ParallelBackprojectorFunction#

class diffct.ParallelBackprojectorFunction(*args, **kwargs)[source]#

Bases: Function

Summary#

PyTorch autograd function for differentiable 2D parallel beam backprojection.

Notes

Provides a differentiable interface to the CUDA-accelerated Siddon ray-tracing method with a cell-constant image basis for parallel beam backprojection. The forward pass computes a 2D reconstruction from sinogram data using parallel beam backprojection, and the backward pass computes gradients via forward projection as the adjoint operation. Requires CUDA-capable hardware and consistent device placements.

Examples

>>> import torch
>>> from diffct import ParallelBackprojectorFunction, circular_trajectory_2d_parallel
>>>
>>> sinogram = torch.randn(180, 192, device='cuda', requires_grad=True)
>>> ray_dir, det_origin, det_u_vec = circular_trajectory_2d_parallel(180, device='cuda')
>>> image = ParallelBackprojectorFunction.apply(sinogram, ray_dir, det_origin, det_u_vec, 1.0, 128, 128)
>>> image.sum().backward()
>>> sinogram.grad.shape
torch.Size([180, 192])
static backward(ctx, grad_output)[source]#
static forward(ctx, sinogram, ray_dir, det_origin, det_u_vec, detector_spacing=1.0, H=128, W=128, voxel_spacing=1.0)[source]#

Compute the 2D parallel beam backprojection with arbitrary trajectories using CUDA acceleration.

Parameters:

  • sinogram (torch.Tensor) – Floating-point CUDA sinogram of shape (n_views, num_detectors), converted to float32 for execution.

  • ray_dir (torch.Tensor) – Ray direction unit vectors for each view, shape (n_views, 2).

  • det_origin (torch.Tensor) – Detector origin positions for each view, shape (n_views, 2), in physical units.

  • det_u_vec (torch.Tensor) – Detector u-direction unit vectors for each view, shape (n_views, 2).

  • detector_spacing (float, optional) – Physical spacing between detector elements (default: 1.0).

  • H (int, optional) – Height of the output reconstruction image (default: 128).

  • W (int, optional) – Width of the output reconstruction image (default: 128).

  • voxel_spacing (float, optional) – Physical size of one voxel (in same units as detector_spacing, default: 1.0).

Returns:

reco – 2D tensor of shape (H, W) containing the reconstructed image on the same device as sinogram.

Return type:

torch.Tensor

Notes

  • Geometry tensors are moved to the sinogram’s CUDA device and converted to float32.

  • Data derivatives support higher orders; geometry derivatives are first-order only.

  • Supports arbitrary parallel beam geometries.

  • Uses the adjoint of cell-constant Siddon ray tracing.

Examples

>>> sinogram = torch.randn(180, 128, device='cuda', requires_grad=True)
>>> ray_dir, det_origin, det_u_vec = circular_trajectory_2d_parallel(180, device='cuda')
>>> reco = ParallelBackprojectorFunction.apply(
...     sinogram, ray_dir, det_origin, det_u_vec, 1.0, 128, 128
... )
Parameters:

  • args (Any)

  • kwargs (Any)

Return type:

Any