pyxu_xrt

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 : ℝ^D → ℝ is defined as

𝒫[f](n, t) = ∫_ℝf(t + nα)dα,

where n ∈ 𝕊^D − 1 and t ∈ n^⊥. 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 t are desired for each 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 o ∈ ℝ^D,
• pixel dimensions are Δ ∈ ℝ₊^D, i.e.

f(r) = ∑_{{q} ⊂ ℕ^D}α_q1_[0, Δ](r − q ⊙ Δ − o), α_q ∈ ℝ.

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.