Аннотация:
One-dimensional variants are considered of the classical first order total variation denoising model introduced by Rudin, Osher, and Fatemi. This study is based on previous work of the authors on various denoising and inpainting problems in image analysis, where variational methods in arbitrary dimensions were applied. More than being just a special case, the one-dimensional setting makes it possible to study regularity properties of minimizers by more subtle methods that do not have correspondences in higher dimensions. In particular, quite strong regularity results are obtained for a class of data functions that contains many of the standard examples from signal processing such as rectangle or triangle signals as a special case. The analysis of the related Euler–Lagrange equation, which turns out to be a second order two-point boundary value problem with Neumann conditions, by ODE methods completes the picture of this investigation.
Ключевые слова:
total variation, signal denoising, variational problems in one independent variable, linear growth, existence and regularity of solutions.
Образец цитирования:
M. Fuchs, J. Müller, C. Tietz, “Signal recovery via TV-type energies”, Алгебра и анализ, 29:4 (2017), 159–195; St. Petersburg Math. J., 29:4 (2018), 657–681
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\pages 159--195
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\vol 29
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1553
https://www.mathnet.ru/rus/aa/v29/i4/p159
Эта публикация цитируется в следующих 5 статьяx:
M. Fuchs, J. Mueller, “A liouville theorem for stationary incompressible fluids of von mises type”, Acta Math. Sci., 39:1 (2019), 1–10
M. Fuchs, J. Weickert, “Iterative TV-Regularization of Grey-Scale Images”, J Math Sci, 242:2 (2019), 323
M. Bildhauer, M. Fuchs, J. Mueller, X. Zhong, “On the local boundedness of generalized minimizers of variational problems with linear growth”, Ann. Mat. Pura Appl., 197:4 (2018), 1117–1129
M. Fuchs, J. Mueller, Ch. Tietz, J. Weickert, “Convex regularization of multi-channel images based on variants of the TV-model”, Complex Var. Elliptic Equ., 63:7–8, SI (2018), 976–995
M. Bildhauer, M. Fuchs, J. Mueller, “Existence and regularity for stationary incompressible flows with dissipative potentials of linear growth”, J. Math. Fluid Mech., 20:4 (2018), 1567–1587
Цитирование в формате AMSBIB
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