Science Score: 44.0%
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Low similarity (6.1%) to scientific vocabulary
Repository
RESESOP (Regularized Sequential Subspace Optimization)
Basic Info
- Host: GitHub
- Owner: kenaj123
- Language: Python
- Default Branch: main
- Homepage: https://github.com/kenaj123/RESESOP
- Size: 59.6 KB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
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
- Repositories: 1
- Profile: https://github.com/kenaj123
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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