28 October 1994 Generalization of Strang's preconditioner with applications to iterative deconvolution
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In this paper, we proposed a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The [n/2]th column of our circulant preconditioner Sn is equal to the [n/2]th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as (S*nSn)1/2. This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. Comparisons of our preconditioner Sn with other circulant-based preconditioners are carried out for some 1D Toeplitz least squares problems: minb - Ax2. Preliminary numerical results show that Sn performs quite well. Test results are also reported for a 2D deconvolution problem arising in ground-based atmospheric imaging.
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Raymond Hon-fu Chan, Raymond Hon-fu Chan, Michael Kwok-po Ng, Michael Kwok-po Ng, Robert J. Plemmons, Robert J. Plemmons, "Generalization of Strang's preconditioner with applications to iterative deconvolution", Proc. SPIE 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, (28 October 1994); doi: 10.1117/12.190864; https://doi.org/10.1117/12.190864

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