signal reconstruction

Multi-layer generalized linear estimation

We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP) algorithm for …

Inferring sparsity: Compressed sensing using generalized restricted Boltzmann machines

In this work, we consider compressed sensing reconstruction from M measurements of K-sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine, can be …

Non-adaptive pooling strategies for detection of rare faulty items

We study non-adaptive pooling strategies for detection of rare faulty items. Given a binary sparse N dimensional signal x, how to construct a sparse binary M × N pooling matrix F such that the signal can be reconstructed from the smallest possible …

Compressed sensing under matrix uncertainty: Optimum thresholds and robust approximate message passing

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a situation …

Compressed sensing of approximately-sparse signals: Phase transitions and optimal reconstruction

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only “approximately sparse”, i.e. even though the signal contains only a small fraction of relevant (large) components the …