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12 May 2011 Toeplitz embedding for fast iterative regularized imaging
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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.
© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
R. Ahmad, C. D. Austin, and L. C. Potter "Toeplitz embedding for fast iterative regularized imaging", Proc. SPIE 8051, Algorithms for Synthetic Aperture Radar Imagery XVIII, 80510E (12 May 2011); https://doi.org/10.1117/12.888952
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