Differentiable Ray Model Calibrates Tomography Without Separate Scan

Geometric misalignments between nominal and actual acquisition parameters in tomography typically degrade reconstruction quality, requiring costly calibration procedures. A team from EPFL (Haouchat, Boquet-Pujadas, Kashani, Thévenaz, Unser) introduces a differentiable ray-based framework that solves this by jointly reconstructing the 3D volume and calibrating the geometry in a single optimization. The core innovation is an x-ray transform operator whose gradients with respect to acquisition parameters are computed efficiently using a ray-tracing method with computational complexity similar to the forward operator. This enables end-to-end learning without separate calibration steps.

To ensure smooth gradients, the volume is represented in a B-spline basis rather than traditional voxels, creating a better-behaved optimization landscape. The method works for arbitrary source-detector configurations, making it adaptable to different tomography setups. The framework was validated on CT, micro-CT, nano-CT, and positron emission tomography (PET) data under a variety of geometric misalignments, consistently producing higher-quality reconstructions. This approach has significant implications for medical imaging, materials science, and industrial inspection, reducing hardware dependency and enabling accurate imaging in dynamic or constrained environments.