Detection and measurement of motion during NMR imaging using orbital navigator echo signals

An NMR image data set is acquired along with interleaved navigator signals. The navigator signals are acquired while two, orthogonal readout gradients are applied such that a circular orbit in k-space is sampled. The navigator signals are analyzed to detect object motion and to produce corrective values for the NMR image data to reduce artifacts caused by object rotation and displacement along two axes.

BACKGROUND OF THE INVENTION 
The field of the invention is nuclear magnetic resonance imaging methods 
and systems. More particularly, the invention relates to the reduction of 
motion artifacts in NMR images using correction methods described in U.S. 
Pat. No. 4,937,526. 
Any nucleus which possesses a magnetic moment attempts to align itself with 
the direction of the magnetic field in which it is located. In doing so, 
however, the nucleus precesses around this direction at a characteristic 
angular frequency (Larmor frequency) which is dependent on the strength of 
the magnetic field and on the properties of the specific nuclear species 
(the magnetogyric constant .gamma. of the nucleus). Nuclei which exhibit 
this phenomena are referred to herein as "spins". 
When a substance such as human tissue is subjected to a uniform magnetic 
field (polarizing field B.sub.0), the individual magnetic moments of the 
spins in the tissue attempt to align with this polarizing field, but 
precess about it in random order at their characteristic Larmor frequency. 
A net magnetic moment M.sub.z is produced in the direction of the 
polarizing field, but the randomly oriented magnetic components in the 
perpendicular, or transverse, plane (x-y plane) cancel one another. If, 
however, the substance, or tissue, is subjected to a magnetic field 
(excitation field B.sub.1) which is in the x-y plane and which is near the 
Larmor frequency, the net aligned moment, Mz, may be rotated, or "tipped", 
into the x-y plane to produce a net transverse magnetic moment M.sub.t, 
which is rotating, or spinning, in the xy plane at the Larmor frequency. 
The practical value of this phenomenon resides in the signal which is 
emitted by the excited spins after the excitation signal B.sub.1 is 
terminated. There are a wide variety of measurement sequences in which 
this nuclear magnetic resonance ("NMR") phenomena is exploited. 
When utilizing NMR to produce images, a technique is employed to obtain NMR 
signals from specific locations in the subject. Typically, the region 
which is to be imaged (region of interest) is scanned by a sequence of NMR 
measurement cycles which vary according to the particular localization 
method being used. The resulting set of received NMR signals are digitized 
and processed to reconstruct the image using one of many well known 
reconstruction techniques. To perform such a scan, it is, of course, 
necessary to elicit NMR signals from specific locations in the subject. 
This is accomplished by employing magnetic fields (G.sub.x, G.sub.x, and 
G.sub.z) which have the same direction as the polarizing field B.sub.0, 
but which have a gradient along the respective x, y and z axes. By 
controlling the strength of these gradients during each NMR cycle, the 
spatial distribution of spin excitation can be controlled and the location 
of the resulting NMR signals can be identified. 
Object motion during the acquisition of NMR image data produces both 
blurring and "ghosts" in the phase-encoded direction. Ghosts are 
particularly apparent when the motion is periodic, or nearly so. For most 
physiological motion each view is acquired in a period short enough that 
the object may be considered stationary during the acquisition window. In 
such case the blurring and ghosting is due to the inconsistent appearance 
of the object from view to view. Motion that changes the appearance 
between views such as that produced by a patient moving, by the 
respiration or the cardiac cycle, or by peristalsis, is referred to 
hereinafter as "view-to-view motion". Motion may also change the amplitude 
and phase of the NMR signal as it evolves during the pulse sequence and 
such motion is referred to hereinafter as "in-view motion". 
Both blurring and ghosting can be reduced if the data acquisition is 
synchronized with the functional cycle of the object to reduce 
view-to-view motion. This method is known as gated NMR scanning, and its 
objective is to acquire NMR data at the same point during successive 
functional cycles so that the object "looks" the same in each view. The 
drawback of gating is that NMR data may be acquired only during a small 
fraction of the object's functional cycle, and even when the shortest 
acceptable pulse sequence is employed, the gating technique can 
significantly lengthen the data acquisition. 
Another proposed method for eliminating ghost artifacts is disclosed in 
U.S. Pat. No. 4,567,893, issued on Feb. 4, 1986. This prior patent teaches 
that the distance in the image between the ghosts and the object being 
imaged is maximized when the NMR pulse sequence repetition time is an odd 
multiple of one-fourth of the duration of the periodic signal variation. 
This can be used to alleviate ghosts due to respiratory motion. While this 
method, indeed, improves image quality, it does impose a constraint on the 
NMR pulse sequence repetition time and it often results in a longer total 
scan time. It also assumes that the motion is periodic. 
Yet another method for reducing the undesirable effects due to periodic 
signal variations is disclosed in U.S. Pat. No. 4,706,026 issued on Nov. 
10, 1987 and entitled "A Method For Reducing Image Artifacts Due To 
Periodic Variations In NMR Imaging." In one embodiment of this method, an 
assumption is made about the signal. variation period (e.g. due, for 
example, to patient respiration) and the view order is altered from the 
usual monotonically increasing phase-encoding gradient to a preselected 
order. For a given signal variation period, a view order is chosen so as 
to make the NMR signal variation as a function of the phase-encoding 
amplitude be at a desired frequency. In one embodiment, the view order is 
selected such that the variation period appears to be equal to the total 
NMR scan time (low frequency) so that the ghost artifacts are brought as 
close to the object being imaged as possible. In another embodiment (high 
frequency), the view order is chosen to make the variation period appear 
to be as short as possible so as to push the ghost artifacts as far from 
the object as possible. 
This prior method is effective in reducing artifacts, and is in some 
respects ideal if the variation is rather regular and at a known 
frequency. On the other hand, the method is not very robust if the 
assumption made about the motion temporal period does not hold (e.g., 
because the patient's breathing pattern changes or is irregular). If this 
occurs, the method loses some of its effectiveness because the focusing of 
the ghosts, either as close to the object or as far from the object as 
possible, becomes blurred. A solution to this problem is disclosed in U.S. 
Pat. No. 4,663,591 which is entitled "A Method For Reducing Image 
Artifacts Due To Periodic Signal Variations in NMR Imaging." In this 
method, the non-monotonic view order is determined as the scan is executed 
and is responsive to changes in the period so as to produce a desired 
relationship (low frequency or high frequency) between the signal 
variations and the gradient parameter. The effectiveness of this method, 
of course, depends upon the accuracy of the means used to sense the 
patient motion, and particularly, any variations in the periodicity of 
that motion. 
Yet another method for reducing motion artifacts in NMR images is referred 
to in the art as "gradient moment nulling". This method requires the 
addition of gradient pulses to the pulse sequence which cancel, or null, 
the effect on the NMR signal phase caused by spins moving in the gradients 
employed for position encoding. Such a solution is disclosed, for example, 
in U.S. Pat. No. 4,731,583 entitled "Method For Reduction of NMR Image 
Artifacts Due To Flowing Nuclei By Gradient Moment Nulling". 
U.S. Pat. No. 4,937,526 describes a method for reducing motion artifacts in 
NMR images in which the NMR data set used to reconstruct the image is 
corrected after its acquisition using information acquired concurrently in 
NMR "navigator" signals. The navigator signals are produced by pulse 
sequences which are interleaved with the imaging pulse sequences and which 
are characterized by the absence of phase encoding. The navigator signal 
is thus a projection along an axis defined by the readout gradient which 
is fixed in direction throughout the scan. As a result, the navigator 
signals detect spin motion only along the direction of this readout 
gradient. A second navigator pulse sequence with an orthogonal readout 
gradient can also be interleaved throughout the scan, but this further 
lengthens the scan time and is seldom done. In addition, even when two 
"orthogonal" navigator signals are acquired during the scan, they do not 
provide the information required to correct for in-plane rotation of the 
subject. Such rotational motion is particularly troublesome when imaging 
certain subjects such as the human heart, or when performing brain 
function MRI. 
SUMMARY OF THE INVENTION 
The present invention is a method for detecting motion along two in-plane 
axes and for detecting rotational motion of the subject. More 
specifically, the invention includes acquiring a series of NMR signals 
using an imaging pulse sequence to acquire an image NMR data set; 
interleaving with the series of imaging pulse sequences a series of pulse 
sequences to acquire a corresponding series of navigator NMR signals, each 
navigator pulse sequence including the application of two, in-plane, 
orthogonal magnetic field gradients during the readout of its navigator 
NMR signal such that the navigator NMR signal samples a substantially 
circular, or "orbital" path in k-space. 
A general object of the invention is to provide information with which an 
acquired image NMR data set can be corrected for in-plane view-to-view 
subject motion. By measuring shifts in the orbital navigator NMR signals 
with respect to a reference orbital navigator signal, corrective values 
can be calculated for each corresponding NMR imaging signal. These 
corrections offset artifact producing errors caused by in-plane 
translational motion of spins in any direction, as well as errors caused 
by in-plane rotational motion of spins. 
Another object of the invention is to acquire information from which 
corrections can be made to an image NMR data set without further 
lengthening the scan time. A single orbital navigator pulse sequence is 
sufficient to acquire corrective information for all in-plane spin motion. 
It requires the same scan time as prior "single axis" navigator pulse 
sequences. 
Yet another object of the invention is to detect in-plane motion of the 
subject being imaged during an NMR scan. By interleaving navigator pulse 
sequences into the NMR scan, in-plane subject motion can be monitored 
throughout the acquisition. The detected movement may be used to correct 
the acquired NMR image data, or it may be used in other ways. For example, 
detected motion may be employed as a means for gating the acquisition of 
NMR image data, or it may be used as a signal to discard and reacquire NMR 
image data, or it may be used to simply stop the NMR scan when the 
detected motion is unacceptable for the procedure being performed. 
The foregoing and other objects and advantages of the invention will appear 
from the following description. In the description, reference is made to 
the accompanying drawings which form a part hereof, and in which there is 
shown by way of illustration a preferred embodiment of the invention. Such 
embodiment does not necessarily represent the full scope of the invention, 
however, and reference is made therefore to the claims herein for 
interpreting the scope of the invention.

GENERAL DESCRIPTION OF THE INVENTION 
It is well known that the NMR signal measured during acquisition in a slice 
disposed in the x-y plane can be defined as follows: 
##EQU1## 
where .OMEGA. is the area of the integral. If the NMR signal is produced 
by sampling a circular path in k-space using the orbital navigator pulse 
sequence of the present invention, the signal may be expressed as follows 
in polar coordinates: 
##EQU2## 
where k.sub.p is the radius of the circular path in k space and .theta. is 
the azimuth angle measured from the starting point on the circular path. 
If the imaged object is rotated by an angle .alpha. and two-dimensionally 
displaced from (x,y) by amounts x.sub.0 and y.sub.0, its new position 
(x',y') is a follows: 
EQU x'=x cos .alpha.+y sin .alpha.-x.sub.0 
EQU y'=-x sin .alpha.+y cos .alpha.-y.sub.0. 
It can be proven that in the polar coordinates of k-space, for global 
motion.sup.1 the altered NMR navigator signal S' would be: 
EQU S'(k.sub.p,.theta.)=S(k.sub.p,.zeta.-.alpha.)e.sup.ik.sbsp.p.sup.(y.sbsp.0 
sin .theta.+x.sbsp.0 cos .theta.) (3) 
This equation indicates that the rotation (.alpha.) of the object can be 
measured as a shift of the modulus of the raw (untransformed) NMR 
navigator signal with respect to the unperturbed (reference) NMR navigator 
signal. It is also clear that the modulus of the orbital NMR navigator 
signal only depends on rotation, thus, detection of rotational motion is 
insensitive to any concurrent translations. 
Furthermore, after the rotation angle (.alpha.) is known, the displacements 
(x.sub.0,y.sub.0) of the object can be measured by comparing the phase 
difference between the perturbed orbital NMR navigator signal and the 
reference navigator signal. Since the phase difference is the sum of sine 
and cosine terms which are linearly independent of each other, the 
displacements (x.sub.0,y.sub.0) can be derived from the following formula: 
##EQU3## 
where .DELTA..psi. is the phase difference between corresponding points in 
a reference navigator signal and the orbital navigator signal, after the 
rotation effect (.alpha.) has been taken into account. 
The view-to-view in-plane motion of an object, both rotational and 
translational, can therefore be determined by analyzing the raw, k-space, 
orbital NMR navigational signal. The reference navigator signal is 
compared with the orbital NMR navigation signal, and the amount of shift 
in their modulus values is measured by a "least-squares-residual" method 
described in Z. W. Fu, D. J. Burkart, J. P. Felmlee, R. C. Grimm, R. L. 
Ehman. "Clinical trial of adaptive correction of motion in shoulder MR 
imaging", JMRI 4(P) 61 (1994). This is a measure of the angle of rotation 
(.alpha.). The displacements x.sub.0 and y.sub.0 can then be calculated 
according to equation (4) above. As explained in U.S. Pat. No. 4,937,526, 
these values (.alpha., x.sub.0, y.sub.0) may then be used to correct the 
NMR image data set. 
DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring first to FIG. 1, there is shown the major components of a 
preferred NMR system which incorporates the present invention and which is 
sold by the General Electric Company under the trademark "SIGNA". The 
operation of the system is controlled from an operator console 100 which 
includes a console processor 101 that scans a keyboard 102 and receives 
inputs from a human operator through a control panel 103 and a plasma 
display/touch screen 104. The console processor 101 communicates through a 
communications link 116 with an applications interface module 117 in a 
separate computer system 107. Through the keyboard 102 and controls 103, 
an operator controls the production and display of images by an image 
processor 106 in the computer system 107, which connects directly to a 
video display 118 on the console 100 through a video cable 105. 
The computer system 107 includes a number of modules which communicate with 
each other through a backplane. In addition to the application interface 
117 and the image processor 106, these include a CPU module 108 that 
controls the backplane, and an SCSI interface module 109 that connects the 
computer system 107 through a bus 110 to a set of peripheral devices, 
including disk storage 111 and tape drive 112. The computer system 107 
also includes a memory module 113, known in the art as a frame buffer for 
storing image data arrays, and a serial interface module 114 that links 
the computer system 107 through a high speed serial link 115 to a system 
interface module 120 located in a separate system control cabinet 122. 
The system control 122 includes a series of modules which are connected 
together by a common backplane 118. The backplane 118 is comprised of a 
number of bus structures, including a bus structure which is controlled by 
a CPU module 119. The serial interface module 120 connects this backplane 
118 to the high speed serial link 115, and pulse generator module 121 
connects the backplane 118 to the operator console 100 through a serial 
link 125. It is through this link 125 that the system control 122 receives 
commands from the operator which indicate the scan sequence that is to be 
performed. 
The pulse generator module 121 operates the system components to carry out 
the desired scan sequence. It produces data which indicates the timing, 
strength and shape of the RF pulses which are to be produced, and the 
timing of and length of the data acquisition window. The pulse generator 
module 121 also connects through serial link 126 to a set of gradient 
amplifiers 127, and it conveys data thereto which indicates the timing and 
shape of the gradient pulses that are to be produced during the scan. The 
pulse generator module 121 also receives patient data through a serial 
link 128 from a physiological acquisition controller 129. The 
physiological acquisition control 129 can receive a signal from a number 
of different sensors connected to the patient. For example, it may receive 
ECG signals from electrodes or respiratory signals from a bellows and 
produce pulses for the pulse generator module 121 that synchronizes the 
scan with the patient's cardiac cycle or respiratory cycle. And finally, 
the pulse generator module 121 connects through a serial link 132 to scan 
room interface circuit 133 which receives signals at inputs 135 from 
various sensors associated with the position and condition of the patient 
and the magnet system. It is also through the scan room interface circuit 
133 that a patient positioning system 134 receives commands which move the 
patient cradle and transport the patient to the desired position for the 
scan. 
The gradient waveforms produced by the pulse generator module 121 are 
applied to a gradient amplifier system 127 comprised of G.sub.x, G.sub.y 
and G.sub.z amplifiers 136, 137 and 138, respectively. Each amplifier 136, 
137 and 138 is utilized to excite a corresponding gradient coil in an 
assembly generally designated 139. The gradient coil assembly 139 forms 
part of a magnet assembly 141 which includes a polarizing magnet 140 that 
produces either a 0.5 or a 1.5 Tesla polarizing field that extends 
horizontally through a bore 142. The gradient coils 139 encircle the bore 
142, and when energized, they generate magnetic fields in the same 
direction as the main polarizing magnetic field, but with gradients 
G.sub.x, G.sub.y and G.sub.z directed in the orthogonal x-, y- and z-axis 
directions of a Cartesian coordinate system. That is, if the magnetic 
field generated by the main magnet 140 is directed in the z direction and 
is termed B.sub.0, and the total magnetic field in the z direction is 
referred to as B.sub.z, then G.sub.x =.differential.B.sub.z 
/.differential.x, G.sub.y=.differential.B.sub.z /.differential.y and 
G.sub.z =.differential.B.sub.z .differential.z, and the magnetic field at 
any point (x,y,z) in the bore of the magnet assembly 141 is given by 
B(x,y,z)=B.sub.0 +G.sub.x X+G.sub.y Y+G.sub.z Z. The gradient magnetic 
fields are utilized to encode spatial information into the NMR signals 
emanating from the patient being scanned. 
Located within the bore 142 is a circular cylindrical whole-body RF coil 
152. This coil 152 produces a circularly polarized RF field in response to 
RF pulses provided by a transceiver module 150 in the system control 
cabinet 122. These pulses are amplified by an RF amplifier 151 and coupled 
to the RF coil 152 by a transmit/receive switch 154 which forms an 
integral part of the RF coil assembly. Waveforms and control signals are 
provided by the pulse generator module 121 and utilized by the transceiver 
module 150 for RF carrier modulation and mode control. The resulting NMR 
signals radiated by the excited nuclei in the patient may be sensed by the 
same RF coil 152 and coupled through the transmit/receive switch 154 to a 
preamplifier 153. The amplified NMR signals are demodulated, filtered, and 
digitized in the receiver section of the transceiver 150. The 
transmit/receive switch 154 is controlled by a signal from the pulse 
generator module 121 to electrically connect the RF amplifier 151 to the 
coil 152 during the transmit mode and to connect the preamplifier 153 
during the receive mode. The transmit/receive switch 154 also enables a 
separate RF coil (for example, a head coil or surface coil) to be used in 
either the transmit or receive mode. 
In addition to supporting the polarizing magnet 140 and the gradient coils 
139 and RF coil 152, the main magnet assembly 141 also supports a set of 
shim coil 156 associated with the main magnet 140 and used to correct 
inhomogeneities in the polarizing magnet field. The main power supply 157 
is utilized to bring the polarizing field produced by the superconductive 
main magnet 140 to the proper operating strength and is then removed. 
The NMR signals picked up by the RF coil 152 are digitized by the 
transceiver module 150 and transferred to a memory module 160 which is 
also part of the system control 122. When the scan is completed and an 
entire array of data has been acquired in the memory modules 160, an array 
processor 161 operates to Fourier transform the data into an array of 
image data. This image data is conveyed through the serial link 115 to the 
computer system 107 where it is stored in the disk memory 111. In response 
to commands received from the operator console 100, this image data may be 
archived on the tape drive 112, or it may be further processed by the 
image processor 106 and conveyed to the operator console 100 and presented 
on the video display 118. 
Referring particularly to FIG. 2, the preferred embodiment of the orbital 
navigation pulse sequence is adapted from a spin-echo pulse sequence in 
which transverse magnetization is produced in a slice by a selective 
90.degree. rf excitation pulse 170 applied in the presence of a slice 
select gradient pulse 172. Spins are rephased in conventional fashion by a 
negative gradient pulse 174 and are dephased by a gradient pulse 176 
directed along one in-plane axis (x axis). A 180.degree. selective rf echo 
pulse 178 is then applied in the presence of a second slice select 
gradient pulse 180 and an NMR echo signal 182 is acquired at the echo time 
(TE). 
The orbital navigator pulse sequence is characterized by the application of 
two sinusoidal readout gradients during the NMR echo signal acquisition. 
More specifically, during the readout of the NMR echo signal 182 the 
in-plane magnetic field gradient G.sub.x is modulated in a cosine waveform 
184, and the orthogonal in-plane magnetic field gradient G.sub.y is 
modulated in a sine waveform 186. Both sinusoidal waveforms 184 and 186 
complete one cycle during the readout of the NMR echo signal 182. 
Referring particularly to FIG. 3, as a result of the sinusoidal readout 
gradients 184 and 186, the NMR echo signal 182 samples a circular path in 
k-space. The G.sub.x dephasing gradient pulse 176 moves the starting 
sample point 190 in the negative direction along the k.sub.x axis by an 
amount k.sub.p. The sinusoidal gradient pulses 184 and 186 then move the 
sample point along a circular path 192 having a radius k.sub.p, centered 
about the origin of k-space. Each sample point on the circular path 192 
has an angular position (.theta.) with respect to the starting point 190, 
and .theta. traverses 2.pi. radians during the sampling of the "orbital 
navigator" signal 182. Since the sampling ends at the same starting point 
190, no residual phase remains at the end of the orbital navigator pulse 
sequence. 
It should be apparent to those skilled in the art that the circular orbit 
of the sampling in k-space can be accomplished in a number of different 
ways and the only requirement is that the same method be used for all the 
orbital NMR navigator signals acquired during the same scan. For example, 
the starting point 190 on the circular path 192 can be changed to any 
point on the path 192 merely by changing the dephasing gradient pulse 176 
and/or adding a G.sub.y dephasing pulse indicated in FIG. 2 by dashed line 
194. The phase of the sinusoidal gradient pulses 184 and 186 must be 
changed accordingly, and their polarity may be reversed, if desired, to 
follow the circular orbit in the opposite direction. 
The radius k.sub.p is determined by the amplitude of the gradient pulses 
184 and 186 and its selection is not arbitrary. With larger k.sub.p values 
the orbital navigator signal 182 is more sensitive to motion and contains 
more spatial features that can be used to measure shifts in the modulus 
values along the sampling axis (.theta.). On the other hand, larger 
k.sub.p values produce orbital navigator signals with less signal-to-noise 
ratio ("SNR") and there is a practical limit at which the corrective shift 
values can be determined with the desired degree of accuracy. Experiments 
with phantoms indicate that the best radius (k.sub.p) for measuring 
in-plane rotational motion to within half a degree is from 3/fov to 5/fov, 
where fov is the field of interest. The best radius (k.sub.p) for 
measuring in-plane translational motion within half a pixel is from 2/fov 
to 4/fov. In both cases, the accuracy was limited by noise. 
Referring particularly to FIG. 4, a scan according to the preferred 
embodiment of the invention is carried out under the direction of a 
program executed by the computer system 107 in FIG. 1. As indicated by 
process block 200, the desired image data is acquired as a series of views 
using the imaging pulse sequence of choice. Orbital navigator signals are 
also acquired, however, by interleaving the navigator pulse sequence of 
FIG. 2 with the acquired image views. In the most exhaustive use of the 
invention, the navigator pulse sequence is interleaved between single 
image pulse sequences, although fewer navigator pulse sequences may also 
be used where correction accuracy is less demanding. In the preferred 
embodiment, for example, the scan acquires 256 phase encoded views of 
image data and 256 corresponding orbital navigator signals. As will now be 
described, each orbital navigator signal is processed to arrive at phase 
corrections for its corresponding view of image data. 
As indicated by process block 202, prior to any transformation, the I and Q 
values of each acquired orbital navigator signal are used to calculate its 
corresponding modulus values: 
##EQU4## 
In the preferred embodiment, for example, each orbital navigator signal is 
comprised of 256 samples and thus a 256 by 256 element array of modulus 
values results. 
As indicated by process block 204, the rotational angle (.alpha.) of each 
orbital navigator signal with respect to a reference orbital navigator 
signal S.sub.R (.theta.) (i.e. the first one acquired) is determined. This 
is accomplished by calculating the shift along the .theta. axis of the 
modulus values S(.theta.) of each orbital navigator signal relative to the 
reference S.sub.R (.theta.). This is accomplished by shifting the modulus 
values S(.theta.) along the .theta. axis until the best fit is found with 
the reference S.sub.R (.theta.). A least squares fit is performed in the 
preferred embodiment. As a result, 256 values of the rotational angle 
(.alpha.) are produced corresponding to the 256 image data views. 
As indicated by process block 206, each untransformed orbital navigator 
signal is then shifted by its corresponding rotational angle (.alpha.). 
This effectively removes the effects of object rotation from the orbital 
navigator signals so that object displacement values (X.sub.0, Y.sub.0) 
can be calculated as indicated at process block 208. Displacement is 
calculated using the above equation (4), where .DELTA..psi. is the phase 
difference at each of the 256 navigator signal samples from the 
corresponding reference signal sample: 
EQU .DELTA..psi.=tan.sup.-1 Q/I-tan.sup.-1 Q.sub.R /I.sub.R. 
A pair of displacement values (x.sub.0, y.sub.0) are thus produced for each 
of the 256 acquired orbital navigator signals and correspond with the 
respective 256 image data views. 
As indicated at process block 210, the next step in the process is to 
correct each of the image data views with the corrective values (.alpha., 
X.sub.0, Y.sub.0) from its corresponding orbital navigator signal. The 
measured translational movements (x.sub.0 and y.sub.0) are used to 
calculate phase corrections for the corresponding NMR image data. This is 
described in U.S. Pat. No. 4,937,526, entitled "Adaptive Method For 
Reducing Motion and Flow Artifacts in NMR Images," issued on Jun. 26, 
1990, and which is incorporated herein by reference. 
The correction for object rotation (.alpha.) is made by back-rotating the 
affected NMR image data samples an offsetting amount. The Fourier rotation 
theorem states that a rotation of the object will produce an equal 
rotation of its Fourier transform. Thus, rotation correction can be made 
on the acquired k-space NMR image data. 
Although corrective rotation of the affected k-space NMR image data is easy 
in concept, a number of practical problems arise. For example, when the 
affected NMR image data is back-rotated, some of the data will be rotated 
onto k-space data acquired in other views. Similarly, the back-rotation 
may leave some blank spots in k-space data array. The first problem is 
overcome by simply ignoring the resulting redundant data and using the 
unrotated data. Where missing data occurs, satisfactory results have been 
achieved by zero filling. 
A number of difficulties arise from the back-rotation process. One problem 
created by back-rotating k-space NMR image data is that the sample points 
do not fall on the expected two-dimensional k-space grid. A bilinear 
interpolation between surrounding samples is employed to calculate the 
k-space NMR image data at each missing data point on the rectilinear 
k-space grid. Another difficulty arises when the object does not rotate 
around the center of the k-space grid. The statement of the rotation 
theorem assumes an axis of rotation at the center of the field of view. If 
this is not the case, the axis of rotation can be shifted to the center by 
applying the appropriate phase term to the k-space data prior to rotation 
correction. This phase term can be derived from the Fourier shift theorem. 
In fact, the offset of the axis of rotation can be determined from the 
data set itself in certain cases. And, finally, back-rotating k-space data 
where there is a significant phase roll across the image due to echo 
miscentering can cause problems because of the abrupt phase transitions 
induced. This can be compensated by tuning the pulse sequence to center 
the echo in the data acquisition window, or by retrospectively shifting 
the echoes. 
The 256 corrected image data views may now be used to reconstruct an image 
as indicated at process block 212. This is a standard 2DFT reconstruction 
in the preferred embodiment, although other methods may also be used. 
While the preferred embodiment of the invention uses the measured in-plane 
motion to correct the concurrently acquired NMR image data, other uses for 
the motion measurements are possible. For example, each acquired orbital 
navigator signal may be processed in real time as the scan is being 
performed, and the resulting motion measurements used to control the scan. 
Such control may be a cessation of the scan when the motion exceeds a 
predetermined amount, or selected views may be reacquired when excessive 
movement is measured. Also, the motion measurements may be used to gate 
the further acquisition of image data when the object movement is periodic 
(e.g., respiratory motion and cardiac motion).