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Proceedings Paper

Toeplitz embedding for fast iterative regularized imaging
Author(s): R. Ahmad; C. D. Austin; L. C. Potter
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Paper Abstract

For large-scale linear inverse problems, a direct matrix-vector multiplication may not be computationally feasible, rendering many gradient-based iterative algorithms impractical. For applications where data collection can be modeled by Fourier encoding, the resulting Gram matrix possesses a block Toeplitz structure. This special structure can be exploited to replace matrix-vector multiplication with FFTs. In this paper, we identify some of the important applications which can benefit from the block Toeplitz structure of the Gram matrix. Also, for illustration, we have applied this idea to reconstruct 2D simulated images from undersampled non-Cartesian Fourier encoding data using three popular optimization routines, namely, FISTA, SpaRSA, and optimization transfer.

Paper Details

Date Published: 12 May 2011
PDF: 8 pages
Proc. SPIE 8051, Algorithms for Synthetic Aperture Radar Imagery XVIII, 80510E (12 May 2011); doi: 10.1117/12.888952
Show Author Affiliations
R. Ahmad, The Ohio State Univ. (United States)
C. D. Austin, The Ohio State Univ. (United States)
L. C. Potter, The Ohio State Univ. (United States)

Published in SPIE Proceedings Vol. 8051:
Algorithms for Synthetic Aperture Radar Imagery XVIII
Edmund G. Zelnio; Frederick D. Garber, Editor(s)

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