Gradient-Based Geometry Learning for Fan-Beam CT Reconstruction

TL;DR

This paper introduces a differentiable framework for fan-beam CT reconstruction that optimizes acquisition geometry parameters, demonstrated through a neural network-based motion compensation method that significantly improves image quality.

Contribution

It extends differentiable CT reconstruction to include geometry parameters, enabling gradient-based optimization for tasks like motion correction and scanner calibration.

Findings

Achieved 35.5% reduction in MSE for motion compensation

Improved SSIM by 12.6% over motion-affected reconstructions

First to optimize autofocus algorithms using analytical gradients in this context

Abstract

Incorporating computed tomography (CT) reconstruction operators into differentiable pipelines has proven beneficial in many applications. Such approaches usually focus on the projection data and keep the acquisition geometry fixed. However, precise knowledge of the acquisition geometry is essential for high quality reconstruction results. In this paper, the differentiable formulation of fan-beam CT reconstruction is extended to the acquisition geometry. This allows to propagate gradient information from a loss function on the reconstructed image into the geometry parameters. As a proof-of-concept experiment, this idea is applied to rigid motion compensation. The cost function is parameterized by a trained neural network which regresses an image quality metric from the motion affected reconstruction alone. Using the proposed method, we are the first to optimize such an autofocus-inspired algorithm based on analytical gradients. The algorithm achieves a reduction in MSE by 35.5 % and an improvement in SSIM by 12.6 % over the motion affected reconstruction. Next to motion compensation, we see further use cases of our differentiable method for scanner calibration or hybrid techniques employing deep models.