Structural Properties of Solutions to Total Variation Regularization Problems

By Wolfgang Ring. 2000

157 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a9883abe0351b3191b008505aba207a9c3058d1e

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Mathematical Physics

Citations in the corpus

Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional (2005, methodology): “However, both from a theoretical (Weickert, 1998; Ring, 2000) and experimental (Lysaker et al., 2003; Chambolle and Lions, 1997; Chan et al., 2000) point of view, it has been shown that the TV-norm transforms smooth signal into piecewise constants, the so-called staircase effect.”
Image restoration: Total variation, wavelet frames, and beyond (2012, background): “However, it will also create the staircase effect for images that are not piecewise constant [24, 25].”
An Iterative Regularization Method for Total Variation-Based Image Restoration (2005, background): “Also, in [12] and subsequently in [31, 32, 33, 36] the “staircasing” effect of this model was analyzed.”
Bilevel approaches for learning of variational imaging models (2015, background): “The artefact introduced by TV regularisation in this case is called staircasing [68], compare Figure 3.”
Solving inverse problems using data-driven models (2019, background): “In this case, TV introduces jumps that are not present in the true solution, which is referred to as staircasing (Ring 2000).”
Modern regularization methods for inverse problems (2018, background): “[112, 343, 331, 120, 322, 342, 77, 104, 4]), computational optimization techniques for nonsmooth problems (cf.”
A duality-based approach to elliptic control problems in non-reflexive Banach spaces (2011, unknown): “Introduction This work is concerned with the study of the optimal control problem (P) minu∈X 1 2 ‖y− z‖2L2(Ω) + α ‖u‖X s.t. Ay = u where Ω ⊂ Rn, n ∈ {2, 3}, is a simply connected bounded domain with Lipschitz boundary ∂Ω, X is a non-reflexive Banach space, and α > 0 and z ∈ L2(Ω) are ∗Institute…”