Efficient Algorithms for Retrospective Motion Correction in MRI

Abstract

Compared with other medical imaging modalities, MR imaging is time consuming due to the relatively slow sequential data acquisition pattern. Hence, motion is often an unavoidable issue for MRI. Object motion during the signal acquisition can reduce image quality due to the induced artifacts, which further hinders diagnosis and scientific research. These degraded images may require repeated scans, which leads to treatment delay and cost increases. If images with motion artifacts are not properly interpreted, erroneous diagnoses and false scientific findings may occur.

To reduce motion artifacts, three groups of methods are used by practitioners: motion prevention, artifact mitigation, and motion correction. Motion prevention methods are the most straightforward way to reduce motion artifacts. However, these may not always be suitable or effective. Artifact mitigation methods mainly include faster imaging and periodic triggering and gating. Imaging speed has limits, and triggering and gating require extra time, effort, and complexity. Therefore, motion correction methods have received significant attention.

MRI motion correction techniques can be classified into three groups: motion correction based on k-space trajectories, prospective motion correction (PMC) and retrospective motion correction (RMC). Motion correction based on k-space trajectories relies on specially designed and implemented trajectories, which limits the flexibility of the techniques and requires more acquisition time. PMC is achieved by obtaining tracking data of the pose (position and orientation) of the object, passing these data to the scanner with minimal delay, and adjusting the MR pulse sequences so that the imaging volume moves to follow the object. PMC requires extra hardware and calibration and sometimes extra acquisition time. RMC postprocesses the data and reconstructs MR images after the data is fully acquired. In RMC the process of acquisition is independent of motion. RMC includes three main groups: self-navigation motion tracking methods to calculate motion information, autofocusing methods based on evaluation of image quality, and motion correction by training neural networks. Self-navigation motion correction methods rely on Fourier properties by taking advantage of overlapping k-space data to track motion. This approach requires additional k-trajectories, which increases both time and complexity of the scan. Autofocusing methods do not rely on a specific data sample pattern, equipment or sequence design. These approaches assume a rigid body or deformable object motion model and estimate motion model parameters by iterative optimization of an image quality metric when the raw k-space data are modified according to the motion model. Artificial neural network methods establish the mapping relationship between the motion-corrupted images and the no-motion images by training a large number of related images, and estimate motion-corrected images from motion-corrupted images. The focus of this thesis is the development of autofocusing and neural-network approaches to RMC.

In this dissertation, we develop three methods to correct MRI motion retrospectively. The first contribution is an autofocusing motion correction method to address the two challenges of previous methods: high calculation load and local minima. We propose to use multiple linear-motion initializations and joint refinement of a global model to decrease and constrain the search space. In the first step, k-space is divided into several segments based on acquisition order. Linear motion is assumed and searched in each segment to get initial motion parameters. In the second step, several control points are chosen on the piecewise linear initial approximation, and then a piecewise cubic Hermite interpolation polynomial is fitted from the control points to obtain smooth motion curves. The motion curves are refined by optimizing a focus criterion. These strategies make the proposed algorithm efficient and robust. Different focus criteria are compared under the proposed method. To further improve computational efficiency, golden-section search is used to estimate rotation, and two map data structures are applied to store calculated data. Simulations and experimental results demonstrate that the proposed method can effectively and efficiently correct rigid motion in MR images.

The second contribution of this work is an efficient motion correction method based on fast robust correlation. Translational search can be computationally demanding. A correlation operation can be used to calculate an image match when the matching criterion is the sum of squared errors. However, this approach cannot be used for nonquadratic matching criteria. Fast robust correlation is a computationally efficient search algorithm for translational image matching in the frequency domain. This method can calculate matching surfaces from nonquadratic criteria using a series of high-speed correlations by defining a kernel with sinusoidal terms. The proposed method corrects motion-distorted images by aligning translational motion between images formed by neighboring frequency segments. Since the squared difference kernel is invariant to motion between partial-Fourier images, we adopt the absolute value kernel, which can be easily approximated by sinusoidal terms. Total variation of the sum of partial-Fourier images is chosen as the new matching criterion. FFTs are used to calculate correlations for computational speed. Different search strategies to combine and correct motion over the whole k-space are discussed and compared. The proposed method can perform real-time processing to reduce image motion artifacts significantly in the simulations and MRI cardiac experiments.

The third contribution of this dissertation is a novel data-driven motion correction method for magnitude MR images using generative adversarial networks (GANs). Although the previous proposed methods can correct motion effectively and efficiently, they both require complex-valued raw data. However, raw data is not usually preserved in a clinical environment. In this case the previous two methods cannot be used. GANs (pix2pix model) are implemented to reduce motion artifacts and reconstruct motion-corrupted images through adversarial training between generator and discriminator networks to estimate a motion-corrected image that is close to the reference image. The training set is made of image pairs consisting of motionless reference images and corresponding motion-simulated images. The proposed method is validated by a simulated motion test set and a real motion (experimental) test set.