28 September 2016 Total variation regularization with bounded linear variations
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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.
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Artyom Makovetskii, Artyom Makovetskii, Sergei Voronin, Sergei Voronin, Vitaly Kober, Vitaly Kober, } "Total variation regularization with bounded linear variations", Proc. SPIE 9971, Applications of Digital Image Processing XXXIX, 99712T (28 September 2016); doi: 10.1117/12.2237162; https://doi.org/10.1117/12.2237162

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