Implicit Image Differentiation and Filtering with Applications to Image Sharpening

Research output: Contribution to journalArticle

Abstract

The paper demonstrates potential advantages of using implicit finite differencing and filtering schemes for fast, accurate, and reliable differentiating and filltering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and Gaussian image debluring are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Pade-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.
Original languageEnglish
Pages (from-to)660–679
Number of pages20
JournalSIAM Journal on Imaging Sciences
Volume6
Issue number1
Early online date21 Mar 2013
DOIs
Publication statusPublished - 21 Mar 2013

Fingerprint

Filtering
Spectral Resolution
Finite Difference Scheme
Gradient Estimation
Padé Approximation
Image Enhancement
Galerkin Approximation
Threefolds
Finite Difference
Grid
Demonstrate

Cite this

@article{1488f38bc7e141ba994cc93ea7bb18ac,
title = "Implicit Image Differentiation and Filtering with Applications to Image Sharpening",
abstract = "The paper demonstrates potential advantages of using implicit finite differencing and filtering schemes for fast, accurate, and reliable differentiating and filltering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and Gaussian image debluring are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Pade-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.",
author = "Alexander Belyaev",
year = "2013",
month = "3",
day = "21",
doi = "10.1137/12087092X",
language = "English",
volume = "6",
pages = "660–679",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

Implicit Image Differentiation and Filtering with Applications to Image Sharpening. / Belyaev, Alexander.

In: SIAM Journal on Imaging Sciences , Vol. 6, No. 1, 21.03.2013, p. 660–679.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Implicit Image Differentiation and Filtering with Applications to Image Sharpening

AU - Belyaev, Alexander

PY - 2013/3/21

Y1 - 2013/3/21

N2 - The paper demonstrates potential advantages of using implicit finite differencing and filtering schemes for fast, accurate, and reliable differentiating and filltering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and Gaussian image debluring are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Pade-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.

AB - The paper demonstrates potential advantages of using implicit finite differencing and filtering schemes for fast, accurate, and reliable differentiating and filltering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and Gaussian image debluring are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Pade-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.

U2 - 10.1137/12087092X

DO - 10.1137/12087092X

M3 - Article

VL - 6

SP - 660

EP - 679

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 1

ER -