7

Original Research

Dynamic Image Reconstruction: MR Movies from Motion Ghosts' Qing-San Xiang, PhD

R. Mark Henkelman, PhD

It has been previously shown that an image with motion ghost artifacts can be decomposed into a ghost mask superimposed over a ghost-free image. The present study demonstrates that the ghost components carry useful dynamic information and should not be discarded. Specifically, ghosts of different orders indicate the intensity and phase of the corresponding harmonics contained in the quasiperiodically varying spin-density distribution. A summation of the ghosts weighted by appropriate temporal phase factors can give a time-dependent dynamic image that is a movie of the object motion. This dynamic image reconstruction technique does not necessarily require monitoring of the motion and thus is easy to implement and operate. It also has a shorter imaging time than point-by-point imaging of temporal variation, because the periodic motion is more efficiently sampled with a limited number of harmonics recorded in the motion ghosts. This technique was tested in both moving phantoms and volunteers. It is believed to be useful for dynamic imaging of time-varying anatomic structures, such as in the cardiovascular system. Index terms: Artifact correction

.

Cine studies

-

lniage processing * Motion

JMRI 1992: 2579-685 Abbreviations: AC = alternatingcurrent. DC = direct current, DIR dynamic image reconstruction. ROI = region of interest.

=

' From the Department of Medical Blophysics and Sunnybrook Heallh Science Centre, Research, University of Toronto. Toronto. Ontario. Canada. Recelved April 13.1992: revision requested July 24: revision received and accepted September 8. Supported in part by the Medlcal Research Council of Canada. the National Cancer Institute of Canada. and GE Medical Systenis of Canada. Q.S.X. is a recipient of a Medlcal Research Council of Canada Postdoctoral Fellowship Award. Address reprint requests to Q.S.X.. Department of Radiology. S t Paul's Hospital. 1081 Hurrard St. Vancouver. Brltish Columbia. Canada. V6Z 1Y6. ' SMRI. 1992

IN TWO-DIMENSIONALFourier transform magnetic resonance (MR)imaging ( 1.2). it is well known that movement of the object in any direction may induce artifacts along the phase-encoding direction (3.4). These artifacts may potentially cause diagnostic misinterpretation when they are superimposed on the anatomic image. For periodic or quasi-periodic physiologic motion, the artifacts appear as equally spaced replicas of the moving structures and are described as "ghosts." Recently, a ghost phase cancellation method was introduced to eliminate such artifacts (5,6). The method uses a decomposition procedure to separate the ghost mask from the desired image. With temporally interleaved data acquisitions, a set of three images are acquired that have a defined relationship among their ghosts, so that both the ghost-free image and ghost mask can be determined. The ghost-free image obtained, being the time-averaged spin-density distribution over the entire course of imaging, is only locally blurred because of the motion. In the present study, it is demonstrated that the ghost component, which was previously discarded, actually contains useful information about the motion. Because the ghosts are nothing but the Fourier components at various frequencies, contained in the time-dependent, spin-density distribution, adding together all the available harmonics weighted by the appropriate Fourier temporal phase factors allows a dynamic image to be reconstructed that is in effect an MR movie of the object motion, representing the unblurred anatomic configuration at different times. Conventionally, MR imaging of periodically moving objects requires real-time monitoring of the motion to prevent artifacts such as ghosting and blurring (7-9). For cardiovascular imaging, the electrocardiogram signal is typically used to control pulse sequence execution and/or data manipulation (8.10). Other techniques use additional MR signal acquisitions to monitor the motion ( 11-14). In cine MR imaging, retrospective sorting and interpolating of the data are done to form complete k-space data sets for various motion phases, which can be further reconstructed by Fourier transformation into a movie of the moving

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object. Successful application of these cine techniques requires reliable and convenient monitoring of the motion, which poses technical challenges and results in long imaging times. With the proposed dynamic image reconstruction (DIR)technique, however, no type of motion monitoring is necessary. Thus, DIR has an advantage in terms of ease and convenience in implementation and operation. This is achieved by using time-interleaved acquisitions that enable decoding of the necessary dynamic information already stored in the ghosts. DIR can also have a higher data-acquisition efficiency than point-by-point measurement of temporal fluctuation, because motion is sampled in the Fourier domain a s a limited number of harmonics that are recorded as ghosts on the images rather than a s a series of discrete time-point images. A s a result, the total imaging time for obtaining the movie can be substantially reduced relative to conventional cine techniques. We believe that the DIR technique can potentially be used a s an alternative to conventional cine MR imaging and should find its applications in the dynamic imaging of time-varying anatomic structures, such a s in the cardiovascular system.

MATERIALS AND METHODS Theory The ghosting mechanism in two-dimensional Fourier transform MR imaging has been well analyzed (4,6,15) and was summarized in an earlier report (6). Herein, we outline only the relevant conclusions and discuss the procedure of movie reconstruction. In a ghosted two-dimensional Fourier transform image, (a)there is always an image component I. representing the time-averaged value of spin density during imaging, which is blurred in a way similar to the motional blurring seen with any other imaging modality (ie, the image component I. is the time-averaged spin-density distribution, or the direct current [DC] value], and ( b )there are equally spaced ghost components of different orders on each side of the image Io, propagating along the phase-encoding direction. These ghost components correspond to harmonics of various orders contained in the temporal fluctuation. A phase cancellation method has been developed (6)to separate the ghost components from the ghostfree image Io(x,y ), thus eliminating the ghost artifacts. The ghost mask g(x,y)that was extracted, although obviously containing information about the motion, was simply discarded. Below, we will discuss how to make use of these ghosts for dynamic imaging of the moving object. In our previous work, it was concluded that the displacement of a given ghost from its source is directly proportional to the temporal frequency of that specific harmonic (6.15).This can be expressed as d, = nP,,

where d,, is the distance between a ghost and its source, n the order of the harmonics (which can be either positive or negative integers), and Po the spacing between adjacent ghosts measured in pixels. Po was also shown to be equal to the total number of cy680

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cles of the motion during the entire course of imaging. It is easy to see that Po is related to the fundamental temporal frequency of the motion wo and total imaging time To by wo =

2.rrP,/To.

(2)

For a given pixel in which spin density is changing with time, the DC component is represented by the pixel value in the central image Io; however, the oscillatory alternating current (AC) components are recorded as signal intensities and phases of various harmonics, which are mapped in the complex ghosts at a distance d , from the pixel, depending on their temporal frequencies. This fact suggests the following equation for DIR: p(x.y:t)= ~ ~ ( x ,+yC) g ( x , y + d , ) e x p ( i n w , t ) , ( 3 ) n

where p(x,y;t) is the reconstructed time-varying image, Io(x,y)the ghost-free image representing the DC component of the spin density, g(x,y) the extracted ghost mask, and t the time in which the spin-density distribution changes. The summation index n represents integers with values from negative to positive, corresponding to harmonics of different orders on both sides of the pixel at location (x,y). Note that the displacement d , is equal to nPo in the phase-encoding direction (y direction) for the ghost mask g(x,y),before the summation is performed. The time-dependent Fourier phase factors exp ( i n o ot ) describe the temporal evolution of the harmonics. Equation ( 3 ) states that the dynamic image as a function of time t is the DC image I. plus AC oscillations of different orders. The amplitude and phase of the oscillations are given by the complex ghost mask g(x.y ) at displaced locations along the phase-encoding direction. During DIR, Equation ( 3 )should be applied only to the source points of ghosts. In other words, one should map the weighted ghost components back only to their origin, or artifacts may result. The details of implementation are discussed below.

Implementation The proposed technique was implemented on a 1.5-TSigna imager (GE Medical Systems, Milwaukee). Studies were performed in both phantoms and volunteers. The phantom for the experiment consisted of a Plexiglas block with five 1.5-cm-diameter bottles mounted diagonally in it (6).The bottles were filled with propylene glycol. During imaging, a wooden bar beneath one side of the block was twisted back and forth manually in synchrony with the quasi-periodic respiration of the operator. Movements with different amplitudes in an oblique direction were produced for different bottles. The raw data were saved and transferred to a Sun Sparcstation computer (Sun Microsystems. Mountain View, Calif) for processing and display. Separation of the DC image and ghost mask,-With the use of time-interleaved and phase-encodingorder-shifted acquisitions identical to those previously introduced (61, three ghosted complex images were obtained. At each pixel, they were decomposed

into image and ghost a s described by the following equations: j = 1.2.3

l,=Io+gj

(4a)

2

(4b) 91 9 3 = g2. In Equation (4). 10,I,. and g, are complex variables at each pixel, denoting the DC image, the acquired ghosted images, and the ghost masks, respectively. To obtain the ghost-free DC image component Io(x,y)and the ghost masks gj(x,y), the acquired images IJ(x,y) are processed pixel by pixel according to the solution of Equation (4). which is given by '

(11 - 121,

g1

r, + I,

- 21,

tor that is also derivable from the phase difference can be mapped back to its source and a dynamic image reconstructed. In practice, however, this approach is sensitive to local noise and may be affected by phase wraparound, which occurs when the three ghost masks gj are acquired with a large phase-encoding-order shift Ak ( 6 ) Therefore, . we took another approach that uses only the global parameter Po and general properties of the DC and AC components. We determined whether each (x,y)point was a source point of ghosts before applying Equation ( 3 ) .The following simple test conditions were applied pixel by pixel to distinguish the source points of ghosts from ghosted pixels:

(5b) (5c)

u3

g3 =

I, +

1,12 l3 - 21, . -

(5d)

As previously described (6).when applying equation (5)the denominator of each expression was compared in each pixel with the noise level in the original images I,(x,y). Only if the noise was smaller than the denominator was equation (5)used: otherwise, 1, was computed as the simple complex average of the three original images, and the ghost masks gJwere simply set to zero. This test avoids any possible large artifactual values that may result if the denominator in equation (5)is very close to zero. In practice, the noise level used can be simply considered the standard deviation in the differential image: Ag(x,y)= g,(x,y) g,(x.y)= Z,(x,y) - l,(x,y),where i f j . This is simply the difference between any two of the three original ghosted images. DZR.-After the DC image lo(x,y)and the ghost masks g,(x,y) ( j = 1 , 2 , 3 )are obtained, they are processed according to Equation (3)to generate the dynamic image p(x,y;t).To apply Equation (31,it is necessary to know Po, the total number of cycles of the motion during the entire acquisition. This number can be obtained if any motion monitoring devices (710) or monitoring signal acquisitions ( 11-14) are used. Alternatively,Po can be readily derived from the available images. Since Po equals the ghost spacing in pixels on the ghosted images, a simple analysis of the ghost mask provides its value. Such analysis can be either a manual measurement on the screen or more sophisticated, automatic computer algorithms, such as an autocorrelation computation of the magnitude of the ghost masks Ig,(x.y)I or the differential image

1 Ag(x.y I.

As mentioned, Equation (3)should be applied only to the source points of ghosts. In fact, the displacement of any ghost from its source point is directly proportional to the known phase difference between any pair of the three ghost masks gJobtained from Equation 15) (6).Thus, in principle, on the basis of this known phase difference, every pixel value in a ghost mask g(x.y)multiplied by a temporal phase fac-

where max 1. . .) and min (. . .] denote operations that select the largest and smallest values. respectively, within the braces. If Equations (6a)and (6b)are satisfied at an (x,y) point, then this point is recognized as a source point of ghosts and Equation (3)is applied; otherwise, Equation (3)is not applied at this point The following facts and the output is simply Io(x,y). are the physical bases for the test in which Equation (6)is applied: 1. The discrete power spectrum of the periodically fluctuating magnetization in a pixel usually has lower peaks for higher frequencies; thus, the DC component of the time-varying spin density should have a greater magnitude than the AC components, or, roughly speaking, the image is usually brighter than the ghosts (somewhat analogous to the property of k-space data in which the central DC value is usually the highest). This corresponds to Equation (6al.This condition is generally valid for most motions unless the motion-induced phase modulation is so great that the DC component, which is the time averaging of the magnetization, is seriously reduced. In that case, the motional phase change can be minimized by using more sophisticated gradient waveforms ( 16). 2. The pixel value (ideally zero) at a ghost source point in the ghost mask image has a smaller magnitude than the positive and negative ghosts on either side of it, a distance Po pixels in the phase-encoding direction. This is described by Equation (6b).

RESULTS With the moving phantom, three ghosted complex images were obtained from a TR-interleaved spinecho pulse sequence (6).Figure l a is the magnitude display for one of the three ghosted images, with the vertical axis chosen as the phase-encoding direction. The central bright spots are the blurred images of the moving bottles, and ghosts were generated on either side of the bottles. Both ghosting and blurring appeared to increase with the amplitude of the motion. By substituting the three complex images into Equation ( 5 ) .a ghost-free image Io(x,y)and three ghost masks gj(x,y)were obtained. Volume2

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Figure 1. Magnitude images ITR msec/TE msec = 300/30, field of view = 48 cm, section thickness = 1 cm, matrix size = 256 x 256) illustrate image-ghost decomposition. (a) On one of the three ghosted images of the moving phantom, ghosts are seen on both sides of the central image. Ghosting and blurring increase with the amplitude of the motion. from left to right. (b)The DC image component I. from Equation (5a)represents the time-averaged spin-density distribution. Note that the circular bottles are locally blurred and appear oval. ( c ) One of the three ghost masks obtainable from Equation (5).Dynamic information is recorded in the ghosts. a.

Figure l b is the magnitude of image lo(x,y),calculated from Equation (5a),and represents the timeaveraged spin density during the course of the acquisition. Ghosts are removed, but blurring is still seen. Figure Ic is the magnitude ofg,(x,y).calculated from Equation (5b1, the first of the three ghost masks gi. The two complex data sets in Figure l b and l c contain complete information regarding the DC and AC components, respectively, of the time-varying spin density. By combining the complex data of Figure 1b and l c according to Equation (3).a dynamic image p(x,y;t )was reconstructed. It is displayed in Figure 2 as a series of representative magnitude images describing the configurations of the moving object at different times. The bottles now appear a s circles rather than ovals, indicating the absence of motion blurring. Also, with the square region-of-interest (ROI)reference cursor, it can be clearly seen that the bottles move from upper left to lower right with time, a s they did in the experiment. The phase-encoding shift Ak was two steps (6)and the number of cycles of motion ( P o )during the entire acquisition was 32. This Po was obtained by a measurement on the magnitude repre, Po sentation of the differential image ( A g ( x , y ) (since simply equals the ghost spacing in pixels. The total imaging time To was 3 x TR (300 msec) x 256, or 230.4 seconds ( =: 3.8 minutes): the factor of 3 was 682

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b.

C.

due to the three TR-interleaved (6)acquisitions. Another experiment was conducted with a volunteer who waved one side of his hand up and down quasi-periodically in the magnet during imaging. One of the three acquired images, with both ghosting and blurring, is shown in Figure 3a. After the complex data were processed according to Equation (3),a dynamic image was obtained. It is displayed in Figure 3b-3e as “snapshots”of the moving hand, as if obtained at four different times. The imaging parameters were the same as in the previous experiment except that Po was 36 and Ak was three steps (6).Again, Po was measured on the available image as the ghost spacing in pixels. The motion traversals demonstrated were not large but were believed to represent a realistic clinical situation. As seen from Equation ( 3 ) ,an essential difference between the DIR technique and conventional cine MR imaging is that the dynamic image p ( x ,y ; t ) is a continuous function of time rather than a limited number of movie frames. The discrete images in Figures 2 and 3 were used solely for the purpose of presentation. Although only four representative movie frames from each experiment were presented in these stationary images, snapshots of the moving object at any other time can be easily generated by using corresponding t values in Equation ( 3 ) For . example, 16 such movie

a. b. C. d. Figure 2. Dynamic images p(x,y; t ) , reconstructed from the complex data of Figure l b and lc, of the moving phantom at 0.0 (a), 1.8 (b), 3.6 ( c ) , and 5.4 (d) seconds (same imaging parameters as in Fig 1). The unblurred circular bottles appear to move from upper left to lower right. as they did in the experiment. The fixed ROI frame is provided for reference. Images at other times can be generated by using corresponding t values in Equation (3).

b. C. d. e. Figure 3. Magnitude images of a moving hand. (a) One of the three ghosted images of the moving hand shows ghosting and blurring due to the motion. (b-e) Dynamic images of the moving hand at 0.0 (b). 1.6 ( c ) , 3.2 (d),and 4.8 (e) seconds. The imagingparameters were the same as in Figure 2. The thumb side of the hand moves up, which can be appreciated by examining the distance between the thumb [the digit on the extreme right) and the bottom boundary of the fixed R01 frame. a.

frames have been produced and displayed in a cine loop a s a continuous movie.

DISCUSSION Although three extracted ghost masks are available, any one of them, when combined with Io, is sufficicnt

for DIR. The redundant data were used in this study only to separate the ghosts from the ghost-free image. Obviously, the other two ghost masks can be processed in the same way to reconstruct two other movies. A movie with an improved signal-to-noise ratio can be obtained by averaging the three sets of data. Of Volume2

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course, a proper temporal delay At (see Appendix) must be introduced between the movies before averaging. lnstead of using Io(x,y)and individual ghost masks gi(x,y)(j= 1, 2, 3 ) for DIR, an alternative is to use the differentialimage: Ag(x,y)= gi(x,y) - gj(x,y)= I,(x,y)- I,(x,y), where i f j .Such differential images can be obtained more easily than the ghost masks g, and contain sufficient information for DIR. This option can avoid all the nonlinear processing steps in Equations 5b-5d. and thus can generally result in better noise behavior. Similarly, the signal-tonoise ratio of the final output can be further improved by averaging dynamic images reconstructed from all independent differential images. More details for this alternative option for DIR are included in the Appendix. If only the local dynamics are of interest and global ghost suppression is not desirable ( 17,18),then, with this option, a movie of the local ROI can be obtained from only two time-interleaved acquisitions. Data processing for DIR is performed in the standard complex image domain, and the operations are rather simple: thus, the computational load is negligible and the time overhead can be ignored for an online image reconstruction. Besides the ease of implementation and operation, the DIR technique can substantially reduce the total imaging time relative to that of conventional cine MR imaging, in which motion is imaged point by point throughout one motion cycle. In fact, the Fourier components of the temporal oscillation are recorded a s ghosts displaced in the phase-encoding direction. Thus, the spatial capacity of the image is actually being used to accommodate temporal information. This is the intrinsic reason for the reduced total imaging time. (This may also suggest an economical strategy for cine image storage. ) The spatial-temporal encoding capacity trade-off is feasible because of the Fourier characteristics of MR imaging. The trade-off also relies on the fact that the signal-modulated region is sparsely distributed in space. Caution should be used when the source of ghosts has a large area, because possible overlapping between ghosts of different orders may complicate the ghosted image and more sophisticated reconstruction algorithms may have to be considered. However, this kind of overlapping between ghosts should be distinguished from the overlapping of a ghost (g)with other anatomic structures (lo).The latter case is well handled by the algorithm and is completely solved (6). Ghost sources are particularly sparse in angiographic imaging of the vascular system. Therefore, DIR seems to be most suitable for vascular applications. A number of investigators are developing nontriggered MR velocity measurements of pulsatile flow ( 17,181,in which only the time-averaged velocity is extracted from the phase map of the central image I, and ghosts are not used. As a dynamic extension of these measurements, the proposed DIR method can produce velocity measurements at various times, provided that a velocity sensitization gradient is applied ( 16.19)and phase maps of the complex dynamic image are displayed. With the present method and with other nontriggered imaging techniques (17,18),ghost overlap and wraparound should be avoided. Ghost spacing can be

controlled by the appropriate choice of imaging parameters based on an estimate of the rate of motion ( 17). More effectively,phase-encoding orders other than the standard sequential order can be used to adjust ghost separation, since ghost distribution is determined by the k-space signal modulation function (6,15), which is highly dependent on k-space data collection strategies. In these cases, some motion monitoring would be useful for estimating the rate of motion. In the present study, the proposed DIR technique has been introduced on the basis of quasi-periodic motion. However, this type of motion is not a fundamental requirement for applying the technique. This technique may also be useful for a monotonic signal change such a s that produced by a small object moving across the field of view during imaging, or b y a regional bolus of contrast agent injected into tissue, provided that the phase-encoding order is arranged in such a way that the k-space signal modulation function appears quasi-periodic. This phase-encoding strategy can be considered the inverse of the ROPE (respiratory-ordered phase encoding) technique (9). ROPE effectively transforms quasi-periodic motion into monotonic motion, whereas our method could do the reverse. A full discussion of this issue is beyond the scope of this report and will be presented elsewhere. In the present study, only rotational rigid body motion was used in the experiments, for simplicity of implementation. However, this is not a fundamental requirement for the algorithm to be valid. Any other types of dynamic change in the magnetization (eg, translation. phase modulation, dilation, compression, and even through-plane motion) are equally well described by the algorithm, which generally accounts for any quasi-periodic temporal signal variation in each pixel regardless of cause. In conclusion, it has been demonstrated that an MR movie can be reconstructed from only three (or even two) time-interleaved image acquisitions. Monitoring of the motion, although sometimes useful, is not necessary. The proposed DIR technique can also have a high data-acquisition efficiency. Thus, compared with conventional cine MR imaging, the DIR technique is advantageous in terms of both ease of implementation and operation and shorter imaging times. This technique is believed to be useful for the dynamic imaging of time-varying anatomic structures, such a s in the cardiovascular system.

APPENDIX The easily obtainable differential image Ag(x,y)= gi(x,y)- g,(x,y)= I,(x,y)- I,(x.y) (where i f j )is not only useful for noise level and ghost spacing ( P o )estimation, as mentioned, but also can be directly combined with Io(x,y)to reconstruct the dynamic image p(x,y;t ) . Consider two movies pl(x,y:t ) and p2(x,y; t ) reconstructed from two ghost masks gl(x,y)and g2(x,y), respectively. According to Equation (3).we have pl(x,y:t)=~,(x,y)+ C g , ( x , y+dn)exp(ino,t) ( A I ) n

and

p2(x,y;t)=lo(x.y)+ z g 2 ( x , y+dn)exp(inoot). (A21 n

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However,

References 1.

pz(x.y;t)= p,(x,y;t+ At)

+ x g , ( x , y+ d,) exp ( i n w 0 t )exp ( i n woAt),

= lo(x,y)

2.

n

(A31

where At is 3(Ak? 1/3)TR,a known delay between the motions in the two movies. This delay is equivalent to a translational k-space shift for the signal modulation function, which is due partly to the intentionally introduced phase-encoding order shift of Ak steps and partly to a “natural shift” of 1/ J steps for J TRinterleaved acquisitions (6). The existence of such a natural shift is more evident if one considers a simple case of J repeated averages with Ak = 0. The choice of the plus or minus sign is determined by the relative direction of the phase-encoding shift Ak, which is specific to the implementation. From Equations ( A l ) and (A21, we have

p1(x,y;t ) - pz(x,y;t ) =

z

3.

4. 5.

6.

7. 8. 9.

[gI(x.y+ d,) - g Z ky + dn)lexp (inmot). (A41

n

From Equations ( A l ) and (A3), we have

10.

p, (x, y;t) - p2(x. y;t ) 11.

Because the left sides of Equations (A4)and (A5) are identical, so must be their corresponding Fourier coefficients on the right. Thus,

g , ( x , y+ d,)ll - exp(inwoAt)l

12.

13.

=gl(X,y + d , ) - g , ( x , y + d n ) , (-46) or

14.

g,(X,y+d,) =Ag(x,y +d,)/ll -exp(inw,At)l, (A71 where Ag(x,y)= g l ( x , y )- gz(x,y)is the differential image. Equation (A7)indicates that the same movie pl(x,y;t ) can be reconstructed by usingAg(x,y + d,,)/ I1 -exp(inooAt)]inplaceofgl(x,y + d,)inEquation ( A l ) . Accordingly, in Equation (6)the terms g ( x , y ) and g(x,y Po) should be replaced by Ag(x,y)and Ag(x,y t P o ) / [1 - exp ( ? i ooAt)], respectively. We have observed that movies reconstructed with the differential image Ag(x,y)generally show better noise behavior, probably due to the absence of nonlinear operations used in obtaining the ghost masks gj. For applications such a s the dynamic study of pulsatile blood flow in vessels in which only the vessel itself is of interest and ghost suppression in other regions is not necessary ( 17,181, only two interleaved acquisitions ( J = 2) will be sufficient for the DIR. 0

*

15.

16. 17.

18.

19.

Kumar A. Welti D. Ernst R. NMR Fourier zeugmatography. J Magn Reson 1975; 18:69-83. Edelstein WA. Hutchison J M S , Johnson G, Redpath T. Spin warp NMR imaging and applications to human wholebody imaging. Phys Med Biol 1980; 25:75 1-756. Schultz CL, Alfidi RJ, Nelson AD, Kopiwoda SY, Clampitt ME. The effect of motion on two-dimensional Fourier transformation magnetic resonance images. Radiology 1984; 152:117-121. Wood ML, Henkelman RM. MR image artifacts from periodic motion. Med Phys 1985; 12:143-151. Xiang Q S . Henkelman RM. Ghost reduction by equalized acquisition triplets (abstr).In: Book of abstracts: Society of Magnetic Resonance in Medicine 1990. Berkeley, Calif Society of Magnetic Resonance in Medicine. 1990: 1346. Xiang Q S , Henkelman RM. Motion artifact reduction with three-point ghost phase cancellation. J M R I 1991: 1:633642. Runge VM,Clanton J A , James AE. Respiratory gating in magnetic resonance imagng at 0.5 Tesla. Radiology 1984; 151:52 1-523. Crooks LE. Baker B, Chang H, et al. Magnetic imaging strategies for heart studies. Radiology 1984; 153:459-465. Bailes DR. Gilderdale D J , Bydder GM, Collins AG. Fermin DN. Respiratory ordered phase encoding (ROPE): method for reducing respiratory motion artifacts in MR imaging. J Comput Assist Tomogr 1985; 9:835-838. Glover GH, Pelc NJ. A rapid-gated cine MRI technique. In: Kressel HY, ed. Magnetic resonance annual 1988. New York: Raven, 1988: 299-333. Hinks RS. Monitored echo gating (MEGA1for the reduction of motion artifacts (abstr). Magn Reson Imaging 1988; G(supp1 1):48. Kim WS. J u n g K J . Lee KD, Ra JB, Cho ZH. Extraction of cardiac and respiratory motion cycles by use of projection data in NMR imaging (abstr).In: Book of abstracts: Society of Magnetic Resonance in Medicine 1988. Berkeley, Calif Society of Magnetic Resonance in Medicine, 1988; 958. Ehman RL. Felmlee JP. Adaptive technique for high-definition MR images of moving structures. Radiology 1989: 173~255-263. S p r a g i n s TA. Wireless retrospective gating: application to cine cardiac imaging. Magn Reson Imaging 1990; 8:675681. Pelc N J , Glover GH. Improved respiratory compensation (abstr).In: Book of abstracts: Society of Magnetic Resonance in Medicine 1987. Berkeley, Calif: Society of Magnetic Resonance in Medicine, 1987; 776. Xiang QS, Nalcioglu 0. A formalism for generating multiparametric encoding gradients in NMR tomography. IEEE Trans Med Imaging 1987: MI-6: 14-20. Hofman MBM. Kouwenhoven M, Sprenger M. Non-triggered MR velocity measurements of pulsatile flow (abstr). In: Book of abstracts: Society of Magnetic Resonance in Medicine 1991. Berkeley, Calif Society of Magnetic Resonance in Medicine, 199 1; 808. Hangiandreou N J , Wright RC, Rossman PJ. Riederer S J . Analysis of MR phase contrast measurements of time-varying velocity waveforms (abstr].In: Book of abstracts: Society of Magnetic Resonance in Medicine 199 I . Berkeley, Calif Society of Magnetic Resonance in Medicine, 199 1: 1 156. Moran PR. A flow velocity zeugmatographic interlace for NMR imaging in humans. Magn Reson Imaging 1982: 1:197-203.

Acknowledgments: Encouragement and stimulating communications from Paul R. Moran. PhD, are greatly appreciated. Support of the Medical Research Council of Canada, the National Cancer Institute of Canada. and GE Medical Systems of Canada is gratefully acknowledged. Q.S.X. is a recipient of an MRC Postdoctoral Fellowship Award.

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Dynamic image reconstruction: MR movies from motion ghosts.

It has been previously shown that an image with motion ghost artifacts can be decomposed into a ghost mask superimposed over a ghost-free image. The p...
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