Mathematics (Jun 2021)

Error Estimations for Total Variation Type Regularization

  • Kuan Li,
  • Chun Huang,
  • Ziyang Yuan

DOI
https://doi.org/10.3390/math9121373
Journal volume & issue
Vol. 9, no. 12
p. 1373

Abstract

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This paper provides several error estimations for total variation (TV) type regularization, which arises in a series of areas, for instance, signal and imaging processing, machine learning, etc. In this paper, some basic properties of the minimizer for the TV regularization problem such as stability, consistency and convergence rate are fully investigated. Both a priori and a posteriori rules are considered in this paper. Furthermore, an improved convergence rate is given based on the sparsity assumption. The problem under the condition of non-sparsity, which is common in practice, is also discussed; the results of the corresponding convergence rate are also presented under certain mild conditions.

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