Step and Smooth Decompositions as Topological Clustering
Abstract
We investigate a class of recovery problems for which observations are a noisy combination of continuous and step functions. These problems can be seen as non-injective instances of non-linear ICA with direct applications to image decontamination for magnetic resonance imaging. Alternately, the problem can be viewed as clustering in the presence of structured (smooth) contaminant. We show that a global topological property (graph connectivity) interacts with a local property (the degree of smoothness of the continuous component) to determine conditions under which the components are identifiable. Additionally, a practical estimation algorithm is provided for the case when the contaminant lies in a reproducing kernel Hilbert space of continuous functions. Algorithm effectiveness is demonstrated through a series of simulations and real-world studies.
Cite
@article{arxiv.2311.05756,
title = {Step and Smooth Decompositions as Topological Clustering},
author = {Luciano Vinas and Arash A. Amini},
journal= {arXiv preprint arXiv:2311.05756},
year = {2023}
}