Scout accelerated motion estimation and reduction (SAMER)

Abstract

Purpose: To demonstrate a navigator/tracking-free retrospective motion estimation technique that facilitates clinically acceptable reconstruction time.

Methods: Scout accelerated motion estimation and reduction (SAMER) uses a single 3-5 s, low-resolution scout scan and a novel sequence reordering to independently determine motion states by minimizing the data-consistency error in a SENSE plus motion forward model. This eliminates time-consuming alternating optimization as no updates to the imaging volume are required during the motion estimation. The SAMER approach was assessed quantitatively through extensive simulation and was evaluated in vivo across multiple motion scenarios and clinical imaging contrasts. Finally, SAMER was synergistically combined with advanced encoding (Wave-CAIPI) to facilitate rapid motion-free imaging.

Results: The highly accelerated scout provided sufficient information to achieve accurate motion trajectory estimation (accuracy ~0.2 mm or degrees). The novel sequence reordering improved the stability of the motion parameter estimation and image reconstruction while preserving the clinical imaging contrast. Clinically acceptable computation times for the motion estimation (~4 s/shot) are demonstrated through a fully separable (non-alternating) motion search across the shots. Substantial artifact reduction was demonstrated in vivo as well as corresponding improvement in the quantitative error metric. Finally, the extension of SAMER to Wave-encoding enabled rapid high-quality imaging at up to R = 9-fold acceleration.

Conclusion: SAMER significantly improved the computational scalability for retrospective motion estimation and correction.

Keywords: parallel imaging; retrospective motion correction; wave-CAIPI.

Figure 1:. Comparisons of alternating and SAMER motion optimization.

Alternating methods use two separate optimizations to repeatedly update the coupled optimization variables $x$ (image vector) and $\theta$ (motion parameters). This separation can lead to convergence issues as updates of $x$ and $\theta$ will be computed on inaccurate information. Moreover, the reconstruction is computationally demanding as repeated updates of $x$ (millions of imaging voxels) are needed. SAMER utilizes a very rapid scout acquisition as the image estimate $\tilde{x}$. This leads to a highly efficient optimization approach that is fully separable across the shots and does not require repeated updates of $x$. Note that SAMER only considers six rigid body motion parameters per motion optimization which results in a much smaller per shot motion problem than the alternating methods (6xN_shot optimization variables).

Figure 2:. Illustration of sequence reorderings for 3D cartesian sampling.

The proposed linear + checkered reordering combines jittered checkerboard sampling in the center of k-space with linear sampling across the remainder of k-space. This retains the desirable linear signal evolution along k_y and in non-steady-state sequences will lead to comparable contrast and blurring as obtained from a pure linear reordering. The signal evolution of a checkered reordering also follows a linear trend but may exhibit undesirable stairsteps (white arrow).

Figure 3:. Optimized sequence reordering.

(a) Radial reordering enabled overall good motion estimation accuracy however, small motion estimation errors are observed in the translation values. Better agreement with the ground motion parameters was obtained for checkered and linear + checkered sampling which provided roughly comparable accuracy. Linear reordering did not allow for accurate motion estimation due to insufficient spectral overlap between the acquired k-space data of a given shot and the low-resolution scout $\tilde{x}$ and was thus omitted in this figure. (b) The final image reconstruction using linear + checkered reordering converged more rapidly than using checkered sampling (ground truth motion values were used). This is demonstrated by the illustrated reconstructions (e.g., after 5 iterations) and the root-mean-squared-error (RMSE) plot. Note that convergence with linear reordering is only shown for comparison but would be infeasible due to inaccurate motion estimation.

Figure 4:. Optimized scout acquisition.

The scout was acquired at low spatial resolution and high parallel imaging acceleration to reduce added scan time to the MR exam. At R=12, the scout reconstruction resulted in residual aliasing artifacts (c.f. yellow arrows). Moreover, necessary changes to the sequence reordering in all low-resolution scout scans led to a slightly different imaging contrast (c.f. red arrows) when compared to the high-resolution reference. Despite these differences, SAMER yielded accurate motion estimation across all shots. Note, that the motion trajectory from Fig. 3a was used in this simulation.

Figure 5:. Computational efficiency.

Faster motion estimation was achieved through (a) coil compression and (b) a reduced model approach where the motion optimization was computed based on a subset of readout voxels. (c) Further speed-up was obtained from our custom gradient descent optimizer which required roughly 2x fewer forward model evaluations than MATLAB’s general-purpose optimizer fminunc while achieving similar motion estimation accuracy. Note, that the motion trajectory from Fig. 3a was used in this simulation.

Figure 6:. Statistical evaluation of motion estimation accuracy.

The mean error and standard deviation of the estimated translation and rotation was computed across 58 realistic motion trajectories.

Figure 7:. Motion correction for MPRAGE (R=4).

Across all three acquisitions, SAMER removed the majority of motion artifacts allowing better depiction of fine anatomical structures (c.f. yellow arrows). This image quality improvement was also reflected by more than 27% improvement in root-mean-squared error (RMSE). Note, that all reference images were obtained from a separate motion-free acquisition with identical sequence parameters.

Figure 8:. Motion correction for T2- and FLAIR-weighted SPACE (R=4).

SAMER improved the image quality allowing, e.g., better delineation of gray and white matter (c.f. yellow arrows). The reference images were obtained from separate motion-free acquisitions with identical sequence parameters. Note, that the stair-case appearance in the estimated motion trajectory is caused by the slow instructed subject motion.

Figure 9:. Motion correction for highly accelerated Wave MPRAGE (R=6 and R=9).

The synergistic combination of SAMER and Wave-encoding facilitated highly accelerated motion robust imaging, revealing fine anatomical structures despite several degrees of head rotation. The reference images were obtained from separate motion-free acquisitions with identical sequence parameters. Note, that the stair-case appearance in the estimated motion trajectory is caused by the slow instructed subject motion.