Error Estimations for Total Variation Type Regularization

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