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Copyright © 2011 American Scientiﬁc Publishers
All rights reserved
Printed in the United States of America
R E S E A R C H A R T I C L E
Journal of Medical Imaging and
Health Informatics
Vol. 1, 1–5, 2011
Overlapped k-Space Acquisition and
Reconstruction Technique for Motion Artifact
Reduction in Magnetic Resonance Imaging
Yasser M. Kadah
Biomedical Engineering Department, Cairo University, Giza 12613, Egypt
A new MRI acquisition strategy based on acquiring the k-space in consecutive overla

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Copyright © 2011 American Scientiﬁc PublishersAll rights reservedPrinted in the United States of America
RESEARCH ARTICLE
Journal of Medical Imaging and Health Informatics
Vol. 1, 1–5, 2011
Overlapped k-Space Acquisition andReconstruction Technique for Motion ArtifactReduction in Magnetic Resonance Imaging
Yasser M. Kadah
Biomedical Engineering Department, Cairo University, Giza 12613, Egypt
A new MRI acquisition strategy based on acquiring the k-space in consecutive overlapped bands was developed.Starting from the general assumption of rigid body motion, we consider the case when the acquisition of thek-space is in the form of bands of ﬁnite number of lines arranged in a rectilinear fashion to cover the k-space areaof interest. We consider cases with an averaging factor of at least 2. Instead of acquiring a full k-space of eachimage and then average the result, we developed a new acquisition strategy based on acquiring the k-space inconsecutive overlapped bands. In case of no motion, this overlap can be used as the second acquisition. Onthe other hand, when motion is encountered, such overlap can be used to substantially reduce motion artifactsin the resultant image. This is achieved by utilizing the overlap area to estimate the motion, which is then takeninto consideration in image reconstruction. We demonstrate the success of this approach using both numericalsimulations as well as real data acquired from a human volunteer. The new method has the potential for practicalapplications to make more efﬁcient use of MRI scanners and making the scanning time lower providing morecomfort to the patient.
Keywords:
Motion Artifact, Magnetic Resonance Imaging, Artifact Suppression, Navigator Echo.
1. INTRODUCTION
Accurate diagnosis in medical procedures has become widelyattainable by the advent of the different medical imaging modal-ities. Among those, magnetic resonance imaging (MRI) is cur-rently one of the most promising non-invasive diagnostic tools inmedicine. In addition to its ability to produce anatomical imagesof remarkable detail and contrast, it can be used to visualizevascular structures, measure blood ﬂow and perfusion, detectneural activation, and identify the metabolic information of dif-ferent areas in the acquired images. Also, its inherently volumet-ric acquisition permits slices at different angles to be computedeasily, which can be advantageous in many applications.One of the major problems with the present MRI technologyis its susceptibility to substantial artifacts when motion occursduring image acquisition. Even though, fast acquisition meth-ods, such as EPI and spiral imaging, provide a solution to thisproblem for some applications, these techniques are extremelysensitive to magnetic ﬁeld inhomogeneity as compared to regu-lar scanning methods and have a generally low signal-to-noiseratio. This makes it difﬁcult to accurately correlate the generatedimages with the physical anatomy because of geometric distor-tion in addition to more profound signal loss within the areas of large susceptibility mismatches. Moreover, when these imagingsequences are used in applications such as functional magneticresonance imaging (fMRI), where a set of slices are acquiredrepeatedly, patient motion persists in the form of low detectionof activation sites as a result of misregistration of images alongthe sequences.
1
Due to practical constraints from the MRI machine hardware,signal-to-noise ratio, and image contrast of MRI, the imagingtime commonly extends to several minutes. As a result, differ-ent parts of the collected k-space are acquired at different timeinstants. In an ideal scenario, the imaged object does not changeduring the period of the experiment, and the image calculated byinverse Fourier transformation is undistorted. However, in clini-cal MRI setups, this scenario is usually not guaranteed, becauseof physiological and occasional voluntary patient motion and canbe even impossible to realize for moving organs such as the heartand abdominal structures. Consequently, the constructed imagessuffer varying degrees of distortion depending on the character-istics of the imaging sequence and the severity of motion duringthe scan duration.Motion artifacts can generally be classiﬁed into either intra-slice or inter-slice motion.
1–2
The ﬁrst is the result of motionin between the acquisition of different portions of the k-spacewhile the second is the result of motion in between acquisitionsof the same slice. An illustration of these types of motion isshown in Figure 1. The techniques in the literature often treated
J. Med. Imaging & Health Infor. Vol. 1, No. 1, 2011
2156-7018/2011/1/001/005 doi:10.1166/jmihi.2011.1007
1
RESEARCH ARTICLE
J. Med. Imaging & Health Infor. 1, 1–5
,
2011
(a)(b)(c)
Fig. 1.
Examples of motion artifacts: inter-slice motion artifact (above) results when images (a) and (b) are averaged to create the ﬁnal image (c) on thesystem. On the other hand, if the same process is repeated with these individual images having an intra-slice motion (below), the result will be a more severecombined intra- and inter-slice motion artifact on image (c) below.
these types in completely different manners with several strate-gies to suppress each type independently. Given their underly-ing similarities, it might be advantageous to treat both problemssimultaneously.Several attempts to solve the problem of intraslice motion arti-fact in MRI have been reported in the literature. In general, theavailable techniques can be classiﬁed into four main categories.The ﬁrst category attempts to suppress relative patient motionamong different k-space lines within a given image through eitherthrough breath holding and chest strapping or by using cardiacand respiratory gating.
7
This minimizes the physiological com-ponent of motion between these lines at the expense of increaseddiscomfort to the patient and/or signiﬁcantly longer acquisitiontimes. The second category uses averaging of different acqui-sitions to suppress the motion artifacts as well as to improvethe signal-to-noise ratio of the ﬁnal image. This can be doneby taking the average of the corresponding k-space lines in anumber of consecutive image acquisitions, or more generallyby composing a weighted average of the two based on opti-mizing a certain objective function under given constraints.
7
18
The third category applies extra magnetic gradient lobes in theimaging sequence to eliminate the effects of motion throughsignal refocusing assuming a simple polynomial model for thismotion.
20
23
This technique is used to minimize signal loss frommoving blood and CSF within a given voxel.
17
Finally, the fourthcategory assumes simple forms of rigid body motion includingtranslational and rotational components and corrects for themin a post-processing step. The motion in this category is esti-mated using external monitoring,
24
navigator echo,
1
2
symme-try constraints,
13
motion periodicity constraint,
8
16
or throughautomated estimation using different measures in postprocessingtechniques.
6
9
10
14
15
19
21
22
25
The effect of translational motioncan be suppressed by post-processing through modifying thephase of the k-space lines according to the a priori knowledgeabout the motion.
11
12
21
In practice, the navigator echo tech-niques are the most useful when they can be incorporated intothe imaging sequence of interest. On the other hand, postpro-cessing techniques are not as useful in practice given their veryhigh computational complexity and convergence problems. Thetechnique in Ref. [6] and its modiﬁcation in Ref. [25] providethe best results in this category.The inter-slice motion problem is a signiﬁcantly simpler prob-lem whereas rigid-body registration between consecutive imagesis sufﬁcient for practical purposes. Among the several availabletechniques to estimate and correct for such motion, the Auto-mated Image Registration (AIR) technique
26
is widely used inMRI applications (such as functional MRI image registration) aswell as in multimodal image registration.In this work, we propose a new approach for suppressingmotion artifacts from both types. The proposed method assumesrigid body motion and corrects for both its translational and rota-tional motion components without need for extra acquisitions.The new method is an extension of an earlier work done byour group
2
3
whereby the ﬂoating navigator is generalized toinclude multiple lines acquired within the regular data acquisi-tion and their data are registered using a similar technique as theAIR technique in the k-space. The new method is veriﬁed usingnumerical simulations as well as real data from a normal humanvolunteer.
2. METHODOLOGY
We consider the case of rigid body motion, which is widelyencountered in magnetic resonance images of the brain andlimbs. The relation between the MR signal and the 2D densitydistribution of the target in the imaging plane is given by,
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RESEARCH ARTICLE
J. Med. Imaging & Health Infor. 1, 1–5, 2011
F k
x
k
y
=
−
−
fxy
exp
−
j
2
k
x
x
+
k
y
ydxdy
(1)where
F k
x
,
k
y
is the MR signal,
k
x
and
k
y
are the spatial fre-quency coordinates in the readout and phase-encoding directions,respectively,
fxy
is the density distribution of the nonmovingimaging target, and
xy
are horizontal and vertical coordinatesin the imaging plane. In (1) it is seen that the MRI signal is the2-D Fourier transform of
fxy
. Considering the case when thek-space is acquired as consecutive bands, as in the case of seg-mented EPI, PROPELLER, and the proposed method, one canneglect the inter-band motion. This is true because the entireband is acquired during a single read-out period. Thus, planarrigid motion parameters during the acquisition can be regardedas a function of the band number. A planar rigid motion is thecombination of translational and rotational motions. It is wellknown that the rotation of an object about the center of theimage domain results in the same rotation of its k-space, whiletranslational shift results in a linear phase term multiplied in thek-space.
2
Thus the effect of the motion can be written as,
F
d
k
x
k
y
=
exp
−
j
2
x
k
x
+
y
k
y
F
k
x
k
y
(2)Here
F
d
k
x
,
k
y
is the motion-distorted MRI signal and
x
,
y
,and
are the translation in the
x
-direction, the translation in the
y
-direction and the rotation angle, respectively, and
F
k
x
k
y
isdeﬁned as,
F
k
x
k
y
=
F k
x
cos
+
k
y
sin
−
k
x
sin
+
k
y
cos
(3)The motion correction problem is that of estimating theunknown motion parameters
x
,
y
, and
and using these param-eters to reconstruct an artifact-free image. An illustration of thismotion when a k-space band is acquired is shown in Figure 2.Starting from the general assumption of rigid body motion,we consider the case when the acquisition of the k-space is inthe form of overlapping bands of ﬁnite number of lines arrangedin a rectilinear fashion to cover the k-space area of interest. Wealso assume that an averaging factor of at least two is desired(i.e., Number of excitation or NEX
≥
2), to make the inter-slicemotion problem nontrivial. Instead of acquiring a full k-spaceof each image and then averaging the result, we propose a newacquisition strategy based on acquiring the k-space in consec-utive bands having (100
·
(NEX-1)/NEX)% overlap going fromone end of the phase encoding direction to the other end. Forexample, when NEX is 2, the overlap will be 50%. Figure 3illustrates the acquisition strategy proposed. Each band consistsof a ﬁnite number of phase encoding lines acquired in a single
Overlap areaRotational motionNo motion orTranslational motion
Fig. 2.
Different cases in k-space band acquisition: no motion or transla-tional motion (left), rotational motion while acquiring the same band (center).The overlap area between consecutive acquisitions in the worst case sce-nario is shown on the right.
Average+ =k-space 1k-space 2Acquisition withoverlapped segmentsMotionestimation &correctionMotion-freeaverageConventional acquisition methodNew acquisition method
Fig. 3.
Basic idea of the new method. Instead of doing the image acqui-sitions independently then performing the average, the acquisitions will beoverlapped in such a way to allow the new overlap localization strategy toreconstruct an artifact-free image while maintaining the same acquisitiontime.
shot so that the inter-band motion effect is limited. In case of nomotion, this overlap provides the additional acquisitions requiredby the selected NEX value, while in the case when inter-bandmotion occurs; the proposed overlap provides the informationthat enables the determination of motion parameters as a gener-alization of the ﬂoating navigator echo.
2
The process of estimating the motion parameters is done intwo steps: rotation estimation then 2-D translation estimation.From the geometry of the acquisition in the k-space in Figure 2,the presence of rotation amounts to varying the area of overlapbetween the two consecutive bands or blades. Hence, given thatthis geometry is known a priori, if we compute a similarity mea-sure between the areas of overlap at each possible rotation anglewithin a predetermined range of possible angles, it is possibleto determine the rotation angle as the one having the highestsimilarity measure. The utilized method is based on computingthe correlation coefﬁcient of the magnitudes of the points in theoverlap areas from the two different acquisitions normalized bythe number of points in the overlap area. This allows for the sim-ilarity measure to be independent of the size of the overlappingarea. This is different from
3
where only an arc navigator is usedin that using the whole overlap area makes the overall SNR of theestimation better. Hence, there is an expected trade-off betweenaccuracy and computational complexity in these two techniques.Once the rotation is determined, it is straightforward to determine
Estimate rotation from overlap localizationEstimate 2-D translationModify k-space values and sampling matrixPerform griddingCorrected imageOverlapped band acquisition
Fig. 4.
Basic block diagram of the new method.
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RESEARCH ARTICLE
J. Med. Imaging & Health Infor. 1, 1–5
,
2011
the 2-D translation using the ﬂoating navigator echo technique.
2
This process is done between each two consecutive bands withcorrection for translational motion for the most recently acquiredband. On the other hand, the rotational motion can be correctedonly during the reconstruction process given the sampling non-uniformity introduced into the k-space by this type of motion.The reconstruction includes an interpolation step to calculate thek-space data on a rectilinear grid using gridding algorithms.
4–5
A block diagram of the new technique is shown in Figure 4.
3. RESULTS
The proposed algorithm was veriﬁed using simulated motion onnumerical phantoms as well as real human head images acquiredfrom a normal human volunteer obtained on a Siemens Mag-netom Trio 3T system. The volunteer was instructed to moveduring the data acquisition to induce motion artifacts. The acqui-sition parameters were as follows: imaging plane: sagittal, imag-ing sequence: fast spin echo, TR: 500 ms, TE: 15 ms, Matrix:256
×
256, and ETL: 16, NEX: 2. Figure 5 shows an exampleof rotation estimation using the proposed method. The correla-tion coefﬁcient is computed and for different overlap angles andthe angle at which maximum correlation is found is used as therotation estimate. In Figure 6, the results of applying the newmethod to numerically simulated axial brain slices are shown.Motion-corrupted images were generated from a single axial slicesimulating random intra-slice and inter-slice motion artifacts as
Fig. 5.
Example of rotation estimation using the proposed method. The cor-relation coefﬁcient is computed and for different overlap angles and the angleat which maximum correlation is found is used as the rotation estimate.
Motion-freeMotion-corruptedCorrected
Fig. 6.
Results of applying the new method to simulated data of axial brainslices of a human. As can be observed, substantial improvement is seen butringing artifacts are visible in the corrected image due to possible k-spacevoids.
No motionDifferencebetween correctedand distortedMotiondistortedCorrected
Fig. 7.
Results of applying the new method to real data of sagittal brainslices of a human volunteer. Arrows point to areas in the image where cor-rection is clearly visible. The difference image show the error removed bythe new method.
shown in Figure 6(b). When the new method was applied to esti-mate and correct the simulated motion, a signiﬁcant improvementin the reconstructed image was obtained as can be observed inFigure 6(c). A wide range of motion parameters was simulatedto test the accuracy of the proposed method and simulation of noisy data was performed to test the robustness of the solutionunder different SNR conditions. The results indicate that the newmethod is capable of detecting rotations with a mean error as lowas
±
0.1 degrees (which is more accurate than
3
) and translationwith an error that is always less than
±
0.2 of the pixel width.Given that the similarity measures used implicitly average thedata, the technique was found to be robust against noise in ourexperiments. Figure 7 shows the results obtained from the realdata. The arrows show several locations where the improvementis most visible. As can be noticed, the correction substantiallyimproves the resolution of the image. However, ringing artifactsappear more prominent in the corrected image due to the problemof k-space voids shown in Figure 8 (also previously reported inRef. [10]). Further investigation is needed to address this problemfrom both acquisition and reconstruction perspectives.
Fig. 8.
Illustration of the problem of k-space voids where the rotatedbands cause small scattered areas of the k-space to be missing thusleaving residual sampling artifacts in the reconstructed image after motioncorrection.
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