Important

Only for educational purposes

Nonlinear Tomography

This project performs nonlinear tomographic reconstruction using algebraic techniques over a triangular mesh. It reconstructs weights on mesh triangles from measurement data and visualizes the results.

Features

• Generates a 2D triangular mesh over a specified grid.
• Constructs linear equation systems from measurements and mappings.
• Solves the reconstruction problem using a masked algebraic reconstruction technique (ART).
• Smooths reconstructed weights using neighboring triangle information.
• Provides visualization tools for reviewing mesh and histogram reconstructions.
• Supports customizable mappings based on parameterized physics simulations (blackbox).

Installation

Make sure you have Python 3.8+ installed. Install dependencies using pip:

git cloe https://github.com/Wandersalamander/nonlinear-tomography
cd nonlinear-tomography
pip install ./

Usage

Generate the histograms for the reconstruction:

python examples/b_make_test_data.py

Then, run the main script:

python examples/c_perform_reconstruction.py

This will:

• Load measurements and parameters.
• Generate mappings between the input and measurement plane using blackbox function.
• Perform reconstruction to recover weights.
• Display plots comparing measured and reconstructed data.

Code Structure

• generate_points_grid: Generate grid points for mesh.
• generate_triangle_mesh: Create triangulation of points.
• generate_linear_equations_system: Builds system matrices and targets from mappings and measurements.
• algebraic_reconstruction_technique_masked: Iteratively solves for weights with masking and relaxation.
• smooth_weights: Smooth weights across neighboring triangles.
• reconstruct: Main pipeline to generate mesh, solve linear system, and smooth weights.
• review_results: Visualizes mesh and histograms for qualitative assessment.

Example

See c_perform_reconstruction.py

Contact

For questions or contributions, please open an issue.