ajinkyakadu / ParametricLevelSet

Geometric Inverse Problem using Parametric Level-Set

Parametric Level Set Framework

A comprehensive implementation of the Parametric Level Set approach for inverse problems, aimed at improving reconstruction accuracy.

Overview

ParametricLevelSet is a MATLAB-based toolkit that employs the Parametric Level Set approach in addressing inverse problems. The framework is designed to be user-friendly and accessible to a wide range of users.

The general least-squares formulation of inverse problems can be expressed as follows:

$$\min_{x \in \mathbb{R}^N} | F(A x) - y |^2 $$

where $A$ is a linear operator and $F$ is a proper, convex and lower-semicontinuous function. This problem represents the so-called primal formulation of the minimization problem, and $x$ is the primal variable of interest that is being recovered.

License

For distribution purposes, commercial or otherwise, please contact Ajinkya Kadu for further information.

Requirements

The framework has been tested on Matlab 2016b.

Usage Instructions

The framework includes examples of usage in the test folder.

Reference

When using this code, please cite the following publication:

@article{Kadu2017,
  doi = {10.1109/tci.2016.2640761},
  url = {https://doi.org/10.1109/tci.2016.2640761},
  year = {2017},
  month = {jun},
  publisher = {Institute of Electrical and Electronics Engineers ({IEEE})},
  volume = {3},
  number = {2},
  pages = {305--315},
  author = {Ajinkya Kadu and Tristan van Leeuwen and Wim A. Mulder},
  title = {Salt Reconstruction in Full-Waveform Inversion With a Parametric Level-Set Method},
  journal = {{IEEE} Transactions on Computational Imaging}
}

A preprint of the article can be found here

Bug Reports

Should you encounter any issues, please do not hesitate to contact Ajinkya Kadu.