Advertisement
Published in:
2011 | OriginalPaper | Chapter
1. The Anti-Reflective Transform and Regularization by Filtering
Authors : A. Aricò, M. Donatelli, J. Nagy, S. Serra-Capizzano
Published in: Numerical Linear Algebra in Signals, Systems and Control
Publisher: Springer Netherlands
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.