Magnification-driven B-spline Interpolation for Cone Beam Projection and Backprojection

Marion Savanier (1, 2) , Cyril Riddell (1) , Yves Trousset (1) , Emilie Chouzenoux (2) , Jean-Christophe Pesquet (2)

1 GE Healthcare - General Electric Medical Systems [Buc]
2 OPIS - OPtimisation Imagerie et Santé

Purpose: Discretizing tomographic forward and backward operations is a crucial step in the design of model-based reconstruction algorithms. Standard projectors rely on linear interpolation, whose adjoint introduces discretization errors during backprojection. More advanced techniques are obtained through geometric footprint models that may present a high computational cost and an inner logic that is not suitable for implementation on massively parallel computing architectures. In this work, we take a fresh look at the discretization of resampling transforms and focus on the issue of magnication-induced local sampling variations by introducing a new magnication-driven interpolation approach for tomography. Methods: Starting from the existing literature on spline interpolation for magnication purposes, we provide a mathematical formulation for discretizing a one-dimensional homography. We then extend our approach to two-dimensional representations in order to account for the geometry of cone-beam computed tomography with a at panel detector. Our new method relies on the decomposition of signals onto a space generated by non-uniform B-splines so as to capture the spatially varying magnication that locally affects sampling. We propose various degrees of approximations for a rapid implementation of the proposed approach. Our framework allows us to define a novel family of projector/backprojector pairs parameterized by the order of the employed B-splines. The state-of-the-art distance-driven interpolation appears to fit into this family thus providing new computational layout for this scheme. The question of data resampling at the detector level is handled and integrated with reconstruction in a single framework Results: Results on both synthetic data and real data using a quality assurance phantom, were performed to validate our approach. We show experimentally that our approximate implementations are associated with reduced complexity while achieving a near-optimal performance. In contrast with linear interpolation, B-splines guarantee full usage of all data samples, and thus the X-ray dose, leading to more uniform noise properties. In addition, higher order B-splines allow analytical and iterative reconstruction to reach higher resolution. These benets appear more significant when downsampling frames acquired by X-ray at-panel detectors with small pixels. Conclusions: Magnification-driven B-spline interpolation is shown to provide highaccuracy projection operators with good quality adjoints for iterative reconstruction. It equally applies to backprojection for analytical reconstruction and detector data downsampling.

Mots clés: Cone Beam CT; projection; backprojection; B-splines; magnification-driven interpolation; homography

Domaines: Traitement du signal et de l'image [eess.SP]

Marion Savanier, Cyril Riddell, Yves Trousset, Emilie Chouzenoux, Jean-Christophe Pesquet. Magnification-driven B-spline Interpolation for Cone Beam Projection and Backprojection. Medical Physics, inPress, 48 (10), ⟨10.1002/mp.15179⟩. ⟨hal-03464469⟩