Directional total variation based image deconvolution with unknown boundaries

Ezgi Demircan-Tureyen*, Mustafa E. Kamasak

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)

Abstract

Like many other imaging inverse problems, image deconvolution suffers from ill-posedness and needs for an adequate regularization. Total variation (TV) is an effective regularizer; hence, frequently used in such problems. Various anisotropic alternatives to isotropic TV have also been proposed to capture different characteristics in the image. Directional total variation (DTV) is such an instance, which is convex, has the ability to capture the smooth boundaries as conventional TV does, and also handles the directional dominance by enforcing piecewice constancy through a direction. In this paper, we solve the deconvolution problem under DTV regularization, by using simple forward-backward splitting machinery. Besides, there are two bottlenecks of the deconvolution problem, that need to be addressed; one is the computational load revealed due to matrix inversions, second is the unknown boundary conditions (BCs). We tackle with the former one by switching to the frequency domain using fast Fourier transform (FFT), and the latter one by iteratively estimating a boundary zone to surrounder the blurred image by plugging a recently proposed framework into our algorithm. The proposed approach is evaluated in terms of the reconstruction quality and the speed. The results are compared to a very recent TV-based deconvolution algorithm, which uses a “partial” alternating direction method of multipliers (ADMM) as the optimization tool, by also plugging the same framework to cope with the unknown BCs.

Original languageEnglish
Title of host publicationComputer Analysis of Images and Patterns - 17th International Conference, CAIP 2017, Proceedings
EditorsAnders Heyden, Michael Felsberg, Norbert Kruger
PublisherSpringer Verlag
Pages473-484
Number of pages12
ISBN (Print)9783319646978
DOIs
Publication statusPublished - 2017
Event17th International Conference on Computer Analysis of Images and Patterns, CAIP 2017 - Ystad, Sweden
Duration: 22 Aug 201724 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10425 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference17th International Conference on Computer Analysis of Images and Patterns, CAIP 2017
Country/TerritorySweden
CityYstad
Period22/08/1724/08/17

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

Keywords

  • Convex optimization
  • Deblurring
  • Deconvolution
  • Directional total variation
  • Image reconstruction
  • Inpainting
  • Primal-dual algorithms

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