Patient motion is a major source of image artifacts for MRI. Breath-holding is effective in reducing patient respiratory motion. However, for many pediatric patients, breath-holding is difficult to perform. For patients under anesthesia, breath-holding is only possible through deep anesthesia and ventilator suspension. Thus, we develop a non-rigid motion correction scheme using PROPELLER and low-rank minimization to enable free-breathing MRI and to hopefully eliminate the need of anesthesia for pediatric imaging.

Data Acquisition: PROPELLER^[1] is adapted to a 2D RF-spoiled GRE sequence. A Cartesian k-space "blade" is collected such that this blade can be reconstructed with high-spatial-resolution in the readout dimension and low-spatial-resolution in the phase-encode dimension. To extend the width of the blade while minimizing motion, the blade is accelerated by a factor of 2. The acquisition is repeated with blades rotated by golden-ratio angle increments^[2], ~68.75° (Figure 1). For multi-slice imaging, one blade is collected for each slice before the next blade is collected.

Image Reconstruction: Each blade is first reconstructed using GRAPPA^[3]. An initial PROPELLER reconstruction is performed for phase correction, global rotation correction (if appropriate), global translation correction, and correlation weighting^[1]. Next, a circularly-symmetric spatial window is applied to limit the image signal to a small localized spatial region. This spatial window is shifted throughout the image to construct a bank of overlapping spatial windows $$$w[n]$$$. For each window $$$w[n]$$$, the following steps are performed:

1. Local motion estimation using low-rank: Because the reference image is unknown and the image after windowing changes depending on the translation correction, low-rank minimization^[4] is used to estimate local motion. Low-frequency k-space for each blade is gridded as $$$m$$$. For $$$n$$$-th window, motion of each blade $$$(d_x[n],d_y[n])$$$ is estimated by solving the following optimization using Gauss-Newton algorithm:$$(d_x[n],d_y[n])=\arg\min_{(d_x,d_y)} \|CW_n(m e^{-i2\pi(k_xd_x + k_yd_y)})\|_*.$$

The spatial window $$$w[n]$$$ is applied as matrix $$$W_n$$$. Matrix $$$C$$$ reformats the data into a matrix with image pixels and channels as rows and blades as columns. The norm $$$\|A\|_*$$$ represents the nuclear norm of $$$A$$$. Motion correcting $$$m$$$ (using $$$e^{-i2\pi(k_xd_x + k_yd_y)}$$$) should minimize the nuclear norm, or rank, of the matrix.

2. Localized PROPELLER reconstruction: Estimated local motion $$$(d_x[n],d_y[n])$$$ is then applied to correct the data. Correlation weights are computed for the spatially windowed blades after motion correction to account for through-plane motion at that particular spatial region. The entire dataset, without the spatial window, is then reconstructed.

After performing the motion estimation and PROPELLER reconstruction for each $$$w[n]$$$, the final image is pieced together through an autofocusing algorithm^[5]: for each image location, image pixels from the sharpest image in the bank of reconstructed images are selected. The reconstruction pipeline is summarized in Figure 1.

Experimental Setup: Healthy and patient volunteers were scanned with IRB approval and informed consent using a 3T GE MR750 scanner. Specific scan parameters are summarized in Table 1.

The different motion paths estimated using the localized spatial windows are shown in Figure 2. Similar A/P motions from respiration were estimated from the windows placed in the upper left and upper right corners of the abdomen. The R/L motion in opposing directions suggest expansion/contraction of the abdomen.

In the volunteer study, sharpening of the anatomical structure can be appreciated after performing the entire reconstruction compared to an initial PROPELLER reconstruction (Figure 3). Residual artifacts are more apparent in the axial scan when compared to the breath-hold scan (also acquired with PROPELLER).

The patient study demonstrates the performance of the approach with gadobutrol enhancement. Autofocusing combines the correction of the different regions into a fully corrected image (Figure 4).

Low-rank minimization attempts to increase robustness of localize motion estimation and potentially enables higher-resolution navigators with matrix-completion algorithms^[4]. For certain window locations, there may be no structures present for accurate motion estimation. Thus, autofocusing allows for another local motion estimate to be used instead. Because images were collected with T₁-weighting, contrast-enhancement improves image contrast and provides more structures for local motion estimation.

Axial scan suffers from more residual motion. Since respiratory motion is primary in the S/I direction, axial scan suffers from considerable through-plane motion. This motion is minimized with a coronal orientation. The simple localized translational motion model can be potentially extended for correcting more complex motions.