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

## TL;DR

This paper extends the GAMP algorithm to handle non-i.i.d. sparse signals by introducing non-uniform priors, enabling more flexible and accurate compressed sensing of structured signals.

## Contribution

It introduces new sparse signal priors for GAMP that support non-i.i.d. signals, advancing model-based compressed sensing capabilities.

## Key findings

- Supports non-i.i.d. sparse signal reconstruction
- Enables model-based compressed sensing with GAMP
- Improves flexibility over traditional i.i.d. assumptions

## Abstract

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.