Pixel recovery VIA ℓ 1 minimization in the wavelet domain

Ivan Selesnick, Richard Van Slyke, Onur G. Guleryuz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper uses probability models on expansive wavelet transform coefficients with interpolation constraints to estimate missing blocks in images. We use simple probability models on wavelet coefficients to formulate the estimation process as a linear programming problem and solve it to recover the missing pixels. Our formulation is general and can be augmented with more sophisticated probability models to obtain even better estimates on a variety of image regions. The presented approach has many parallels to recently introduced dictionary based signal representations with which it shares certain optimality properties. We provide simulation examples over edge regions using both critically-sampled and expansive (over-complete) wavelet transforms.

Original languageEnglish (US)
Title of host publication2004 International Conference on Image Processing, ICIP 2004
Pages1819-1822
Number of pages4
Volume3
DOIs
StatePublished - 2004
Event2004 International Conference on Image Processing, ICIP 2004 - , Singapore
Duration: Oct 18 2004Oct 21 2004

Other

Other2004 International Conference on Image Processing, ICIP 2004
CountrySingapore
Period10/18/0410/21/04

Fingerprint

Pixels
Recovery
Wavelet transforms
Glossaries
Linear programming
Interpolation

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Selesnick, I., Van Slyke, R., & Guleryuz, O. G. (2004). Pixel recovery VIA ℓ 1 minimization in the wavelet domain. In 2004 International Conference on Image Processing, ICIP 2004 (Vol. 3, pp. 1819-1822) https://doi.org/10.1109/ICIP.2004.1421429

Pixel recovery VIA ℓ 1 minimization in the wavelet domain. / Selesnick, Ivan; Van Slyke, Richard; Guleryuz, Onur G.

2004 International Conference on Image Processing, ICIP 2004. Vol. 3 2004. p. 1819-1822.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Selesnick, I, Van Slyke, R & Guleryuz, OG 2004, Pixel recovery VIA ℓ 1 minimization in the wavelet domain. in 2004 International Conference on Image Processing, ICIP 2004. vol. 3, pp. 1819-1822, 2004 International Conference on Image Processing, ICIP 2004, Singapore, 10/18/04. https://doi.org/10.1109/ICIP.2004.1421429
Selesnick I, Van Slyke R, Guleryuz OG. Pixel recovery VIA ℓ 1 minimization in the wavelet domain. In 2004 International Conference on Image Processing, ICIP 2004. Vol. 3. 2004. p. 1819-1822 https://doi.org/10.1109/ICIP.2004.1421429
Selesnick, Ivan ; Van Slyke, Richard ; Guleryuz, Onur G. / Pixel recovery VIA ℓ 1 minimization in the wavelet domain. 2004 International Conference on Image Processing, ICIP 2004. Vol. 3 2004. pp. 1819-1822
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