Filtering methods are used in signal and image restoration to reconstruct an approximation of a signal or image from degraded measurements. Filtering methods rely on computing a singular value decomposition or a spectral factorization of a large structured matrix. The structure of the matrix depends in part on imposed boundary conditions. Anti-reflective boundary conditions preserve continuity of the image and its (normal) derivative at the boundary, and have been shown to produce superior reconstructions compared to other commonly used boundary conditions, such as periodic, zero and reflective. The purpose of this paper is to analyze the eigenvector structure of matrices that enforce anti-reflective boundary conditions. In particular, a new anti-reflective transform is introduced, and an efficient approach to computing filtered solutions is proposed. Numerical tests illustrate the performance of the discussed methods.

The anti-reflective transform and regularization by filtering

DONATELLI, MARCO;SERRA CAPIZZANO, STEFANO
2011-01-01

Abstract

Filtering methods are used in signal and image restoration to reconstruct an approximation of a signal or image from degraded measurements. Filtering methods rely on computing a singular value decomposition or a spectral factorization of a large structured matrix. The structure of the matrix depends in part on imposed boundary conditions. Anti-reflective boundary conditions preserve continuity of the image and its (normal) derivative at the boundary, and have been shown to produce superior reconstructions compared to other commonly used boundary conditions, such as periodic, zero and reflective. The purpose of this paper is to analyze the eigenvector structure of matrices that enforce anti-reflective boundary conditions. In particular, a new anti-reflective transform is introduced, and an efficient approach to computing filtered solutions is proposed. Numerical tests illustrate the performance of the discussed methods.
2011
Numerical Linear Algebra in Signal, Systems, and Control
9789400706019
International Workshop on Numerical Linear Algebra in Signal, Systems, and Control
9-11 January 2007
Kharagpur, India
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2415
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