- Poster presentation
- Open Access
Compressed sensing with stochastic spikes
© Rotermund and Pawelzik; licensee BioMed Central Ltd. 2011
- Published: 18 July 2011
- Compression Ratio
- Sparse Representation
- Compress Sensing
- Rate Code
- Spike Activity
Compressed Sensing (CS) refers to the mathematical finding that perfect reconstruction of a high dimensional state can be possible also from much lower dimensional samples provided the state representation is sufficiently sparse. Since neuronal activities in cortex are in fact sparse it is tempting to explain certain aspects of neuronal coding in terms of CS ( and ). The applicability of CS to neuronal structures and activities, however, critically relies on realistic assumptions about the neuronal mechanisms that could implement efficient algorithms. Here we investigated the feasibility of CS with rate coding neurons. Also, we are interested in the speed-precision tradeoff of reconstructions using spike-based algorithms similar to the one we introduced previously .
We find that a biologically plausible algorithm for non-negative activities can efficiently exploit the information contained in stochastic spike events and converges to close solutions for a wide range of sparsenesses and under-samplings.
We also investigated conditions on the generating matrix that would facilitate satisfactory reconstructions from limited numbers of spikes. Learning such structures with sparseness constraints can speed up estimations but will in general not match the 'true' generating model. Therefore the construction of sparse representations from spikes can be considered a bias favoring speed in contrast to faithfulness. In  we showed that learning generating matrices is possible using only spike activity. Taken together, our results underline the potential relevance of CS for understanding connectivity structures, sparseness and activity dynamics in the brain.
Financial support for this work was provided by the Bundesministerium für Bildung und Forschung Grants 01 EZ 0867 (Innovationswettbewerb Medizintechnik), 01GQ0705 (Bernstein Group for Computational Neuroscience Bremen), and 01GQ0964 (Bernstein Focus Learning).
- Olshausen BA, Field DJ: Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images. Nature. 1996, 381: 607-609. 10.1038/381607a0.View ArticlePubMedGoogle Scholar
- Coulter WK, Hillar CJ, Sommer FT: Adaptive compressed sensing – a new class of self-organizing coding models for neuroscience. NIPS. 2010Google Scholar
- Ernst U, Rotermund D, Pawelzik KR: Efficient computation based on stochastic spikes. Neural Computation. 2007, 19 (5): 1313-1343. 10.1162/neco.2007.19.5.1313.View ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.