Magnetic Resonance in Medicine 63:339–348 (2010)
Motion Correction Using an Enhanced Floating Navigator and GRAPPA Operations Wei Lin,1* Feng Huang,1 Peter Bo¨rnert,2 Yu Li,1 and Arne Reykowski1 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 throughplane and nonrigid motion). Phantom and in vivo imaging experiments with turbo spin-echo sequence demonstrate the correction of severe motion artifacts. Magn Reson Med C 2009 Wiley-Liss, Inc. 63:339–348, 2010. V Key words: motion correction; parallel imaging; rotational motion; floating navigator; GRAPPA
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
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Invivo Corporation, Philips Healthcare, Gainesville, Florida, USA. Philips Research Europe, Hamburg, Germany. *Correspondence to: Wei Lin, Ph.D., Invivo Corporation, Philips Healthcare, 3545 SW 47th Ave, Gainesville, FL 32608. E-mail:
[email protected] Received 6 May 2009; revised 23 July 2009; accepted 14 August 2009. DOI 10.1002/mrm.22200 Published online 13 November 2009 in Wiley InterScience (www.interscience. wiley.com). 2
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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 phaseencode (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 kspace, 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 kspace 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 kspace 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
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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. MATERIALS AND METHODS
FIG. 1. The scheme for the proposed enhanced FNAV method. a: The signal along a phase-encoding line ky ¼ 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.
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 ¼ 0 line, FNAV (see Fig. 1a) samples along ky ¼ kf = 0, where kf is typically small to ensure sufficient signal-tonoise ratio (SNR) and to avoid phase-wrapping along ydirection. The FNAV signal is ZZ Fðkx Þ ¼ f ðx; yÞ ej2pðkx xþkf yÞ dxdy [1] Taking a one-dimensional inverse FT along the kx direction, the following complex ‘‘generalized projection’’ for the prescribed FNAV line can be obtained: Z PðxÞ ¼ f ðx; yÞ ej2pkf y dy [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 (Dx, Dy) occurs, the corresponding generalized projection signal reads Z PDx;Dy ðxÞ ¼ f ðx Dx; y DyÞ ej2pkf y dy ¼ ej2pkf Dy P0;0 ðx DxÞ
½3
Here, the subscript denotes the amount of motion. Therefore, 2D in-plane translation introduces both a shift of signal profile (depending on Dx) and an additional complex phase factor (depending on Dy) for the generalized projection. In the original FNAV paper (10), Dx and Dy are detected separately in two steps. In this work, both Dx and Dy are detected in a single step. For this purpose, the normalized correlation function is proposed: CðdxÞ ¼
Pmoved Pref jPmoved j Pref
[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(dx) is always less than or equal to 1. The latter is only attained at dx ¼ Dx when Pmoved ðxÞ ¼ Pref ðx DxÞej/
[5]
In other words, the magnitude of correlation will be 1 when there is only 2D in-plane translation present. Dx can be detected by the location of the correlation maxima, while Dy can be determined from the phase of the maximum correlation by Dy ¼ /=2pkf
[6]
Equation 6 shows that there is a tradeoff between the range and the accuracy of Dy detection concerning the selection of kf value, or the phase-encoding position for FNAV line. The range of Dy that can be uniquely determined from / without any phase wrapping is 1/kf. Therefore, a smaller kf allows a larger range for Dy 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 / more dramatically, resulting in higher Dy error. Therefore, a moderate value of kf ¼ 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
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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: ðDh; DxÞ ¼ arg maxjCðh; xÞj h;x
Cðh; xÞ ¼
Pmoved Pref ðhÞ jPmoved j Pref ðhÞ [7]
Here, h is k-space rotation angle. Once again, Dy 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 hr 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: Dky ¼ Nx tanðhr =2Þ=FOV
[8]
For example, if the readout matrix size is 256 and the rotation search range is 10 , then Dky ¼ 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 ¼ 8/ FOV. This is similar to 5/FOV previously proposed for the radius of the orbital navigator (8). 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-
FIG. 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 ¼ 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).
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 inplane 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
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FIG. 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.
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 kspace. When a GRAPPA extrapolation kernel is used, each acquired readout line is expanded along the phaseencode 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 kspace are filled in, a 2D inverse Fourier transform is performed for image reconstruction. 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 þ 1, 2N þ 1, 3N þ 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
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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 kspace 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., throughplane and nonrigid) motion. In this work, the following empiric weight is used according to the average maximum correlation values for each subset: 0 if Cm < 0:9 w¼ [9] ðCm 0:9Þ 10 if 0:9 < C m < 1 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 kspace 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
FIG. 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.
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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 ¼ 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 ¼ 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 (600 ms). To validate the motion-detection capability of the enhanced FNAV method, a series of phantom experiments was carried out using the modified turbo spinecho 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 motioncorrection imaging experiments were carried out on the same system, using an eight-element head coil, an eightelement 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 ¼ 5 mm, echo train length ¼ 16, number of slices ¼ 10 (phantom, head and spine) and 20 (knee). Both T1- and T2-weighted images were acquired. T1weighted 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
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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 ¼ 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.
RESULTS 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 inplane 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 throughplane motion. While the maximum correlation remains very close to 1 for in-plane rotation (average ¼ 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.
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
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FIG. 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: Inplane rotation. d: The maximal correlation versus rotation angles for both in-plane and through-plane rotation.
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. 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).
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 ¼ 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,
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FIG. 6. T1-weighted knee images acquired with an eight-channel coil and a linear phase-encoding order (TR/TE ¼ 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.
according to Eq. 9, through-plane motion artifacts were further alleviated (Fig. 8d). 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
