Convex Shape Recovery Program for Single-shot tomography
This MATLAB toolbox computes an image composed of K copies of shapes from its single-shot X-ray tomographic projections. It assumes that the shapes are known, and creates a dictionary consisting of extensive roto-translations copies of the shapes. The algorithmic framework, called CoShaRP, converts the estimation of roto-translation parameters of shapes to computing the dictionary coefficients with imposed constraints (here, K-simplex constraints).
We solve the optimization problem
to compute the shape coefficients. Here, A is a tomography matrix (which is either fan-beam or cone-beam) of size m times n, y consists of m tomographic measurements, Ψ is a shape dictionary of size n times p, and z is a shape coefficient vector of length p. K are the number of shapes present in the target image. Once we obtain an optimal estimate of shape coefficient vector, we get an image using
- Ajinkya Kadu (ajinkyakadu125@gmail.com)
You can distribute the software as you wish.
This framework has been tested on Matlab 2020b.
The examples scripts are
- test2D : single-shot fan-beam tomography on 2D image with circular disks as shape
- test2D_4shapes : single-shot fan-beam tomography on 2D image with 4 different shapes
- test3d : single-shot cone-beam tomography on 3D image with spheres
If you use this code, please use the following citation
@article{kadu2020cosharp,
title={CoShaRP: A Convex Program for Single-shot Tomographic Shape Sensing},
author={Kadu, Ajinkya and van Leeuwen, Tristan and Batenburg, K Joost},
journal={arXiv preprint arXiv:2012.04551},
year={2020}
}
A preprint of the article can be found here
In case you experience any problems, please contact Ajinkya Kadu