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 is also considered.
A Polynomial Fit Preconditioner for Band Toeplitz Matrices in Image Reconstruction
MENCHI, ORNELLA
2002-01-01
Abstract
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 is also considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
