Efficient Dynamic Image Reconstruction with motion estimation

TL;DR

This work addresses dynamic inverse problems in tomography by introducing MMGKS-OF, a joint image reconstruction and motion estimation method that integrates optical-flow-based motion models into a Majorization-Minimization Generalized Krylov Subspace framework. The algorithm alternates between estimating motion fields and reconstructing the entire image sequence, solving regularized subproblems with automatic parameter selection via discrepancy principle and GCV. Key innovations include encoding optical-flow information in a linear regularization matrix, using MMGKS to efficiently solve large-scale subproblems, and strategies to reduce computational costs for dynamic, ill-posed CT problems. Numerical experiments across limited-angle and single-shot tomography demonstrate consistent improvements in reconstruction quality, especially under severe data sparsity, highlighting the method's potential for robust, scalable dynamic imaging with motion.

Abstract

Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous computational challenge. In this work, in addition to the use of edge-enhancing regularization of spatial features, we propose a new regularization method that incorporates a temporal model that estimates the motion of objects in time. In particular, we consider the optical flow model that simultaneously estimates the motion and provides an approximation for the desired image, and we incorporate this information into the cost functional as an additional form of temporal regularization. We propose a computationally efficient algorithm to solve the jointly regularized problem that leverages a generalized Krylov subspace method. We illustrate the effectiveness of the prescribed approach on a wide range of numerical experiments, including limited angle and single-shot computerized tomography.

Figures (12)

• Figure 1: Slices of ground truth images of (a) Test 1 at $t = \{1,6,12\}$, (b)Test 2at $t = \{1, 11, 20\}$
• Figure 1: Sensitive Dependence on Parameter $\gamma$
• Figure 2: Test 1: RRE convergence plots
• Figure 3: Test 1: Estimated optical flow when $n_\text{views} = 3$ at $t = 1, 5, 10$.
• Figure 4: Test 1: Reconstructed images at $t = \{2,6,10\}$ when $n_{\text{views}} = 3$.

Theorems & Definitions (2)

• Remark 3.1: On Estimating the Reverse Optical Flow
• Remark 5.1