242. Adaptive Bregman-Kaczmarz: An Approach to Solve Linear Inverse Problems with Independent Noise Exactly
Invited abstract in session WF-7: Regularization methods for Machine Learning and Inverse Problems, stream Optimization for Inverse Problems and Machine Learning.
Wednesday, 16:20 - 18:00Room: M:I
Authors (first author is the speaker)
| 1. | LIONEL TONDJI
|
Abstract
We consider the block Bregman-Kaczmarz method for finite dimensional linear inverse
problems. The block Bregman-Kaczmarz method uses blocks of the linear system and
performs iterative steps with these blocks only. We assume a noise model that we call
independent noise, i.e. each time the method performs a step for some block, one obtains
a noisy sample of the respective part of the right-hand side which is contaminated with
new noise that is independent of all previous steps of the method. One can view these
noise models as making a fresh noisy measurement of the respective block each time it is
used. In this framework, we are able to show that a well-chosen adaptive stepsize of the
block Bergman-Kaczmarz method is able to converge to the exact solution of the linear
inverse problem. The plain form of this adaptive stepsize relies on unknown quantities (like
the Bregman distance to the solution), but we show a way how these quantities can be
estimated purely from given data. We illustrate the finding in numerical experiments and
confirm that these heuristic estimates lead to effective stepsizes.
Keywords
- Convex and non-smooth optimization
Status: accepted
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