Wavelet deblurring algorithms for spatially varying blur from high-resolution image reconstruction
Publication in refereed journal


Times Cited
Web of Science18WOS source URL (as at 20/10/2020) Click here for the latest count
Altmetrics Information
.

Other information
AbstractHigh-resolution image reconstruction refers to reconstructing a higher resolution image from multiple low-resolution samples of a true image. In Chan et al. (Wavelet algorithms for high-resolution image reconstruction, Research Report #CUHK-2000-20, Department of Mathematics, The Chinese University of Hong Kong, 2000), we considered the case where there are no displacement errors in the low-resolution samples, i.e.,,the samples are aligned properly, and hence the blurring operator is spatially invariant. In this paper, we consider the case where there are displacement errors in the low-resolution samples. The resulting blurring operator is spatially varying and is formed by sampling and summing different spatially invariant blurring operators. We represent each of these spatially invariant blurring operators by a tensor product of a lowpass filter which associates the corresponding blurring operator with a multiresolution analysis of L-2(R-2). Using these filters and their duals, we derive an iterative algorithm to solve the problem based on the algorithmic framework of Chan et al. (Wavelet algorithms for high-resolution image reconstruction, Research Report #CUHK-2000-20, Department of Mathematics, The Chinese University of Hong Kong, 2000). Our algorithm requires a nontrivial modification to the algorithms in Chan et al. (Wavelet algorithms for high-resolution image reconstruction, Research Report #CUHK-2000-20, Department of Mathematics, The Chinese University of Hong Kong, 2000), which apply only to spatially invariant blurring operators. Our numerical examples show that our algorithm gives higher peak signal-to-noise ratios and lower relative errors than those from the Tikhonov least squares approach. (C) 2002 Elsevier Science Inc. All rights reserved.
All Author(s) ListChan RH, Chan TF, Shen LX, Shen ZW
Journal nameLinear Algebra and its Applications
Year2003
Month6
Day1
Volume Number366
PublisherELSEVIER SCIENCE INC
Pages139 - 155
ISSN0024-3795
LanguagesEnglish-United Kingdom
Keywordshigh-resolution image reconstruction; Tikhonov least squares method; wavelet
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2020-21-10 at 00:42