Dror Baron 
Distributed Compressed Sensing
Compressed sensing (CS) is a new framework for integrated sensing and
compression. The fundamental revelation is that, if an Nsample signal
x is sparse and has a good Kterm approximation in some basis, then
it can be reconstructed using M =O(K log(N/K)) << N linear projections of x
onto another basis.
Furthermore, x can be reconstructed using linear
programming, which has polynomial complexity.
Some of the CS projects I have worked on are described here, and
links to numerous other papers appear on the
Nuit Blanche
blog and the
compressed sensing resource page.
This webpage describes some of my work in distributed CS.
Distributed compressed sensing:
Ensembles of signals often contain both inter and intra
signal correlation structures. (For example, sensor network
data often contain spatial and temporal correlations.)
Such structures can be exploited by distributed source coding algorithms,
where each signal is encoded separately and all signals are recovered
jointly. Unfortunately, practical schemes for distributed compression
of sources with both types of correlation have remained a challenging
problem for quite some time.
CS offers a new way to approach these problems. Each sensor takes
random projections of its data, and the measurements of all the
sensors are used by the decoder jointly. We call this approach
distributed compressed sensing (DCS).
The DCS theory rests on the joint sparsity of a
signal ensemble. We proposed several simple models for jointly
sparse signals, developed algorithms for joint reconstruction,
and characterized the number of measurements required.
Similar to distributed compression,
DCS enables to reduce the number of measurements,
and is applicable to sensor networks.
We also provided a unifying theory that considers generic joint
sparsity models using bipartite graphical models.
The interesting point is that in the world of noiseless measurement
of strictly sparse signals, dimensionality plays a volumetric role
analogous to entropy in the data compression world. We have shown a
bound that applies in the following settings:

Single signal CS: one signal being measured noiselessly.

Joint CS: one encoder looks at an ensemble of signals and
measures them jointly (together); the CS measurements are obtained via
multiplication of a
matrix by the vector of the entire ensemble. Not surprisingly, the
bounds here are similar to single signal CS.

Distributed CS: here the multiple signals are measured in
a distributed manner, and each is encoded
differently by a different measurement matrix. We provide a region
describing the number of noiseless measurements required for each of
the the signals. The number of measurements required for
each sensor must account for the minimal features unique to that sensor,
while features that appear among multiple sensors are amortized.
The contribution here is that in the idealized world of noiseless
measurement of exactly sparse signals, the dimensionality of the
signal ensemble under evaluation provides a precise characterization
of the number of measurements required. This result emphasizes
the role that dimensionality plays in these systems. Despite the
idealized setting, it provides
insights into noisy measurement systems.
Publications appear in chronological order:

D. Baron,
M. F. Duarte,
S. Sarvotham,
M. B. Wakin,
and R. G. Baraniuk,
"An InformationTheoretic Approach to Distributed Compressed Sensing,"
Proc. 43d Allerton Conf. Communication,
Control, and Computing,
Monticello, IL, September 2005
(pdf).

M. F. Duarte,
S. Sarvotham,
D. Baron,
M. B. Wakin,
and R. G. Baraniuk,
"Distributed Compressed Sensing of Jointly Sparse Signals,"
Proc. 39th Asilomar Conf. Signals, Systems, and
Computers,
Pacific Grove, CA, November 2005
(pdf).

M. F. Duarte,
S. Sarvotham,
M. B. Wakin,
D. Baron,
and R. G. Baraniuk,
"Joint Sparsity Models for Distributed Compressed Sensing,"
Online Proc. Workshop Signal Process. with
Adaptive Sparse Structured Representations (SPARS),
Rennes, France, November 2005.

M. B. Wakin,
S. Sarvotham,
M. F. Duarte,
D. Baron,
and R. G. Baraniuk,
"Recovery of Jointly Sparse Signals from Few Random Projections,"
Workshop Neural Inf. Process. Systems,
Vancouver, Canada, December 2005
(pdf).

M. F. Duarte,
M. B. Wakin,
D. Baron,
and R. G. Baraniuk,
"Universal Distributed Sensing via Random Projections,"
Proc. Symp. Inf. Process. Sensor Networks
(IPSN2006), Nashville, TN, April 2006
(pdf).

M. F. Duarte,
S. Sarvotham,
D. Baron,
M. B. Wakin,
and R. G. Baraniuk,
"Performance Limits for Jointly Sparse Signals via Graphical Models,"
Proc. Sensor, Signal Inf. Process. Workshop
(SenSIP), Sedona, AZ, May 2008
(pdf,
poster).

M. F. Duarte,
M. B. Wakin,
D. Baron,
S. Sarvotham,
and R. G. Baraniuk,
"Measurement Bounds for Sparse Signal Ensembles via Graphical Models,"
IEEE Trans. Inf. Theory,
vol. 59, no. 7, pp. 42804289, July 2013
(pdf,
talk from
2011 AMS Southeastern Section Meeting).
Back to my homepage.
Last updated June 2014.