Distributed Compressive Sensing Dror Baron - Distributed Compressed Sensing

Compressed sensing (CS) is a new framework for integrated sensing and compression. The fundamental revelation is that, if an N-sample signal x is sparse and has a good K-term 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:

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:
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Last updated June 2014.