Generalization of Strang's preconditioner with applications to iterative deconvolution

Raymond Hon-fu Chan; Michael Kwok-po Ng; Robert J. Plemmons

doi:10.1117/12.190864

28 October 1994 Generalization of Strang's preconditioner with applications to iterative deconvolution

Raymond Hon-fu Chan, Michael Kwok-po Ng, Robert J. Plemmons

Proceedings Volume 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V; (1994) https://doi.org/10.1117/12.190864
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

In this paper, we proposed a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices A_n. The [n/2]th column of our circulant preconditioner S_n is equal to the [n/2]th column of the given matrix A_n. Thus if A_n is a square Toeplitz matrix, then S_n is just the Strang circulant preconditioner. When S_n is not Hermitian, our circulant preconditioner can be defined as (S^*_nS_n)^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 S_n with other circulant-based preconditioners are carried out for some 1D Toeplitz least squares problems: minb - Ax₂. Preliminary numerical results show that S_n performs quite well. Test results are also reported for a 2D deconvolution problem arising in ground-based atmospheric imaging.

Citation Download Citation

Raymond Hon-fu Chan, Michael Kwok-po Ng, and 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); https://doi.org/10.1117/12.190864

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available