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Towards optimal nonlinearities for sparse recovery using higher-order statistics

 
: Limmer, S.; Stariczak, S.

:

Palmieri, F.A.N. ; Institute of Electrical and Electronics Engineers -IEEE-; IEEE Signal Processing Society:
MLSP 2016, IEEE International Workshop on Machine Learning for Signal Processing. Proceedings : September 13-16, Vietri sul Mare, Salerno, Italy
Piscataway, NJ: IEEE, 2016
ISBN: 978-1-5090-0746-2
ISBN: 978-1-5090-0747-9
pp.483-488
International Workshop on Machine Learning for Signal Processing (MLSP) <26, 2016, Salerno>
English
Conference Paper
Fraunhofer HHI ()

Abstract
We consider machine learning techniques to develop low-latency approximate solutions for a class of inverse problems. More precisely, we use a probabilistic approach to the problem of recovering sparse stochastic signals that are members of the lp-balls. In this context, we analyze the Bayesian mean-square-error (MSE) for two types of estimators: (i) a linear estimator and (ii) a structured estimator composed of a linear operator followed by a Cartesian product of univariate nonlinear mappings. By construction, the complexity of the proposed nonlinear estimator is comparable to that of its linear counterpart since the nonlinear mapping can be implemented efficiently in hardware by means of look-up tables (LUTs). The proposed structure lends itself to neural networks and iterative shrinkage/thresholding-type algorithms restricted to a single iteration (e.g. due to imposed hardware or latency constraints). By resorting to an alternating minimization technique, we obtain a sequence of optimized linear operators and nonlinear mappings that converge in the MSE objective. The result is attractive for real-time applications where general iterative and convex optimization methods are infeasible.

: http://publica.fraunhofer.de/documents/N-444924.html