CT 2D Image Reconstruction

This repository provides a Python-based implementation of Computed Tomography (CT) reconstruction for 2D images.

Description

The task is to reconstruct the image of a sample from its X-ray detector readings (also called sinogram). Given the experiment geometry details, it generates lines representing the X-ray path through the object and calculates their intersections with each pixel. These intercept lengths form an intercept matrix A. Using the detector readings $d$, the code solves the inverse problem $A \lambda = d$ to obtain the attenuation constant distribution of the material, which is the reconstruction image.

Mathematical statement

The CT reconstruction problem is expressed mathematically as: A λ = d

• A is the intercept matrix, containing lengths of X-ray intercepts on each pixel within the object.
• λ is the attenuation coefficient data for each pixel, which is the desired output.
• d is the sinogram vector, calculated as -

$$d=\ln(\frac{I_o}{I})$$ where,

• $I_o$ is the intensity of the X-ray source.
• $I$ is the intensity observed by the detectors.

The solution of the image ie λ gives us the image of the object.

Note that we are considering only a 2D cross-section of the object.

Experiment Geometry

References

1. Original experiment paper
2. Siddon's Algorithm