least mean squares methods

Performance Limits for Noisy Multimeasurement Vector Problems

Compressed sensing (CS) demonstrates that sparse signals can be estimated from underdetermined linear systems. Distributed CS (DCS) further reduces the number of measurements by considering joint sparsity within signal ensembles. DCS with jointly …

The mutual information in random linear estimation

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has been a number …

MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel

This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on non-rigorous but …

Adaptive damping and mean removal for the generalized approximate message passing algorithm

The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of x observed from a noisy version of the transform coefficients z = Ax. In fact, for large zero-mean i.i.d sub-Gaussian A, GAMP …