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Proceedings Paper

Jacobi-like method for a control algorithm in adaptive-optics imaging
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Paper Abstract

A study is made of a non-smooth optimization problem arising in adaptive-optics, which involves the real-time control of a deformable mirror designed to compensate for atmospheric turbulence and other dynamic image degradation factors. One formulation of this problem yields a functional f(U) equals (Sigma) iequals1n maxj[(UTMjU)ii] to be maximized over orthogonal matrices U for a fixed collection of n X n symmetric matrices Mj. We consider first the situation which can arise in practical applications where the matrices Mj are nearly pairwise commutative. Besides giving useful bounds, results for this case lead to a simple corollary providing a theoretical closed-form solution for globally maximizing f if the Mj are simultaneously diagonalizable. However, even here conventional optimization methods for maximizing f are not practical in a real-time environment. The genal optimization problem is quite difficult and is approached using a heuristic Jacobi-like algorithm. Numerical test indicate that the algorithm provides an effective means to optimize performance for some important adaptive-optics systems.

Paper Details

Date Published: 2 October 1998
PDF: 12 pages
Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); doi: 10.1117/12.325691
Show Author Affiliations
Nikos P. Pitsianis, BOPS, Inc. (United States)
Brent L. Ellerbroek, Air Force Research Lab. (United States)
Charles Van Loan, Cornell Univ. (United States)
Robert J. Plemmons, Wake Forest Univ. (United States)

Published in SPIE Proceedings Vol. 3461:
Advanced Signal Processing Algorithms, Architectures, and Implementations VIII
Franklin T. Luk, Editor(s)

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