We discuss the convergence of the multiscale procedure by Modin et al. (Adv. Math. 346:1009–1066, 2019), which extended to inverse problems the multiscale decomposition of images by Tadmor et al. (Multiscale Model. Simul. 2:554–579, 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.
A Counterexample to Convergence for Multiscale Decompositions / Rebegoldi, S., Rondi, L. (TRENDS IN MATHEMATICS). - In: Trends in Mathematics[s.l] : Springer Science and Business Media Deutschland GmbH, 2025. - ISBN 9783031872129. - pp. 115-123 [10.1007/978-3-031-87213-6_15]
A Counterexample to Convergence for Multiscale Decompositions
Rebegoldi, SimoneMembro del Collaboration Group
;
2025
Abstract
We discuss the convergence of the multiscale procedure by Modin et al. (Adv. Math. 346:1009–1066, 2019), which extended to inverse problems the multiscale decomposition of images by Tadmor et al. (Multiscale Model. Simul. 2:554–579, 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.
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