MIRT: a simultaneous reconstruction and affine motion compensation technique for four dimensional computed tomography (4DCT)

2024-02-07

arXiv.org

AI Summary

Motion artifacts in 4DCT cause severe image distortion; existing methods rely on nested iterative schemes lacking convergence guarantees, and mainstream toolboxes lack analytical adjoints for 3D affine motion operators, hindering gradient-based optimization. Method: We propose the first unified iterative framework jointly reconstructing images and compensating affine motion—integrating parameterized affine transformations (rigid + scaling) directly into analytical CT gradient optimization. Our method jointly updates image and motion parameters in a single step, eliminating dependence on reference images and nested structures. It enforces projection consistency and employs analytically derived adjoints to ensure theoretical convergence. Results: Experiments on both simulated and real data demonstrate significant improvements over state-of-the-art affine correction methods: higher projection-domain accuracy, improved computational efficiency, and successful high-fidelity 4DCT reconstruction of micron-scale dynamic diamond structures.

Technology Category

• Computer Vision: Motion & Tracking
• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning with Manifolds

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In four-dimensional computed tomography (4DCT), 3D images of moving or deforming samples are reconstructed from a set of 2D projection images. Recent techniques for iterative motion-compensated reconstruction either necessitate a reference acquisition or alternate image reconstruction and motion estimation steps. In these methods, the motion estimation step involves the estimation of either complete deformation vector fields (DVFs) or a limited set of parameters corresponding to the affine motion, including rigid motion or scaling. The majority of these approaches rely on nested iterations, incurring significant computational expenses. Notably, despite the direct benefits of an analytical formulation and a substantial reduction in computational complexity, there has been no exploration into parameterizing DVFs for general affine motion in CT imaging. In this work, we propose the Motion-compensated Iterative Reconstruction Technique (MIRT)- an efficient iterative reconstruction scheme that combines image reconstruction and affine motion estimation in a single update step, based on the analytical gradients of the motion towards both the reconstruction and the affine motion parameters. When most of the state-of-the-art 4DCT methods have not attempted to be tested on real data, results from simulation and real experiments show that our method outperforms the state-of-the-art CT reconstruction with affine motion correction methods in computational feasibility and projection distance. In particular, this allows accurate reconstruction for a proper microscale diamond in the appearance of motion from the practically acquired projection radiographs, which leads to a novel application of 4DCT.

Problem

• Existing 4DCT methods use nested iterations increasing computational complexity
• Current toolboxes lack analytic adjoints preventing exact motion parameter derivatives
• No theoretical convergence proof exists for iterative 4DCT reconstruction schemes

Innovation

• Combines image reconstruction and motion estimation in single step
• Uses analytic adjoints of motion operators for exact derivatives
• Proves convergence despite non-convex objective function