
By leveraging prior information about the observed signal, such as sparsity in a known dictionary, GAMP enables reconstructing 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.
We present sparse signal priors to estimate non-identically distributed signals through a non-uniform weighting, e.g. enabling model-based compressed sensing with GAMP.