A polynomial fit preconditioner for band Toeplitz matrices in image reconstruction

The preconditioned conjugate gradient (CG) is often applied in image reconstruction as a regularizing method. When the blurring matrix has Toeplitz structure, the modified circulant preconditioner and the inverse Toeplitz preconditioner have been shown to be effective. We introduce here a preconditi...

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Bibliographic Details
Published in:Linear algebra and its applications 2002-05, Vol.346 (1), p.177-197
Main Authors: Favati, P., Lotti, G., Menchi, O.
Format: Article
Language:English
Subjects:
Algebra
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Image processing
Image reconstruction
Information, signal and communications theory
Linear and multilinear algebra, matrix theory
Linear and multilinear algebra, matrix theory (finite and infinite)
Logic, set theory, and algebra
Mathematical methods in physics
Mathematics
Miscellaneous
Physics
Preconditioned conjugate gradient (PCG)
Sciences and techniques of general use
Signal processing
Telecommunications and information theory
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Summary:The preconditioned conjugate gradient (CG) is often applied in image reconstruction as a regularizing method. When the blurring matrix has Toeplitz structure, the modified circulant preconditioner and the inverse Toeplitz preconditioner have been shown to be effective. We introduce here a preconditioner for symmetric positive definite Toeplitz matrices based on a trigonometric polynomial fit which has the same effectiveness of the previous ones but has a lower cost when applied to band matrices. The case of band block Toeplitz matrices with band Toeplitz blocks (BTTB) corresponding to separable point spread functions (PSFs) is also considered.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(01)00513-4