arXiv subjects

Kwang Eun Jang

Publications and source records attributed to Kwang Eun Jang.

3 recordsLinked to original sources

arXiv2026

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

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.

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arXiv2025

Design of 3D Non-Cartesian Trajectories for Fast Volumetric MRI via Analytic Coordinate Discretization

3D non-Cartesian trajectories offer several advantages over rectilinear trajectories for rapid volumetric imaging, including improved sampling efficiency and greater robustness to motion, flow, and aliasing artifacts. In this paper, we present a unified framework for designing three widely used non-Cartesian trajectories: 3D Radial, 3D Cones, and Stack-of-Spirals. Our approach is based on the idea that a non-Cartesian trajectory can be interpreted as a discretized version of an analytic coordinate defined by a set of template trajectories. Equivalently, the analytic coordinate is conceptualized as a non-Cartesian trajectory composed of an infinite number of copies of a set of template trajectories. The discretization is accomplished by constructing a continuous spiral path on a surface and sampling points along this path at unit intervals, leaving only the essential spokes/interleaves, thereby yielding the practical non-Cartesian trajectory from the analytic coordinate. One of the advantages of our approach is that the analytic density compensation factor can be readily derived using Jacobian determinants, which quantify changes in unit areas due to the transformation from the analytic coordinate to the Cartesian grid. Additionally, the proposed approach derives analytic formulae to compute the number of readouts based on prescribed parameters, allowing us to specify the trajectory's acceleration factor for a given total scan time. Furthermore, variable-density sampling can be easily incorporated, and spokes/interleaves are smoothly distributed in k-space along the derived spiral path, even for a small number of readouts. In a preliminary phantom study, the proposed method demonstrated improved sampling efficiency and image quality compared to the conventional approach.

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arXiv2025

Image-Space Gridding for Nonrigid Motion-Corrected MR Image Reconstruction

Motion remains a major challenge in magnetic resonance (MR) imaging, particularly in free-breathing cardiac MR imaging, where data are acquired over multiple heartbeats at varying respiratory phases. We adopt a model-based approach for nonrigid motion correction, addressing two challenges: (a) motion representation and (b) motion estimation. For motion representation, we derive image-space gridding by adapting the nonuniform fast Fourier transform (NUFFT) to represent and compute nonrigid motion, which provides an exact forward-adjoint pair of linear operators. We then introduce nonrigid SENSE operators that incorporate nonrigid motion into the multi-coil MR acquisition model. For motion estimation, we employ both low-resolution 3D image-based navigators (iNAVs) and high-resolution 3D self-navigating image-based navigators (self-iNAVs). During each heartbeat, data are acquired along two types of non-Cartesian trajectories: a subset of a high-resolution trajectory that sparsely covers 3D k-space, followed by a full low-resolution trajectory. We reconstruct 3D iNAVs for each heartbeat using the full low-resolution data, which are then used to estimate bulk motion and identify the respiratory phase of each heartbeat. By combining data from multiple heartbeats within the same respiratory phase, we reconstruct high-resolution 3D self-iNAVs, allowing estimation of nonrigid respiratory motion. For each respiratory phase, we construct the nonrigid SENSE operator, reformulating the nonrigid motion-corrected reconstruction as a standard regularized inverse problem. In a preliminary study, the proposed method enhanced sharpness of the coronary arteries and improved image quality in non-cardiac regions, outperforming translational motion-corrected reconstruction.

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