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Total variation regularization with bounded linear variations
Author(s): Artyom Makovetskii; Sergei Voronin; Vitaly Kober
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Paper Abstract

One of the most known techniques for signal denoising is based on total variation regularization (TV regularization). A better understanding of TV regularization is necessary to provide a stronger mathematical justification for using TV minimization in signal processing. In this work, we deal with an intermediate case between one- and two-dimensional cases; that is, a discrete function to be processed is two-dimensional radially symmetric piecewise constant. For this case, the exact solution to the problem can be obtained as follows: first, calculate the average values over rings of the noisy function; second, calculate the shift values and their directions using closed formulae depending on a regularization parameter and structure of rings. Despite the TV regularization is effective for noise removal; it often destroys fine details and thin structures of images. In order to overcome this drawback, we use the TV regularization for signal denoising subject to linear signal variations are bounded.

Paper Details

Date Published: 28 September 2016
PDF: 9 pages
Proc. SPIE 9971, Applications of Digital Image Processing XXXIX, 99712T (28 September 2016); doi: 10.1117/12.2237162
Show Author Affiliations
Artyom Makovetskii, Chelyabinsk State Univ. (Russian Federation)
Sergei Voronin, Chelyabinsk State Univ. (Russian Federation)
Vitaly Kober, Chelyabinsk State Univ. (Russian Federation)
Ctr. de Investigación Científica y de Educación Superior de Ensenada B.C. (Mexico)

Published in SPIE Proceedings Vol. 9971:
Applications of Digital Image Processing XXXIX
Andrew G. Tescher, Editor(s)

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