Rigid Motion Estimation using Accelerated Iterative Coordinate Descent (REACT) for MR Imaging

Abstract

Purpose: To develop a computationally viable autofocus method for estimating 3D rigid motion in MR imaging. Theory and Methods: The proposed method, REACT, assumes a piecewise-constant motion trajectory and estimates the rigid motion parameters of individual temporal segments by optimizing an image-quality metric. Coordinate descent is adopted to decompose the high-dimensional optimization problem into a series of subproblems, each updating the motion parameters of a single temporal segment. The cost function of each subproblem is assumed to be approximately locally convex under suitable acquisition conditions. Each subproblem is then solved using a derivative-free solver, thereby avoiding an exhaustive grid search. Numerical simulations were conducted to investigate the local convexity assumption. REACT was evaluated for respiratory motion correction on in vivo free-breathing coronary MR angiography datasets acquired using a 3D cones trajectory with image-based navigators (iNAVs). An autofocus nonrigid motion correction method was also evaluated for comparison. Coronary artery sharpness was quantified using unbounded image edge profile acutance (u-IEPA). Results: In numerical simulations, the objective surfaces of the subproblems were approximately locally convex when the current motion estimate was close to the desired solution. In the in vivo study, REACT yielded higher u-IEPA than the conventional iNAV-based translational motion-estimation method for both the left anterior descending artery (LAD) and right coronary artery. REACT also yielded higher u-IEPA for the LAD than the autofocus nonrigid motion correction method. Conclusion: This study demonstrates the feasibility of coordinate descent for autofocus motion correction in MR imaging.

Figures (7)

• Figure 1: Conceptual overview of the proposed approach, where the motion parameters of one temporal segment are updated while all others are kept fixed. A "beat" refers to a temporal segment during which the object is assumed stationary.
• Figure 2: Numerical simulation (2D translation) with EPI (top) and spiral (bottom) acquisitions. Top row: motion-corrected reconstructions from iteration 0 (no correction) to iteration 3. Bottom row: objective values near the ground truth sampled within $\pm 5$ mm. Rightmost: motion-free noisy reference (SNR=3) and an example EPI shot/spiral interleaf. As iterations progressed, the objective surface near the ground truth increasingly resembled a locally convex function.
• Figure 3: Curved MPR images along the LAD for NoCo (top), Tran (middle), and REACT (bottom). Left: image-gradient magnitudes ($\mathbf{H}$ in \ref{['eq:abs_gradient']}). Right: corresponding reconstructions. Compared with NoCo and Tran, REACT suppressed background graininess and produced sharper, more continuous vessel edges in the image-gradient magnitude map, resulting in improved vessel visibility in the reconstruction.
• Figure 4: Axial images comparing NoCo, Tran, REACT, NR-Tran, and NR-REACT. Arrows highlight the LAD (purple), RCA (green), and internal thoracic vessels (blue). Compared with Tran, REACT substantially improved vessel depiction, whereas NR-Tran primarily enhanced overall sharpness with more limited gains in vessel delineation.
• Figure 5: Curved MPR images along the LAD and RCA comparing NoCo, Tran, REACT, NR-Tran, and NR-REACT. REACT showed improved LAD delineation compared to Tran and NR-Tran, while autofocus nonrigid refinement (NR-Tran and NR-REACT) yielded moderate additional sharpening over their respective baselines. Similar, less pronounced differences were observed for the RCA.