https://hal.inria.fr/inria-00369584Hegde, ChinmayChinmayHegdeElectrical and Computer Engineering - Rice University - Rice University [Houston]Duarte, Marco F.Marco F.DuarteElectrical and Computer Engineering - Rice University - Rice University [Houston]Cevher, VolkanVolkanCevherElectrical and Computer Engineering - Rice University - Rice University [Houston]Compressive Sensing Recovery of Spike Trains Using A Structured Sparsity ModelHAL CCSD2009[INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processingRennes, IstRĂ©mi Gribonval2009-03-20 14:00:572016-06-20 14:10:322009-03-20 14:11:58enConference papersapplication/pdf1The 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.