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SSG Seminar Abstract

Distributed Compressed Sensing

Dror Baron
Rice University

Sensors, signal processing hardware, and algorithms are under increasing pressure to accommodate ever larger data sets; ever faster sampling and processing rates; ever lower power consumption; and radically new sensing modalities.  Fortunately, over the past few decades, there has been an enormous increase in computational power and data storage capacity, which provides a new angle to tackle these challenges.  We could be on the verge of moving from a "digital signal processing" (DSP) paradigm, where analog signals are sampled periodically to create their digital counterparts for processing, to a "computational signal processing" (CSP) paradigm, where analog signals are converted directly to any of a number of intermediate, "condensed" representations for processing using optimization techniques. As an example of CSP, I will overview our recent work in "Compressed Sensing", an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. The implications of compressed sensing are promising for many applications and enable the design of new kinds of cameras and analog-to-digital converters.

I will then focus on our new theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms that exploit both intra- and inter-signal correlation structures in multi-signal ensembles. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We study in detail three simple models for jointly sparse signals, propose algorithms for joint recovery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction. We establish a parallel with the Slepian-Wolf theorem from information theory and establish upper and lower bounds on the measurement rates required for encoding jointly sparse signals. In two of our three models, the results are asymptotically best-possible, meaning that both the upper and lower bounds match the performance of our practical algorithms. Moreover, simulations indicate that the asymptotics take effect with just a moderate number of signals. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem for some time. DCS is immediately applicable to a range of problems in sensor networks and

For more information, a compressed sensing resource page is available on the
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