A local spectral inversion of a linearized TV model for denoising and deblurring

Author

Candela, Vicente F. ; Marquina, Antonio ; Serna, Susana

Author_Institution

Departament de Matematica Aplicada, Univ. de Valencia, Burjassot, Spain

Volume

12

Issue

7

fYear

2003

fDate

7/1/2003 12:00:00 AM

Firstpage

808

Lastpage

816

Abstract

We propose a model for denoising and deblurring. It consists of a system of linear partial differential equations with locally constant coefficients, obtained as a local linearization of the total variation (TV) models (see Rudin, L. et al., Physica D, vol.60, p.259-68, 1992). The keypoint of our model is to get the local inversion of the Laplacian operator, which is done via the fast Fourier transform (FFT). Two local schemes are developed: a pointwise one and a piecewise one. We analyze them both, and their advantages and limitations.

Keywords

fast Fourier transforms; image denoising; image restoration; linear differential equations; partial differential equations; spectral analysis; variational techniques; FFT; Laplacian operator; fast Fourier transform; image deblurring; image denoising; linear differential equations; linearized total variation model; local inversion; local linearization; local spectral inversion; partial differential equations; piecewise scheme; pointwise scheme; Difference equations; Fast Fourier transforms; Image analysis; Image denoising; Image restoration; Laplace equations; Noise reduction; Partial differential equations; Signal resolution; TV;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/TIP.2003.812760

Filename

1212656