Fast Hartley transform and truncated singular value algorithm for circular deconvolution

Lizhi Cheng

doi:10.1117/1.601429

1 August 1997 Fast Hartley transform and truncated singular value algorithm for circular deconvolution

Lizhi Cheng

Optical Engineering, Vol. 36, Issue 8, (August 1997). https://doi.org/10.1117/1.601429

The fast Hartley transform (FHT) algorithm for solving wellconditioned circular deconvolution is suggested. The arithmetic operations save about half compared to the fast Fourier transform (FFT) deconvolution algorithm. The Moore-Penrose generalized inverse of the circulant matrix connection to FHT matrices is investigated, then the least-squares solution for circular deconvolution is developed. An efficient numerical stable circular deconvolution algorithm is suggested by using FHT and truncated singular value decomposition (TSVD) techniques. An open problem is partially solved.

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Lizhi Cheng "Fast Hartley transform and truncated singular value algorithm for circular deconvolution," Optical Engineering 36(8), (1 August 1997). https://doi.org/10.1117/1.601429

Published: 1 August 1997

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