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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