GPUs are faster (sometimes, much faster) when working with Float32 than with Float64.

Introduction to CUDA.jl tutorial: https://cuda.juliagpu.org/stable/tutorials/introduction/

Prototyping #4 revealed a humorous bug. Need to reparameterize the detector plane.

Parameters that should be differentiable

• Camera location (3D point)
• Detector location (3D point)
• Detector orientation (normal vector is easy, 3 angles not sure how to do?)

Want the gradients wrt to

• Camera.center (the 3D coordinates of the camera)
• Detector.center (the 3D coordinates of the center of the detector plane)
• Detector.normal (the orientation of the detector plane)

Specifically, the GPU accelerated version from this article https://aapm.onlinelibrary.wiley.com/doi/epdf/10.1118/1.3190156

• Average point sampler
• Trilinear interpolation

Visualization of #1 and #2

Inspired by this https://makie.juliaplots.org/stable/documentation/backends/wglmakie/#record_a_statemap

Contains imaging data and directional spacings

We are interested in solving the following inverse problem:

Given a DRR, recover the model parameters that were used to generate it.

Our idea is to use inverse rendering to solve this with gradient descent (#11). However, the prevailing strategy in medical imaging is to perform a heuristic search to solve this problem (i.e., genetic algorithm, simulated annealing, etc.).

Implement this approach for benchmarking!