DeepAI AI Chat
Log In Sign Up

Performance Limits with Additive Error Metrics in Noisy Multi-Measurement Vector Problem

by   Junan Zhu, et al.

Real-world applications such as magnetic resonance imaging with multiple coils, multi-user communication, and diffuse optical tomography often assume a linear model where several sparse signals sharing common sparse supports are acquired by several measurement matrices and then contaminated by noise. Multi-measurement vector (MMV) problems consider the estimation or reconstruction of such signals. In different applications, the estimation error that we want to minimize could be the mean squared error or other metrics such as the mean absolute error and the support set error. Seeing that minimizing different error metrics is useful in MMV problems, we study information-theoretic performance limits for MMV signal estimation with arbitrary additive error metrics. We also propose a message passing algorithmic framework that achieves the optimal performance, as verified through numerical examples. As an application of our MMV algorithm, we propose a novel setup for active user detection in multi-user communication and demonstrate the promise of our proposed setup.


page 1

page 2

page 3

page 4


An Approximate Message Passing Algorithm for Rapid Parameter-Free Compressed Sensing MRI

For certain sensing matrices, the Approximate Message Passing (AMP) algo...

Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing

Bayesian approximate message passing (BAMP) is an efficient method in co...

On the Universality of Noiseless Linear Estimation with Respect to the Measurement Matrix

In a noiseless linear estimation problem, one aims to reconstruct a vect...

MRI Image Recovery using Damped Denoising Vector AMP

Motivated by image recovery in magnetic resonance imaging (MRI), we prop...

Mixed Regression via Approximate Message Passing

We study the problem of regression in a generalized linear model (GLM) w...

Deep Learning Assisted User Identification in Massive Machine-Type Communications

In this paper, we propose a deep learning aided list approximate message...

Limits of Detecting Extraterrestrial Civilizations

The search for extraterrestrial intelligence (SETI) is a scientific ende...