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.

Date Published: 1 May 2017
PDF: 10 pages
Proc. SPIE 10222, Computational Imaging II, 102220P (1 May 2017); doi: 10.1117/12.2257670

Published in SPIE Proceedings Vol. 10222:
Computational Imaging II
Abhijit Mahalanobis; Amit Ashok; Lei Tian; Jonathan C. Petruccelli; Kenneth S. Kubala, Editor(s)