Motion correction using an enhanced floating navigator and GRAPPA operations



A method for motion correction in multicoil imaging applications, involving both data collection and reconstruction, is presented. The floating navigator method, which acquires a readout line off center in the phase-encoding direction, is expanded to detect translation/rotation and inconsistent motion. This is done by comparing floating navigator data with a reference k-space region surrounding the floating navigator line, using a correlation measure. The technique of generalized autocalibrating partially parallel acquisition is further developed to correct for a fully sampled, motion-corrupted dataset. The flexibility of generalized autocalibrating partially parallel acquisition kernels is exploited by extrapolating readout lines to fill in missing “pie slices” of k-space caused by rotational motion and regenerating full k-space data from multiple interleaved datasets, facilitating subsequent rigid-body motion correction or proper weighting of inconsistent data (e.g., with through-plane and nonrigid motion). Phantom and in vivo imaging experiments with turbo spin-echo sequence demonstrate the correction of severe motion artifacts. Magn Reson Med, 2010. © 2009 Wiley-Liss, Inc.

In many MR applications, imaging artifacts caused by patient motion remain a major challenge. Severe motion artifact could be a source of misdiagnosis, or a reduced throughput for the MR scanner, due to the need to repeat scans, which does not necessarily guarantee improved image quality. Over the years, both prospective and retrospective techniques have been proposed for motion compensation. For periodic physiologic (e.g., cardiac and respiratory) motion, effective motion-compensation methods have been developed and are accepted in clinical practice. A gating signal, from electrocardiography (ECG), respiratory belt, or navigator echo, is often utilized to time the data acquisition, as well as to reject and reorder data (1–3). Random, spontaneous patient motion, however, is much more challenging due to its irregularity and complexity. First, depending on the frequency of the motion, there may be insufficient data at any single patient position. Therefore, it is often necessary to correct for motion-corrupted data rather than simply rejecting a portion of them, as is often done for periodic physiologic motion. Second, spontaneous patient motion often consists of both translational and rotational, in-plane and through-plane and even nonrigid motion components. Therefore, any robust motion correction technique must be able to handle different types of motion.

The “self-navigating” properties of radial, spiral, and periodically rotated overlapping parallel lines with enhaced reconstruction (PROPELLER) acquisition schemes have been extremely useful in detecting and compensating for various motion artifacts (4–6). However, these techniques require nonconventional (i.e., non-Cartesian) imaging sequences and reconstruction algorithms, which represent some additional challenges regarding hardware imperfection such as field inhomogeneity and gradient timing delay. As a result, they have not been not widely used in clinical practice.

One of the most effective means for motion detection and compensation is the navigator echo technique and its variants (7–10). In the original formulation of the technique (7), an extra line at the center of k-space is repetitively acquired either along the readout (x) or phase-encode (y) direction. One can then compare the projection of the imaged object along either direction by taking a one-dimensional inverse Fourier transform (FT) of the acquired signal, in which translational motion appears as a simple shift in the corresponding projection. When navigator signal is acquired along a circular path in the k-space, rotational motion can also be detected (8,9). Recently, a modified version of the original navigator technique, called floating navigator (FNAV) (10), was proposed for two-dimensional (2D) translational motion sensing and correction. With a single extra readout line at ky ≠ 0, translation along both orthogonal directions can be detected by comparing the phase of the corresponding FNAV signals. In this work, it is shown that the capability of FNAV can be enhanced to further detect rotation and inconsistent (e.g., through-plane) motion, in addition to translation, if a reference k-space region surrounding the FNAV line position is also acquired.

For retrospective motion compensation techniques, reconstruction of motion-corrupted data following motion detection remains a challenging problem. When through-plane motion occurs, k-space data become inconsistent because signal from different slices are mixed together. In-plane motion correction is also nontrivial when large rotation happens. While translational motion only introduces a linear phase term to the k-space data, rotational motion causes data sampling along a similarly rotated k-space readout line. For Cartesian acquisitions, this can result in a “pie-slice” missing k-space data problem, which makes the subsequent reconstruction challenging (11). Recent developments in parallel imaging techniques provide new opportunities for motion correction and artifact reduction. The coil sensitivity profiles provide additional information for the correction of artifacts either directly in the image domain (12–14) or in the k-space domain through estimating data points near the sampled trajectories (15–17). Among various parallel imaging methods, the generalized autocalibrating partially parallel acquisition (GRAPPA) (18,19) method is adopted in this work since its kernels can be flexibly positioned for either k-space interpolation or extrapolation.

The present work combines the motion-detection capability of the enhanced FNAV and the reconstruction flexibility of GRAPPA technique to compensate for translational, rotational, and inconsistent (e.g., through-plane) motion in multicoil imaging applications. We present a detailed description of the technique, followed by evaluation in both phantom and in vivo experiments.


Enhanced FNAV

FNAV was previously proposed to detect translation along both readout (x) and phase-encode (y) directions with a single readout (10). Unlike the traditional navigator technique that involves acquiring signal along the ky = 0 line, FNAV (see Fig. 1a) samples along ky = kf ≠ 0, where kf is typically small to ensure sufficient signal-to-noise ratio (SNR) and to avoid phase-wrapping along y-direction. The FNAV signal is

Figure 1.

The scheme for the proposed enhanced FNAV method. a: The signal along a phase-encoding line ky = kf ≠ 0 is repetitively acquired during the scan. In addition, a reference (gray) region centering on the FNAV line position is also acquired at the beginning of the scan. b: To detect rotation, the reference data are rotated to various angles prior to the computation of a correlation measure.

equation image(1)

Taking a one-dimensional inverse FT along the kx direction, the following complex “generalized projection” for the prescribed FNAV line can be obtained:

equation image(2)

Instead of a simple projection of the object, the generalized projection represents the projection of the object function modulated by a periodic function (with a frequency of kf) along the phase-encode direction. If a 2D in-plane translation with a displacement of (Δx, Δy) occurs, the corresponding generalized projection signal reads

equation image(3)

Here, the subscript denotes the amount of motion. Therefore, 2D in-plane translation introduces both a shift of signal profile (depending on Δx) and an additional complex phase factor (depending on Δy) for the generalized projection.

In the original FNAV paper (10), Δx and Δy are detected separately in two steps. In this work, both Δx and Δy are detected in a single step. For this purpose, the normalized correlation function is proposed:

equation image(4)

Here, * denotes cross-correlation, |·| denotes L2 norm, and Pmoved and Pref are the motion-corrupted and the reference-generalized projections, respectively. Since correlation in the image space is equivalent to data multiplication in the k-space, the numerator in the Eq. 4 is computed rapidly by first multiplying the motion-corrupted FNAV signal with the complex conjugate of reference FNAV data, followed by a one-dimensional inverse FT. To achieve subpixel resolution, zero-filling can be carried out prior to the inverse FT. Since the L2 norm of a generalized projection equals the L2 norm of the corresponding FNAV data, the denominator in the Eq. 4 can also be computed directly in k-space.

According to the cross-correlation theorem, the magnitude of a normalized cross-correlation function C(δx) is always less than or equal to 1. The latter is only attained at δx = Δx when

equation image(5)

In other words, the magnitude of correlation will be 1 when there is only 2D in-plane translation present. Δx can be detected by the location of the correlation maxima, while Δy can be determined from the phase of the maximum correlation by

equation image(6)

Equation 6 shows that there is a tradeoff between the range and the accuracy of Δy detection concerning the selection of kf value, or the phase-encoding position for FNAV line. The range of Δy that can be uniquely determined from ϕ without any phase wrapping is 1/kf. Therefore, a smaller kf allows a larger range for Δy detection. A FNAV line with a smaller kf value also has a higher SNR. On the other hand, a smaller kf amplifies the phase error in ϕ more dramatically, resulting in higher Δy error. Therefore, a moderate value of kf = 8/field of view (FOV) is used in this work, consistent with recommendations from the original FNAV paper (10).

While translation only introduces a linear phase factor to the k-space data, rotation around the image center causes the same amount of rotation in k-space. Therefore, we propose to acquire a reference k-space region near the FNAV line, as shown in Fig. 1a. This allows the correlations of the projection Pmoved with multiple copies of Pref, each corresponding to the FNAV line position when the entire k-space is rotated to different angles, as illustrated in Fig. 1b. The global correlation maximum then yields both rotation and 2D translation:

equation image(7)

Here, θ is k-space rotation angle. Once again, Δy can be determined from the phase of the maximum correlation according to Eq. 6. The computation cost of the proposed motion detection method for each FNAV line is a one-dimensional FT for each rotation angle searched, in addition to the shared overall cost to rotate the reference data to various angles.

The width of FNAV reference region (gray rectangles in Fig. 1) can be determined by the desired search range for rotation θr and the matrix size along readout direction Nx, so that the FNAV line always remains within the rotated reference region (see Fig. 1b). To ensure this the following condition has to be fulfilled:

equation image(8)

For example, if the readout matrix size is 256 and the rotation search range is 10°, then Δky = 22/FOV. In practice, a smaller reference region around the FNAV line is usually sufficient due to the reduced signal contribution near the edge of the k-space, as will be demonstrated.

The sensitivity of the rotational motion detection using FNAV increases when kf increases. For the same amount of rotation, the FNAV lines obtained at larger kf value are shifted by a larger amount in the azimuthal direction (c.f. Fig. 1b), similar to the orbital navigator with a larger radius (8). Another way to look at this problem is to compare the signal profile of generalized projections. Figure 2a compares the magnitude of the generalized projection of FNAV lines at different kf values, using a brain image data set. Since FNAV lines with larger kf values contain more high-frequency information, they are more sensitive to changes caused by rotation. This is confirmed by the profile of maximum correlation versus rotation angles, as shown in Fig. 2b. However, SNR considerations favor a moderate kf value, such as kf = 8/FOV. This is similar to 5/FOV previously proposed for the radius of the orbital navigator (8).

Figure 2.

The effect of FNAV line position (kf) on the accuracy of rotational motion detection demonstrated for a brain dataset. a: The generalized projection of the FNAV line at different kf values (0–16), in the unit of 1/FOV, FOV = 230 mm. The variation of magnitude provides sensitivity to rotation. b: The maximum correlation versus rotation angles, for FNAV line at different kf positions (0–16).

When the imaging object moves and the coils remain stationary, the accuracy of motion detection using the proposed FNAV method depends on a relatively uniform coil sensitivity profile. Therefore, a channel combination method previously proposed (20) is used to combine FNAV signals from different coils prior to the motion detection.

When only in-plane rotation and translation are present, the proposed correlation measure will yield a magnitude close to 1 at the correct rotation angle and shift along readout direction. However, if motion (e.g., through-plane motion) destroys the consistency of the k-space data, the magnitude of the maximum correlation measure will be less than 1, as will be demonstrated below. Since the correlation value still gauges the similarity between motion-corrupted and reference k-space data, one can use this information to reject or weight these inconsistent data, similar to the approach previously proposed for PROPELLER (6) and real-time averaging (21).

In summary, the FNAV concept is enhanced by acquiring a reference k-space region around it and applying the correlation method proposed for the detection of in-plane translation and rotation, as well as for the indication of inconsistent (e.g., through-plane) motion.

Reconstruction of Motion-Corrupted Data With GRAPPA Operations

In partial parallel imaging methods such as simultaneous acquisition of spatial harmonies (SMASH), sensitivity encoding (SENSE), and GRAPPA (18,22,23), the additional spatial encoding provided by coil sensitivity profiles has been used to reduce the number of acquired phase-encoding lines. The same concept is used in this work, not for scan acceleration, but to fill in missing k-space data caused by motion (e.g., rotation) and to reduce motion artifacts. In this context, the framework of estimating missing k-space points through linear combination of neighboring acquired data points from multiple coil elements, first established in the GRAPPA method (18,19), proves to be very flexible. In this work, two methods for the reconstruction of motion-corrupted data benefiting from the GRAPPA method are proposed, based on linear and interleaved phase-encoding order, respectively.

The first method uses a GRAPPA extrapolation kernel to correct for rotational motion when a linear phase encoding order is used. As shown in Fig. 3a, in-plane rotational motion causes missing “pie slices” in the k-space. When a GRAPPA extrapolation kernel is used, each acquired readout line is expanded along the phase-encode direction into a k-space segment. A shearing method is then used to rotate the segment to its actual position (24), therefore filling in missing data. The width of the extrapolation region (light gray rectangle in Fig. 3a) is determined by the number of coil elements and their sensitivity profiles. A phased array with a high acceleration capability will support a wider extrapolation segment, therefore allowing for a larger filling area in the k-space. When all missing “pie slices” in the k-space are filled in, a 2D inverse Fourier transform is performed for image reconstruction.

Figure 3.

Two proposed approaches to correct for motion-corrupted data using GRAPPA operations. a: When a linear phase-encode order is used, a GRAPPA extrapolation kernel is used to estimate the missing “pie-slice” (darker gray) regions in k-space caused by rotation. The narrow white rectangle is the acquired k-space line affected by in-plane rotation. Two light-gray rectangles are data estimated using a GRAPPA extrapolation kernel. b: When an interleaved data ordering is used, a GRAPPA interpolation kernel generates missing k-space (dashed) lines from an interleaved dataset (solid lines) prior to the application of subsequent rotation of the entire k-space.

The second method regenerates multiple copies of full k-space using GRAPPA interpolation kernels. In this method, k-space data are acquired in multiple interleaved subsets, with phase-encoding line positions of [0, N, 2N, 3N…]; [1, N + 1, 2N + 1, 3N + 1…]; … [N − 1, 2N − 1, 3N − 1…]. Here, N is the interleaving factor and is chosen according to the accelerating capability of the phased-array coil. Note that each data subset further contains data from several echo-trains (shots), each of which contains one FNAV line and therefore one set of motion information. For each subset, a GRAPPA interpolation kernel is used to reconstruct a full k-space. This full k-space can then be corrected for both translational and rotational motion by applying proper linear phase factors and data rotation, as shown in Fig. 3b. However, translational and rotational correction is applied at different temporal resolutions. Phase correction for translational motion is applied shot by shot, while an average rotation is applied to the entire subset after the full k-space regeneration. When a large discrepancy in rotation exists among different shots within each subset, the k-space sampling pattern is no longer a group of equally spaced parallel lines. This makes the application of GRAPPA interpolation operation difficult; therefore, data from such subset were discarded in our implementation. Finally, multiple full k-spaces from different subsets are combined in a weighted manner prior to the final inverse Fourier transform in order to reduce the contribution from subsets with significant inconsistent (e.g., through-plane and nonrigid) motion. In this work, the following empiric weight is used according to the average maximum correlation values for each subset:

equation image(9)

Even when inconsistent motion occurs for all interleaved data subsets, motion artifacts can also be reduced due to an “artifact averaging” mechanism. It has been previously shown in continuous moving-table MRI that the combination of multiple copies of regenerated k-space with GRAPPA operations (GRAPPA averaging) cancels out aliasing artifacts from different data subsets (17). The same mechanism also works for motion artifacts reduction since different data subsets will have different, noncoherent motion artifacts.

Imaging Experiments

A conventional multislice 2D turbo spin-echo sequence is modified to allow motion detection with the enhanced FNAV method, as shown in Fig. 4. An additional echo train is added before the actual imaging phase-encoding steps, and use of the FNAV reference. To reduce possible interference to motion detection accuracy introduced by the T2 decay, FNAV reference data are acquired in a center-out manner, with the first echo train centering on the desired FNAV line position (kf = −8/FOV). The reason behind such a design choice is that rotational motion detection is most sensitive to the data fidelity around the FNAV line position at ky = kf. Within each subsequent echo train, an additional echo is first acquired at FNAV line position, followed by normal imaging echoes. Motion detected from the FNAV line is then used to correct for all echoes in the same echo train. In this work, an identical object position is assumed for all echoes within a single echo train, since echo train duration (<100 ms) is typically much shorter than the pulse repetition time (TR) (>600 ms).

Figure 4.

The diagram for a turbo spin-echo imaging sequence with the enhanced FNAV. The first echo train (train 0) acquires the FNAV reference data in a center-out fashion. The subsequent echo trains acquire a FNAV line first, followed by normal imaging echoes.

To validate the motion-detection capability of the enhanced FNAV method, a series of phantom experiments was carried out using the modified turbo spin-echo sequence on a 3.0-T Achieva scanner (Philips, Best, Netherlands). To examine the accuracy of 2D in-plane translation detection, the imaging FOVs were shifted by 3.1, 6.3, 9.5, 12.7, and 15.9 pixels in either the readout or phase-encode direction. FNAV data were subsequently processed to determine the amount of in-plane shifts and compared with the actual shifts. To examine the accuracy of in-plane rotation, the phantom was manually rotated to five different positions (up to around 15°) within the same imaging plane. An image registration procedure was then used to determine the actual rotation of the phantom to an accuracy of 0.1°. FNAV data were then processed to determine the rotation angles and compared with the actual rotation angles. To examine the ability to detect through-plane motion, the prescribed imaging orientation was rotated along through-plane direction to various angles in the range of [0°, 10°], with 2° increments. FNAV were processed to determine the maximal correlation.

Phantom and in vivo brain, knee, and spine motion-correction imaging experiments were carried out on the same system, using an eight-element head coil, an eight-element knee coil, and a 16-channel spine coil (In Vivo, Gainesville, FL), with following scan parameters: FOV 230 × 230 mm2 (phantom and head), 200 × 200 mm2 (knee), 250 × 250 mm2 (spine), matrix size 256 × 256, slice thickness = 5 mm, echo train length = 16, number of slices = 10 (phantom, head and spine) and 20 (knee). Both T1- and T2-weighted images were acquired. T1-weighted images were acquired using relatively shorter TRs and center-out echo ordering with short echo time (TE), while T2-weighted images were acquired using longer TRs and linear echo ordering with longer TE. The detailed TR/TE values for each experiment are given in the caption for the figures.

In each experiment, a motion-free reference scan was always acquired first. For in vivo experiments, the volunteer was then requested to move randomly inside the scanner while two more scans were acquired, using a linear and an interleaved data ordering, respectively. In the phantom experiment, the phantom was also manually moved during these two scans. For the linear phase encode order, phase-encode lines of adjacent echo trains were incremented by 1. For the interleaved phase encode order, phase-encode lines of adjacent echo trains within each data subset were incremented by 4, resulting in an interleaving factor of 4. As a result, each data subset (64 phase-encoding lines) consisted of four echo trains, each with 16 echoes.

After data acquisition, raw data were saved and processed. A shearing method (24) is used to rotate FNAV reference region to various angles in the range of [-5°, 5°] with an increment of 0.5° prior to the computation of maximum correlation. GRAPPA extrapolation operators used a 5 (readout) × 1 (phase-encode) kernel with an extrapolation factor of 5, meaning that two additional phase-encoding lines are estimated on both sides of each acquired phase-encoding line. GRAPPA interpolation operators used a 5 (readout) × 4 (phase-encode) kernel with a reduction factor R = 4. The calibration data for GRAPPA consisted of 32 central phase-encoding lines in k-space. Two different choices for the GRAPPA calibration data were investigated, either directly from the echo trains acquired at the beginning of the scan or directly from the actual acquired motion-corrupted k-space. The typical computation time of the proposed method, including both motion detection and correction, is about 10 sec for each imaging slice on a 2.2-GHz personal computer.


Validation of Enhanced FNAV

Figure 5 shows results of the phantom experiments to validate the motion-detection capability for the enhanced FNAV method. In-plane shifts detected using FNAV along both readout and phase-encode direction are highly accurate, with a range up to 16 pixels and the coefficient of determination R2 > 0.99 (Fig. 5a,b). For in-plane rotation, the enhanced FNAV is able to accurately detect rotation up to 15° (Fig. 5c). Please note that although theoretically an FNAV reference region with 45 phase-encoding lines (according to Eq. 8) is needed to detect a rotation range of ± 10°, only 16 phase-encoding lines are sufficient in this case. This demonstrates that data near the edge of k-space have a minimal contribution to the accuracy of the correlation method proposed for motion detection. Figure 5d further demonstrates the ability of the proposed FNAV method to detect through-plane motion. While the maximum correlation remains very close to 1 for in-plane rotation (average = 0.998), through-plane motion is characterized by a significant decrease in the maximum correlation values. Obviously, the amount of change in maximum correlation will depend on how rapidly imaging features change between different slices. For this experiment, a through-plane rotation of 2° results in a maximal correlation of 0.97, while a 10° through-plane rotation reduces the maximal correlation to 0.89.

Figure 5.

Validation of motion detection capability for the enhanced FNAV in a phantom experiment. a-c: The motion parameters derived from the enhanced FNAV were compared with the actual motion. a: Shift along readout direction. b: Shift along phase encoding direction. c: In-plane rotation. d: The maximal correlation versus rotation angles for both in-plane and through-plane rotation.

Translational/Rotational Motion Correction

For all phantom and in vivo imaging experiments, the proposed method significantly reduced the motion artifact and improved the image quality. All images presented in this work are phase encoded along the horizontal axes.

Figure 6 shows results from a T1-weighted knee imaging experiment, where data were acquired in a linear order along the phase-encode direction. Motion introduces severe ghosting and blurring artifacts (Fig. 6b), which severely degrades the overall image quality. The enhanced FNAV was able to detect an abrupt motion (a translation of 2.5 mm and a rotation of 1.3°) during the middle of data acquisition for this imaging slice. When only translational motion correction was applied, significant ghosting artifact remains (Fig. 6c). When both rotation and translation detected from the enhanced FNAV method were corrected, the majority of the ghosting artifacts were removed (Fig. 6d). However, the image appears blurred, since a “pie slice” of k-space is missing due to rotational motion. Finally, when the missing data are filled in with the GRAPPA extrapolation operation, followed by both rotational and translational correction, the best image quality is attained (Fig. 6e). The boundary of muscle and tendon, the intricate pattern within the trabecular bone, is sharply delineated, similar to the reference motion-free scan (Fig. 6a). Some minor residual artifact is likely due to through-plane motion, which is not accounted for when data are acquired in a linear phase encoding order. Figure 6f and g shows zoomed-in images of the bone region, which clearly demonstrates the improvements in image quality with the GRAPPA extrapolation.

Figure 6.

T1-weighted knee images acquired with an eight-channel coil and a linear phase-encoding order (TR/TE = 650/15 ms). a: Motion-free image. Weak ghost along vertical (readout) direction is due to residual magnetization from other slices. b: Motion-corrupted image. c: Image corrected for translation only. d,e: Image corrected for both rotation and translation, without (d) and with (e) GRAPPA extrapolation to fill in missing pie-slice of k-space caused by rotation. f,g: The 2× zoomed-in view for the bone region of images for (d) and (e), respectively.

Combined rotational/translational correction for data acquired in an interleaved data order is demonstrated in a brain imaging experiment (Fig. 7). This dataset was acquired with an eight-element head coil array and an interleaving factor of 4. Compared with motion-free image (Fig. 7a), the motion-corrupted image exhibits strong ghosting artifacts (Fig. 7b). Figure 7e shows the in-plane rotation detected from the enhanced FNAV data, showing that the amount of motion within different data subsets (separated by vertical lines) is quite different. When all data subsets are corrected using their respective average rotation angles and combined for the final reconstruction, SNR is maximized (Fig. 7c). However, some minor residual artifact does exist due to residual shot-to-shot motion within subsets 1 and 3. If these two interleaves are excluded from the final reconstruction, then artifact is further reduced, at a cost of slightly lower SNR (Fig. 7d).

Figure 7.

Images from a T2-weighted brain imaging experiment (TR/TE = 3000/80 ms), acquired with an eight-channel coil and an interleaving factor of 4. a: Motion-free image. b: Motion-corrupted image. c,d: Motion-corrected image with the proposed method, without (c) and with (d) rejection of subsets with strong intraset rotation. e: In-plane rotation detected from FNAV, with different interleaved subsets separated by vertical lines.

Through-Plane and Nonrigid Motion Correction

Figure 8 shows through-plane motion correction results in a phantom experiment, where data were acquired with an eight-head coil and an interleaved data ordering (N = 4). When compared with motion-free reference image (Fig. 8a), motion-corrupted image shows significant ghosting artifacts (Fig. 8b). Figure 8c shows images corrected for in-plane rotation and translation, where data from all four data subsets are weighted equally. Residual artifact (arrow in Fig. 8c) shows some image features from neighboring slices, indicating the presence of through-plane motion. This is confirmed by the maximal correlation value detected from the enhanced FNAV data (Fig. 8e). Both data subsets 1 and 2 give an average maximal correlation close to 1.0, while the latter parts of interleaf 3 and the entire interleaf 4 give an average maximal correlation value near 0.94. When these correlation values were used to weight inconsistent data less, according to Eq. 9, through-plane motion artifacts were further alleviated (Fig. 8d).

Figure 8.

Through-plane motion correction demonstrated in a phantom imaging experiment. Data were acquired with an interleaving factor of 4 and an eight-channel head coil. a: Motion-free reference image. b: Motion-corrupted image. c,d: Motion correction without (c) and with (d) weighting based on maximal correlation of FNAV lines. The arrow points to a through-plane artifact that is reduced by data weighting. e: Maximum correlation detected from FNAV signals. Different interleaved data subsets were separated by vertical lines.

The capability of the proposed method to correct for nonrigid body motion is demonstrated in a spine dataset acquired with four interleaves (Fig. 9). Since the prescribed sagittal imaging volume includes head, cervical spine, and a part of thoracic spine, the nodding and swallowing movement of the subject is intrinsically nonrigid body motion. Severe ghosting artifacts due to motion can be observed around the head and near the cervical spine (Fig. 9b). The maximal correlation values detected from the enhanced FNAV are less than 0.95 for all echo trains, which is an indication of nonrigid body motion. The amount of in-plane motion detected, in contrast, was very small (rotation <1° for all echo trains). After GRAPPA interpolation and data combination, Fig. 9c shows that ghosting artifacts were mostly removed, while the image quality was maintained at regions with little motion (e.g., lower part of the image). The difference image (Fig. 9d) shows that motion-induced ghosts were removed after correction.

Figure 9.

Nonrigid motion correction in T2-weighted spine imaging. Data were acquired with a 16-channel coil and an interleaving factor of 4 (TR/TE = 3000/120 ms). a: Motion-free image. b: Motion-corrupted image. The difference between (a) and (b) near the eye area is due to the change of subject position. c: Motion-corrected image with the proposed method. d: The difference image between (b) and (c) amplified by five times.


The proposed method was shown to be effective in a variety of motion-correction applications by combining the motion detection capability of the enhanced FNAV and the reconstruction flexibility provided by the GRAPPA operations.

The enhanced FNAV method was shown to detect in-plane translation and rotation in a robust manner. When compared with previous orbital navigator method for rotational motion detection (8), the FNAV method acquires data along a linear k-space path, which is less demanding on the gradient performance of the MR scanner. The FNAV reference region required for robust motion detection is typically much smaller than the theoretical requirement (Eq. 8), due to the reduced signal contribution from the edge of the k-space. The proposed correlation function also provides a means to gauge the consistency of the data, therefore enabling the alleviation of through-plane and nonrigid body motion artifacts.

The present work proposes two approaches for the reconstruction of motion-corrupted data with GRAPPA operators, depending on whether data are acquired linearly or interleaved along the phase-encode direction. If data are acquired linearly, each phase encoding line is treated independently. GRAPPA extrapolation operation is used to fill in missing “pie slices” of k-space caused by rotational motion, followed by data rotation and translational phase correction. If data are acquired in an interleaved manner, each interleaved subset is treated as a data block. Although translational motion is still corrected on a shot-by-shot basis, an average rotation is applied for the entire interleaved subset. Multiple full k-spaces are generated using GRAPPA interpolation prior to subsequent correction. These two approaches have their respective advantages and disadvantages. Since GRAPPA extrapolation is most accurate for data points near the acquired k-space line, a linear acquisition scheme is more suited for continuous motion. In contrast, interleaved acquisition is more suited for large, sudden motion where large rotation can be applied separately for each interleaved data subset after the regeneration of the full k-space. However, as demonstrated in Fig. 7c and d, there is a tradeoff between motion artifact reduction and SNR if intraset rotation is significant.

For data acquired with a linear phase-encode order, our approach for rotational correction is to compute k-space data points on a rotated grid, followed by data rotation with shearing. In the future, it may be worth comparing the method presented here with other methods that have been previously proposed in the literature, such as those based on matrix inversion (11,25) and GRAPPA operator gridding (26). However, it is expected that these methods will have much higher computation cost due to the more computationally intensive steps involved. For the data acquired with interleaved subsets, the proposed method may introduce some SNR penalty since the actual g-factor introduced by GRAPPA interpolation is typically higher than the ideal value, which is the square root of the interleaving factor.

Two choices of GRAPPA calibration data have been investigated in this work, either using the separate echo train acquired at the beginning of the scan (also used as FNAV reference), or simply using the central 32 lines of motion-corrupted k-space data. Each choice has its advantage and disadvantage. Using separate echo trains reduces the chance that calibration data themselves are corrupted by motion. On the other hand, T2 decay may introduce error when calibration data are acquired using long echo train(s). In all in vivo experiments, using the central 32 lines of motion-corrupted data as autocalibration signal gave satisfactory results. This is understandable since the GRAPPA calibration procedure is equivalent to the estimation of the coil sensitivity profile, which typically has a low spatial frequency and therefore is less sensitive to motion.

Although data presented in this work were all acquired using a turbo spin-echo sequence, the method can be readily applied to other segmented acquisition methods such as echo-planar imaging and segmented magnetization prepared gradient echo imaging. For these sequences, motion detected from the FNAV signal can be used to correct for all other echoes in the same echo train. For other imaging sequences, the proposed method is still applicable, provided that an FNAV line is acquired with sufficient temporal resolution allowing for motion detection. Although the FNAV line is always acquired as the first echo in this work, it is possible to acquire it at other positions within the echo train, provided that SNR is sufficient.

In this work, the proposed method is used to correct motion artifact for fully acquired datasets. Although the proposed enhanced FNAV method can easily be extended to detect motion from a partially acquired dataset, the subsequent reconstruction problem will be much more challenging. For example, the k-space data could become very sparse when large rotation occurs.

When compared with previous motion-correction techniques exploiting parallel imaging methods (12–17), the method proposed here explicitly corrects for both in-plane translation and rotation. In addition, data inconsistency introduced by through-plane and nonrigid motion is alleviated with proper data weighting and GRAPPA averaging. The proposed method does require the acquisition of additional FNAV reference data, which is typically around 5% of the overall scan time. Further clinical studies are needed to prove the expected benefits in actual practice.