pyxu-xrt 0.7

Pyxu X-Ray Transform Operators

pyxu_xrt provides Pyxu operators to compute samples of the X-Ray Transform in 2D and 3D.

The X-Ray Transform (XRT) of a function \(f: \mathbb{R}^{D} \to \mathbb{R}\) is defined as

where \(\mathbf{n}\in \mathbb{S}^{D-1}\) and \(\mathbf{t} \in \mathbf{n}^{\perp}\). \(\mathcal{P}[f]\) hence denotes the set of line integrals of \(f\).

Two class of algorithms exist to evaluate the XRT:

• Fourier methods leverage the Fourier Slice Theorem (FST) to efficiently evaluate the XRT when multiple values of \(\mathbf{t}\) are desired for each \(\mathbf{n}\).

• Ray methods compute estimates of the XRT via quadrature rules by assuming \(f\) is piecewise constant on short intervals.

The operators in pyxu_xrt allow one to efficiently evaluate samples of the XRT assuming \(f\) is a pixelized image/volume where:

• the lower-left element of \(f\) is located at \(\mathbf{o} \in \mathbb{R}^{D}\),

• pixel dimensions are \(\mathbf{\Delta} \in \mathbb{R}_{+}^{D}\), i.e.

In the 2D case, the parametrization is best explained by the figure below:

Installation

You can install pyxu_xrt via pip:

pip install pyxu_xrt

The host system must have CUDA 11.x or 12.x installed to use the GPU. Similarly, using drjit-backed operators on the CPU requires LLVM. If problems arise, we provide Docker receipes to easily create Pyxu developer environments.

License

Distributed under the terms of the MIT license, pyxu_xrt is free and open source software.

Issues

If you encounter any problems, please file an issue along with a detailed description.