Copyright (c) 2024, Roland Griesmaier, Lisa Schätzle
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***
# Editing this README
When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!). Thanks to [makeareadme.com](https://www.makeareadme.com/) for this template.
## Suggestions for a good README
This software is released under GNU General Public License, Version 3.
The full license text is provided in the file LICENSE included in this repository
or can be obtained from http://www.gnu.org/licenses/
Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.
## Content of this project
## Name
Choose a self-explaining name for your project.
This is a guide to generate the figures and tables that have been used in the work
## Description
Let people know what your project can do specifically. Provide context and add a link to any reference visitors might be unfamiliar with. A list of Features or a Background subsection can also be added here. If there are alternatives to your project, this is a good place to list differentiating factors.
**"Far field operator splitting and completion in inverse medium scattering"**
## Badges
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by Roland Griesmaier and Lisa Schätzle.
## Visuals
Depending on what you are making, it can be a good idea to include screenshots or even a video (you'll frequently see GIFs rather than actual videos). Tools like ttygif can help, but check out Asciinema for a more sophisticated method.
The following versions of the paper are available:
## Installation
Within a particular ecosystem, there may be a common way of installing things, such as using Yarn, NuGet, or Homebrew. However, consider the possibility that whoever is reading your README is a novice and would like more guidance. Listing specific steps helps remove ambiguity and gets people to using your project as quickly as possible. If it only runs in a specific context like a particular programming language version or operating system or has dependencies that have to be installed manually, also add a Requirements subsection.
- [ ]
## Usage
Use examples liberally, and show the expected output if you can. It's helpful to have inline the smallest example of usage that you can demonstrate, while providing links to more sophisticated examples if they are too long to reasonably include in the README.
You find all needed Matlab files to generate the figures and tables.
## Support
Tell people where they can go to for help. It can be any combination of an issue tracker, a chat room, an email address, etc.
## Requirements
## Roadmap
If you have ideas for releases in the future, it is a good idea to list them in the README.
The following additional software is necessary to run the code in this project:
## Contributing
State if you are open to contributions and what your requirements are for accepting them.
- [ ] a recent version of Matlab
For people who want to make changes to your project, it's helpful to have some documentation on how to get started. Perhaps there is a script that they should run or some environment variables that they need to set. Make these steps explicit. These instructions could also be useful to your future self.
## An overview
You can also document commands to lint the code or run tests. These steps help to ensure high code quality and reduce the likelihood that the changes inadvertently break something. Having instructions for running tests is especially helpful if it requires external setup, such as starting a Selenium server for testing in a browser.
- [ ] *addNoise.m* adds p% complex valued uniformly distributed additive error to a matrix.
- [ ] *applyRP.m* completes a matrix according to the symmetrie resulting from the reciprocity relation.
- [ ] *CG_secondOrder.m* solves the least squares problem for the splitting and/ or completion problem in Born approximation of order 2 numerically by using the cg method.
- [ ] *evaluateFarfieldNystrom.m* evaluates the far field patterns for n2 incident and observation directions on an equidistant grid on the unit sphere for each configuration, i.e. simulates the far field operator, by using a Nyström method.
- [ ] *evaluateFarfieldSecondOrder.m* Simulates the Born far field operator of order 2 by using trigonometric interpolation.
- [ ] *example_5_1.m* tests both methods for the splitting problem and two scatterers, adding 5% equally distributed random noise to the synthetic data for two different szenarios (varying distance, varying size of one scatterer).
- [ ] *example_5_2.m* tests both methods for the completion problem and two scatterers, adding 5% equally distributed random noise to the synthetic data for two different geometric setups for Omega.
- [ ] *example_5_3.m* tests both methods for the completion and splitting problem and two scatterers, adding 5% equally distributed random noise to the synthetic data for two different geometric setups for Omega.
- [ ] *figure_2_1.m* provides plots of the factors causing the essential decay behaviour of the expansion coefficients of far field operators for different choices of kR.
- [ ] *figure_2_2.m* provides plots of the absolute values of the expansion coefficients of a far field operator as well as of the geometry of the corresponding scatterer.
- [ ] *figure_3_1.m* provides plots of the absolute values of the expansion coefficients of a Born far field operator of order 2 as well as of the geometry of the corresponding two scatterers.
- [ ] *FISTA_secondOrder.m* solves the l1xl1 minimization problem for the splitting and/ or completion problem in Born approximation of order 2 numerically by using fast iterative thresholding.
- [ ] *generateOmega.m* simulates projection operator corresponding to some missing data segment Omega.
- [ ] *kurve.m* provides curve values for different shapes of scatterers.
- [ ] *MyCMap.mat* provides colormap for the plots of expansion coefficients of far field operators.
- [ ] *projOp.m* simulates projection operator on generalized subspace of non-evanescent far field operators.
- [ ] *softshrink.m* applies soft-shrinkage operator to a matrix F.
- [ ] *translOp.m* applies generalized translation operator to a far field matrix.
## Authors and acknowledgment
Show your appreciation to those who have contributed to the project.
## Generating the files
## License
For open source projects, say how it is licensed.
For generating the Figures 2.1, 2.2 and 3.1 from the work, run
## Project status
If you have run out of energy or time for your project, put a note at the top of the README saying that development has slowed down or stopped completely. Someone may choose to fork your project or volunteer to step in as a maintainer or owner, allowing your project to keep going. You can also make an explicit request for maintainers.
**figure_2_1.m* - **Figure 2.1** (Plots of the factors causing the decay behaviour of the expansion coefficients)
**figure_2_2.m* - **Figure 2.2** (Example 2.6, geometry of kite-shaped scatterer, expansion coefficients of corr. far field operator)
**figure_3_1.m* - **Figure 3.1** (Example 3.4, geometry of kite- and nut-shaped scatterer, expansion coefficients of corr. Born far field operator of order 2)
**example_5_1.m* - **Figure 5.1**, **Table 5.1** (Example 5.1, splitting only for two diifferent szenarios, varying distance and size of one scatterer)
**example_5_2.m* - **Figure 5.2**, **Table 5.2** (Example 5.1, completion and Splitting for two diifferent geometrical setups for Omega)
**example_5_3.m* - **Table 5.3** (Example 5.3, completion and Splitting for two diifferent geometrical setups for Omega)
