Abstract
Regularization with functions of bounded variation has been proven to be effective for denoising signals and images. This nonlinear regularization technique, in contrast with linear regularization techniques like Tikhonov regularization, has the advantage that discontinuities in signals and images can be located very precisely. In this paper bounded variation regularization is generalized to functions with higher order derivatives of bounded variation. This concept is applied to locate discontinuities in derivatives, which has important applications in parameter estimation problems.
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This work is supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, Grant J01088-TEC; most of this work has been done, when O.S. visited the Department of Mathematics, College Station, Texas 77843-3368, USA. Present address: Institut für Industriemathematik, Universität Linz, Altenberger Str. 69, A-4040 Linz, Austria.
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Scherzer, O. Denoising with higher order derivatives of bounded variation and an application to parameter estimation. Computing 60, 1–27 (1998). https://doi.org/10.1007/BF02684327
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DOI: https://doi.org/10.1007/BF02684327