Deciphering subsampled data: adaptive compressive sampling as a principle of brain communication

A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the sparse codes. We verify that the new algorithm performs efficient data compression on par with the recent method of compressive sampling. Further, we demonstrate that the algorithm performs robustly when stacked in several stages or when applied in undercomplete or over-complete situations. The new algorithm can explain how neural populations in the brain that receive subsampled input through fiber bottlenecks are able to form coherent response properties.

[1]  D C Van Essen,et al.  Information processing in the primate visual system: an integrated systems perspective. , 1992, Science.

[2]  Michael S. Lewicki,et al.  Efficient auditory coding , 2006, Nature.

[3]  Richard G. Baraniuk,et al.  Sparse Coding via Thresholding and Local Competition in Neural Circuits , 2008, Neural Computation.

[4]  Rajat Raina,et al.  Efficient sparse coding algorithms , 2006, NIPS.

[5]  R. Wyman,et al.  What genes are necessary to make an identified synapse? , 1983, Cold Spring Harbor Symposia on Quantitative Biology.

[6]  Michael Elad,et al.  Optimized Projections for Compressed Sensing , 2007, IEEE Transactions on Signal Processing.

[7]  M. Sur,et al.  Experimentally induced visual projections into auditory thalamus and cortex. , 1988, Science.

[8]  Hyun Sung Chang,et al.  Learning Compressed Sensing , 2007 .

[9]  William Bialek,et al.  Statistics of Natural Images: Scaling in the Woods , 1993, NIPS.

[10]  Yonina C. Eldar,et al.  Blind Compressed Sensing , 2010, IEEE Transactions on Information Theory.

[11]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[12]  Martin Rehn,et al.  A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields , 2007, Journal of Computational Neuroscience.

[13]  A. Schüz,et al.  Quantitative aspects of corticocortical connections: a tracer study in the mouse. , 2006, Cerebral cortex.

[14]  E.J. Candes.  Compressive Sampling , 2022 .

[15]  T J Sejnowski,et al.  Learning the higher-order structure of a natural sound. , 1996, Network.

[16]  Martin J. Wainwright,et al.  Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$ -Constrained Quadratic Programming (Lasso) , 2009, IEEE Transactions on Information Theory.