Exploring instabilities of inverse problem solvers with low-dimensional manifolds - Archive ouverte HAL
Preprints, Working Papers, ... Year : 2024

Exploring instabilities of inverse problem solvers with low-dimensional manifolds

Abstract

Inverse problem solvers are mappings S : Y → X , where Y is the space of measurements and X the space of signals we wish to recover. We propose a simple algorithm to visualize the main instability of a solver implemented within an automatic differentiation framework. We justify it through simple considerations and illustrate its behavior on a deconvolution problem solved with a neural network based reconstruction method. The proposed algorithm can be used to provide additional insights on the properties of inverse problem solvers, and can be viewed as a simple uncertainty quantification technique.
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Dates and versions

hal-04753218 , version 1 (25-10-2024)

Identifiers

  • HAL Id : hal-04753218 , version 1

Cite

Nathanaël Munier, Emmanuel Soubies, Pierre Weiss. Exploring instabilities of inverse problem solvers with low-dimensional manifolds. 2024. ⟨hal-04753218⟩
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