resesop

RESESOP (Regularized Sequential Subspace Optimization)

https://github.com/kenaj123/resesop

Science Score: 44.0%

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RESESOP (Regularized Sequential Subspace Optimization)

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Created almost 2 years ago · Last pushed over 1 year ago
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README.md

Goal: Find solution f of multiple linear inverse problems $Ai f = gi$.

Setting: Only noisy versions of gi are available $||gi - gi^\delta|| < \deltai$ (L2-norm). Further, there may only be access to inexact versions $Ai^\eta$ of forward operators: $||Ai - Ai^\eta|| \leq \etai$ (operator norm).

In this repository we provide some implementation of the RESESOP-Kaczmarz method presented in the article: S. Blanke, B. Hahn and A. Wald; Inverse problems with inexact forward operator: Iterative regularization and application in dynamic imaging; Inverse Problems, 36 (2020).

Second, we present a differentiable loss function that can be used to train a Deep Image Prior, while taking into account the discrepancy between the inexact and exact forward operators $Ai^\eta$ and $Ai$, respectively. As a recall, the DIP approach seeks for a neural network $\varphi\theta$ that maps a given random prior $z$ to the solution $f$ of the inverse problem(s) $Ai f = g^\deltai$. Since only inexact versions $A^\etai$ of $Ai$ are available, we propose to train $\varphi\theta$ by minimizing the following loss-function:

$\frac{1}{n} \sum{i=1 \ldots n} \Big\vert \vert Ai^\eta \varphi\theta(z) - gi^\delta \vert^2 - c_i \Big\vert^2$

where $c\in \mathbb{R}^n{\geq 0}$ is some discrepancy term describing the model uncertainty between $Ai$ and $Ai^\eta$. Ideally, $ci^2$ should be close to $\vert Ai f - gi^\delta \vert^2$.

Both implementations have been used in the article: J. Gödeke and G. Rigaud; Imaging based on Compton scattering: model uncertainty and data-driven reconstruction methods; Inverse Problems, 39 (2023).

Owner

  • Name: Janek Gödeke
  • Login: kenaj123
  • Kind: user

Citation (citation.cff)

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
- family-names: "Janek"
  given-names: "Gödeke"
  orcid: "https://orcid.org/0000-0002-4633-6963"
title: "Implementation of the RESESOP-Kaczmarz method"
version: 1
date-released: 2024-05-10
url: "https://github.com/kenaj123/RESESOP"

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