Matrix sparsification and non-negative factorization for task partitioning in computational sensing and imaging

David G. Stork; Neda Rohani; Aggelos K. Katsaggelos

doi:10.1117/12.2257670

1 May 2017 Matrix sparsification and non-negative factorization for task partitioning in computational sensing and imaging

David G. Stork, Neda Rohani, Aggelos K. Katsaggelos

Author Affiliations +

Proceedings Volume 10222, Computational Imaging II; 102220P (2017) https://doi.org/10.1117/12.2257670
Event: SPIE Commercial + Scientific Sensing and Imaging, 2017, Anaheim, CA, United States

Abstract

We address the mathematical foundations of a special case of the general problem of partitioning an end-to-end sensing algorithm for implementation by optics and by a digital processor for minimal electrical power dissipation. Specifically, we present a non-iterative algorithm for factoring a general k × k real matrix A (describing the end-to-end linear pre-processing) into the product BC, where C has no negative entries (for implementation in linear optics) and B is maximally sparse, i.e., has the fewest possible non-zero entries (for minimal dissipation of electrical power). Our algorithm achieves a sparsification of B: i.e., the number s of non-zero entries in B: of s ≤ 2k, which we prove is optimal for our class of problems.

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David G. Stork, Neda Rohani, and Aggelos K. Katsaggelos "Matrix sparsification and non-negative factorization for task partitioning in computational sensing and imaging", Proc. SPIE 10222, Computational Imaging II, 102220P (1 May 2017); https://doi.org/10.1117/12.2257670

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