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Compressive Sensing Recovery of Spike Trains Using A Structured Sparsity Model

Abstract : The theory of Compressive Sensing (CS) exploits a well-known concept used in signal compression - sparsity - to design new, efficient techniques for signal acquisition. CS theory states that for a length-N signal x with sparsity level K, M = O(K log(N/K)) random linear projections of x are sufficient to robustly recover x in polynomial time. However, richer models are often applicable in real-world settings that impose additional structure on the sparse nonzero coefficients of x.Many such models can be succinctly described as a union of K-dimensional subspaces. In recent work, we have developed a general approach for the design and analysis of robust, efficient CS recovery algorithms that exploit such signal models with structured sparsity. We apply our framework to a new signal model which is motivated by neuronal spike trains. We model the firing process of a single Poisson neuron with absolute refractoriness using a union of subspaces. We then derive a bound on the number of random projections M needed for stable embedding of this signal model, and develop a algorithm that provably recovers any neuronal spike train from M measurements. Numerical experimental results demonstrate the benefits of our model-based approach compared to conventional CS recovery techniques.
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https://hal.inria.fr/inria-00369584
Contributor : Ist Rennes <>
Submitted on : Friday, March 20, 2009 - 2:00:57 PM
Last modification on : Monday, June 20, 2016 - 2:10:32 PM
Long-term archiving on: : Thursday, June 10, 2010 - 5:45:19 PM

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Chinmay Hegde, Marco F. Duarte, Volkan Cevher. Compressive Sensing Recovery of Spike Trains Using A Structured Sparsity Model. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369584⟩

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