English

A counterexample to convergence for multiscale decompositions

Numerical Analysis 2025-03-04 v1 Numerical Analysis

Abstract

We discuss the convergence of the multiscale procedure by Modin, Nachman and Rondi, Adv. Math. (2019), which extended to inverse problems the multiscale decomposition of images by Tadmor, Nezzar and Vese, Multiscale Model. Simul. (2004). We show that, for the classical multiscale procedure, the multiscale decomposition might fail even for the linear case with a Banach norm as regularization.

Cite

@article{arxiv.2503.00556,
  title  = {A counterexample to convergence for multiscale decompositions},
  author = {Simone Rebegoldi and Luca Rondi},
  journal= {arXiv preprint arXiv:2503.00556},
  year   = {2025}
}

Comments

6 pages

R2 v1 2026-06-28T22:03:10.180Z