###
Compressed sensing and parallel acquisition

A new phase transition !

Compressed sensing and parallel acquisition by

Il Yong Chun,

Ben Adcock

Parallel acquisition systems arise in various applications in order to
moderate problems caused by insufficient measurements in single-sensor systems.
These systems allow simultaneous data acquisition in multiple sensors, thus
alleviating such problems by providing more overall measurements. In this work
we consider the combination of compressed sensing with parallel acquisition. We
establish the theoretical improvements of such systems by providing recovery
guarantees for which, subject to appropriate conditions, the number of
measurements required per sensor decreases linearly with the total number of
sensors. Throughout, we consider two different sampling scenarios -- distinct
(corresponding to independent sampling in each sensor) and identical
(corresponding to dependent sampling between sensors) -- and a general
mathematical framework that allows for a wide range of sensing matrices (e.g.,
subgaussian random matrices, subsampled isometries, random convolutions and
random Toeplitz matrices). We also consider not just the standard sparse signal
model, but also the so-called sparse in levels signal model. This model
includes both sparse and distributed signals and clustered sparse signals. As
our results show, optimal recovery guarantees for both distinct and identical
sampling are possible under much broader conditions on the so-called sensor
profile matrices (which characterize environmental conditions between a source
and the sensors) for the sparse in levels model than for the sparse model. To
verify our recovery guarantees we provide numerical results showing phase
transitions for a number of different multi-sensor environments.

**Join the CompressiveSensing subreddit or the Google+ Community or the Facebook page and post there !**

Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.
## 1 comment:

- Available Ph.D position:

Title: Big data processing using sparse tensor representations

Involved laboratories:

1. L2S lab., Signals and Statistics Dep., CentraleSupelec, CNRS, UPS

2. ENS/Cachan, SATIE lab.

3. I3S lab.UNS/CNRS

4. UFC (Universidade Federal do Ceará, Brazil)

Research area: advanced mathematical methods applied to big data processing.

Keywords: compressed sensing, tensor models, sparse tensor recovery, massive antennas, large-scale systems, parametric estimation theory, random matrix theory, Bayesian inference, machine learning

http://www.l2s.centralesupelec.fr/perso/remy.boyer

Post a Comment