Gradient-Based Geometry Learning for Fan-Beam CT Reconstruction
This work addresses the need for precise geometry in CT reconstruction, offering a novel differentiable method for applications like motion compensation and scanner calibration, though it is incremental in extending existing differentiable pipelines.
The paper tackles the problem of improving fan-beam CT reconstruction by learning acquisition geometry parameters through gradient-based optimization, achieving a 35.5% reduction in MSE and 12.6% improvement in SSIM for motion compensation.
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.