Roll-over aliasing suppression in undersampled images

A fully sampled data set is generated and stored in a fully sampled memory (42). An undersampled data set corresponding to a portion of the same field of view as the fully sampled data set is generated and stored in an undersampled data memory (62). The fully sampled data set includes a frequency encoded data line corresponding to each of the phase encode gradient steps or angles required to span the selected field of view with a selected resolution. The undersampled data set includes data lines with only a fraction of the phase encoding steps or angles. The fully sampled data set is Fourier transformed (44) into a fully sampled image representation (50) and stored in a fully sampled image memory (46). The undersampled data is Fourier transformed (44) into an undersampled image representation (66) and stored in an undersampled image memory (64). The undersampled image (FIG. 2B) from the views of the undersampled data set between boundaries (58a, 58b) includes a representation of the tissue (52a, 52b, 54) within these boundaries as well as a representation from tissue (52c, 52d) outside of the boundaries superimposed thereon. Portions (72, 74) of the fully sampled image representing tissue outside of the undersampled image are translated and combined (86) and subtracted (88) from the undersampled image representation to generate a corrected undersampled image (90) for display on a video monitor (48). In this manner, a portion of fully sampled image representation that is free of roll-over artifacts is utilized to correct an undersampled, incomplete image representation of the same region that includes the roll-over artifacts.

BACKGROUND OF THE INVENTION 
The present invention relates to the signal processing art. It finds 
particular application in conjunction with magnetic resonance image 
reconstruction and will be described with particular reference thereto. It 
is to be appreciated, however, that the invention will also find utility 
in other signal processing techniques in which undersampled signals are 
processed by transforms or other mathematical operations that are 
cyclically repeating, e.g. Fourier transforms. 
For rapid data acquisition, such as single shot cardiac imaging, 
rectangular fields of view are often used to reduce the data acquisition 
time. More specifically to cardiac imaging, a typical field of view might 
be defined by the boundaries of the patient's torso. The heart, of course, 
only occupies a fraction of this field of view. The size of the field of 
view is related to the amount which the phase encoding gradient is 
stepped, incremented or decremented, between adjacent views. By 
appropriately selecting the phase encode gradient steps, data generation 
and collection can be limited to the half, quarter, or other fraction of 
the whole torso field of view, i.e. undersampled. 
A Fourier transform operation tends to treat image data as if the subject 
were an infinite series of identical subjects at regular spacing. 
Structure bordering a selected field of view is transposed into the 
selected field of view and superimposed on the resultant image by the 
Fourier transform operation. That is, the Fourier transform "assumes" that 
the selected field of view and the adjoining fields of view contain 
identical samples and superimposes the images. This superimposed 
out-of-field-of-view structure is denoted herein as roll-over aliasing. In 
the cardiac imaging example in which only the central patient portion with 
the heart is imaged, patient data from the portion of the patient above 
the undersampled data and from below the portion of the patient 
corresponding to the undersampled data becomes superimposed on the 
resultant image as artifacts. Various techniques have been utilized for 
suppressing these artifacts. 
In presaturation, RF pulses are applied prior to the main imaging sequence 
to saturate spins in the image slice that are located outside the desired 
region of interest. In the above cardiac example, the presaturation pulses 
saturate the spins of tissue above and below the central portion of the 
patient in which the heart is located corresponding to the undersampled 
region. The imaging procedure is performed immediately following 
presaturation while the spins are still saturated. Because the spins in 
the presaturated region have only a very short time to recover 
longitudinal magnetization, they contribute very little signal to the 
resultant image data set, reducing the alias signal. 
In selective volume techniques, two or more radio frequency pulses are 
applied to excite and refocus the magnetization in only a preselected 
region of interest. In an exemplary embodiment, 90.degree. and 180.degree. 
radio frequency pulses are applied with slice select gradients on each of 
two axes in a spin echo sequence. Only the material in the volume seeing 
both RF pulses, i.e. the intersection of the two orthogonally defined 
regions, generates a signal with the appropriate phase history to be 
refocused during data collection. 
In the selective undersampling technique, the region of interest is 
centered on the zero phase encode axis. The zero phase encode view has the 
most energy of all of the views with the highest phase encode view having 
the least. By having the region of interest correspond to the central 
views, the views with the most energy per view are imaged and the 
relatively weak views are not. Because most of the energy or signal 
magnitude is located at the central views of the raw data set, most of the 
energy does not alias--it is fully sampled. Intrinsically, the unsampled, 
high frequency information does alias. There is no suppression of this 
high spatial frequency information. However, the high spatial frequency 
information is of a sufficiently lower energy level or signal magnitude 
that the aliasing which it contributes to the resultant image is 
relatively weak and hard to discern. 
These three techniques each have disadvantages. The selective volume 
technique is limited to RF spin echo sequences. Such spin echo sequences 
require two RF pulses as opposed to the single RF pulse used for field 
echoes. Thus, spin echoes are inherently less well suited to high speed 
imaging than field echoes. Further, they tend to require much higher 
specific absorption rates than field echoes. The selective volume 
techniques are also subject to imperfect slice profiles along the phase 
encoding/slice select direction. This results in image non-uniformity. A 
compensation is made by phase encoding for larger than the ideal field of 
view which results in a less than optimal reduction in the minimum number 
of phase encoding views. 
The presaturation pulse techniques are subject to imperfect slice profiles 
which gave rise to non-uniformities in the undersampled regions. They are 
also subject to imperfect radio frequency calibration which gives rise to 
incomplete suppression of aliased information. When only a single 
preparatory presaturation pulse is applied prior to the acquisition of the 
entire raw data set, there may be a significant recovery of longitudinal 
magnetization causing significant levels of aliasing. If more than one 
presaturation pulse is used, e.g. one pulse before each phase encoding 
view, the gradient demands and specific absorption rates are vastly 
increased. The presaturation pulses are subject to imperfect calibration 
of radio frequency pulses which can result in inadequate alias 
suppression. Moreover, the side lobes of the presaturation pulses can 
themselves produce artifacts and non-uniformities within the image region 
of interest. 
Selective undersampling makes no attempt to prevent the aliasing of high 
spatial frequency information. The lower energy levels at the high spatial 
frequency information in the central views tend to make the artifacts more 
subtle and difficult to distinguish from genuine structure creating more 
uncertainty as to the diagnostic interpretation of the resultant image. 
Moreover, the resolution information corresponding to the non-sampled high 
spatial frequencies is lost. 
The present invention contemplates a new and improved technique for 
suppressing aliasing in undersampled data. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, an undersampled data set is 
collected which corresponds to a selected subregion of a field of view. 
The undersampled data set inherently includes roll-over aliasing artifacts 
corresponding to structure within the field of view but outside of the 
selected subregion. When the undersampled data set is reconstructed into 
an image representation, it includes artifacts from regions of the field 
of view outside of the selected subregion. A second image representation 
is generated from a set of data that at least in part includes data 
corresponding to a second subregion of the field of view outside of the 
selected subregion. Portions of the second image representation that 
correspond to the aliasing artifacts in the first image are subtracted 
from the first image representation to produce an aliasing artifact 
corrected image representation. 
In accordance with a more limited aspect of the present invention, the 
second image representation is generated from a fully sampled set of data 
of the field of view taken contemporaneously with the undersampled data 
set. 
In accordance with another aspect of the present invention, the second 
image representation is generated from a combination of undersampled data 
sets. 
One advantage of the present invention resides in its rapid image data 
collection. 
Another advantage of the present invention is that it is compatible with 
field echoes. 
Another advantage of the present invention is that it places less stringent 
requirements on specific absorption rate, gradient rise times, duty 
cycles, and radio frequency amplifiers. 
Another advantage of the present invention is that alias suppression is 
independent of the relaxation rates of tissues being imaged. 
Yet another advantage of the present invention is that it suppresses 
aliasing over a full range of spatial frequencies. 
Still further advantages of the present invention will become apparent to 
those of ordinary skill in the art upon reading and understanding the 
following detailed description of the preferred embodiments.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
With reference to FIGS. 1A and 1B, a magnetic resonance imaging apparatus 
includes a main magnetic field means A for generating a substantially 
uniform magnetic field through an examination region. A radio frequency 
means B selectively transmits radio frequency excitation pulses for 
exciting selected dipoles within the region of interest. The radio 
frequency means also provides radio frequency pulses for selectively 
rotating or otherwise manipulating the selected components of the 
magnetization, e.g. selective 90.degree. pulses, 180.degree. pulses, or 
the like. A gradient field means C selectively applies gradient fields, 
preferably along three selectable orthogonal axes across the examination 
region. A pulse sequence control means D controls the radio frequency 
means in the gradient field means to cause the generation of preselected 
pulse sequences, preferably gradient echo sequences. An image means E 
processes received magnetic resonance signals or views and reconstructs an 
electronic image representation for archiving, display on a video monitor, 
or the like. 
The magnetic field means A includes a control circuit 10 and a plurality of 
superconducting or resistive coils 12 for generating the magnetic field. 
The control circuit causes the magnets to generate a substantially uniform 
magnetic field axially therethrough, particularly in a centrally located 
examination or image region 14. Magnetic field shimming devices (not 
shown), as are conventional in the art, may be provided for improving the 
uniformity of the magnetic field. 
The radio frequency means B includes a radio frequency coil 20 such as a 
quadrature coil which surrounds the examination region 14. A radio 
frequency transmitter 22 selectively applies radio frequency pulses to the 
RF coil to excite and manipulate magnetic resonance of the magnetization 
of selected dipoles in the examination region. 
The gradient field means C includes gradient coils 30 for causing gradients 
across the main magnetic field at selectable angles. A gradient field 
control means 32 applies current pulses to the gradient coils to cause 
gradients along the three orthogonal axes, commonly designated as slice 
select, read, and phase encode axes or directions. The gradient field 
control commonly causes a linear gradient along the read axis to cause a 
linear frequency encoding in the read direction. Along the phase encode 
axis, the gradient field control means applies phase encode gradients that 
change in magnitude in regular steps or increments with each sequence, 
repetition, or view. Commonly, the phase encoding varies from zero or no 
phase encoding at a central view in regular steps to a maximum positive 
phase encoding and in analogous regular steps from the zero phase encoding 
to a negative maximum phase encoding. Conventionally, the number of phase 
encoding steps or views that are acquired is an even power of two, such as 
32, 64, 128, or the like. The size of the steps of the phase encode 
gradient are selected such that the views from the maximum negative to the 
maximum positive phase encode view span a selected field of view. The 
gradient along the slice select direction may be applied to define a 
single slice or may be stepped analogous to the gradients along the phase 
encode axis to define multiple slices or volumes. 
The radio frequency means B also includes a radio frequency receiver 34 
that receives magnetic resonance signals at least during an induced 
magnetic resonance echo. The magnetic resonance signal or view from the 
receiver is digitized by an analog-to-digital converter 36 to produce the 
individual elements of a digital data line or view. Typically, the 
analog-to-digital converter digitizes the analog magnetic resonance 
signals by an even power of two, e.g. 32, 64, 128, 256, etc. samplings. 
The sampling rate and the slope of the read gradient are selected such 
that the digital data line or view spans the selected field of view in the 
read or frequency encode direction. Typically, a square field of view such 
as 128.times.128 is selected in which the number of views matches the 
number of digitized elements within each view. However, it is to be 
appreciated that the invention is also applicable to the acquisition of 
data in rectangular and other non-square arrangements. 
With continuing reference to FIGS. 1A and 1B and further reference to FIG. 
2A, the sequence control means D causes the gradient control means 32 and 
radio frequency transmitter 34 to generate a fully sampled set of magnetic 
resonance data. That is, the analog-to-digital converters 36 digitize each 
view N times. In each sequence repetition, the phase encode gradients 
assume each step between -((N/2)-1) and N/2. A resonance data memory 40 
includes fully sampled data memory 42 for storing the fully sampled 
complex data set. A Fourier transform means 44, preferably a fast Fourier 
transform means, Fourier transforms the fully sampled resonance data set 
into a fully sampled complex image representation whose real and imaginary 
components are stored in a fully sampled image memory 46. Suitable 
hardware and software for performing the Fourier transform function are 
illustrated in U.S. Pat. No. 4,749,411. A video monitor 48 selectively 
displays the fully sampled image representation as an image 50. 
Conventionally, the image is the square root of the sum of the squares of 
the real and imaginary image data values corresponding to each picture. 
Utilizing cardiac imaging by way of example, the image 50 includes an 
outline 52 of the patient's torso, and an outline 54 of the patient's 
heart. Although the slice includes the tissue detail within the torso 
outline 52 and within the heart outline 54, this detail has been omitted 
from FIG. 2 for simplicity of illustration. A subregion of interest 
selection means 56 is utilized to designate boundaries 58a, 58b of a 
selected portion of the field of view or a subregion of interest. 
Preferably, the subregion of interest is defined by N/2, N/4, N/8, or some 
other fraction of the views which is an even power of two to facilitate 
the use of the preferred fast Fourier transform means. A subregion which 
is not an even power of two may be processed by a fast Fourier transform 
means with the technique and hardware illustrated in U.S. Pat. No. 
4,748,411. The subregion of interest selection means 56 controls the 
sequence control means D such that the phase encode views between the 
designated field of view portion boundaries 58a and 58b are generated and 
channelled by a sorting means 60 into an undersampled data memory means 
for portion 62 of the resonance data memory 40. The fast Fourier transform 
means 44 Fourier transforms the undersampled data set into an undersampled 
image representation that is stored in an undersampled image memory 64. 
If the magnitude of the undersampled image representation in the memory 64 
were displayed on the video monitor, an image 66 would be produced. With 
reference to FIG. 2B, the image 66 includes side portions 52a and 52b of 
the torso and the full periphery 54 of the heart. However, as discussed in 
the "Background of the Invention" portion of the application, a top 
portion 52c of the torso periphery from above the boundary 58a is 
rolled-over into the undersampled image 66 and becomes an objectionable 
aliasing artifact that is superimposed on the cardiac image. The tissue 
structure defined within the boundary 58a and the upper periphery 52c of 
the patient's torso is also rolled-over and superimposed on the 
undersampled image. This same roll-over artifacting causes a lower 
periphery 52d of the patient's torso and tissue between the boundary 58b 
and the lower periphery of the torso to be rolled-over into and 
superimposed on the undersampled image 66. Because the tissue represented 
inside of the cardiac periphery 54 is now the superimposition of the 
cardiac tissue and portions of the upper and lower torso, the diagnostic 
value of the undersampled image is compromised. The subregion of interest 
designating routine 56 controls a fully sampled image memory read-out 
means or memory controller 70 to read out portions 72 and 74 of the fully 
sampled image 50. Image portion 72 is the portion of image 50 above 
boundary 58a and image portion 74 is the portion of image 50 below 
boundary 58b. The read-out means 70 reads out the upper image portion 72 
into a translating means 78 that translates the upper image 72 downward 
such that its lower surface 80 has the same physical position as boundary 
58b, i.e. the lowermost surface of the undersampled image 66. The read out 
means channels the lower image portion 74 to a translate means 82 which 
translates the position of the lower image portion 74 such that its upper 
most surface is shifted to the position of the boundary 58a, i.e. the 
uppermost edge of the undersampled image 66. Optionally, an adding means 
84 may add the upper and lower image portions 72 and 74 together to form a 
composite correction image 86 (FIG. 2D). 
An image correction means e.g. a subtraction device or routine 88, 
subtracts the real and imaginary components of the composite correction 
image 86, or the upper and lower image portions 72 and 74 individually, 
from the corresponding real and imaginary components of the undersampled 
image 66. A magnitude image means 90 calculates a magnitude of each pixel 
of a corrected undersampled image 90 from the square root of the sum of 
the squares of the corresponding real and imaginary values. The corrected, 
undersampled image is stored in a corrected undersampled image memory 94. 
With reference to FIG. 2E, the subtraction device or routine 88 removes the 
roll-over artifacts such that the tissue within the heart periphery 54 
represents only heart tissue and is not the superimposition of tissue from 
upper and lower portions of the torso. If appropriate, the adding means, 
e.g. an adder 84, can adjust the magnitude of the composite correction 
image 86. 
In the cardiac imaging embodiment, it is often desirable to obtain a series 
of high speed, freeze frame images of the heart. To this end, a series of 
undersampled data memories 100 is provided for receiving subsequent 
undersampled images at short time displaced intervals after the initial 
time displaced image. Rather than providing separate undersampled image 
memories, a single undersampled image data memory may be provided and used 
serially if the processing speed of the Fourier transform means 44 and 
other hardware permit. The series of resultant corrected undersampled 
images are stored in the corrected undersampled image memory 94 or other 
memory means. 
The composite correction image 86 may be utilized as long as it remains a 
valid correction, generally for one respiratory cycle. Typically, the 
patient holds his breath while a series of cardiac images are taken. As 
long as the tissue above boundary 58a and below boundary 58b of image 50 
remain stationary, the composite correction image 86 remains valid. 
Pulmonary motion typically moves this tissue. Accordingly, a new fully 
sampled image is preferably taken each respiratory cycle. 
Although the method has been described as generating the fully sampled data 
set first for convenience of illustration, it is to be appreciated that 
the fully sampled data set may be taken at any time in the series of high 
speed undersampled images including at the beginning of the series, at the 
end of the series, at one point during the series, or distributed over the 
series. Indeed, the data corresponding to the phase encode views between 
the boundaries 58a and 58b of the fully sampled image may be channelled by 
the sorting means 60 to both the undersampled image memory 62 and the 
fully sampled image memory 42 to be processed as one of the series of high 
speed cardiac images. 
In another implementation of the present invention, the collection of the 
fully sampled data set is distributed over the series of undersampled data 
sets. For example, the first undersampled image may be a first fraction of 
the phase encode views between -((N/2-1) and N/2, e.g. every fourth view. 
The second undersampled image may be a different quarter of the views and 
so on for the third and fourth undersampled views. Although each of the 
four data sets is undersampled, cumulatively they comprise a fully sampled 
data set. In this embodiment, the sorting means 60 directs each of the 
undersampled views to one of the undersampled image memories as well as to 
the fully sampled image memory 42 which accumulates all four views into 
the fully sampled data set. The above described Fourier transform and 
subtraction procedure is repeated to generate four time displaced, 
corrected undersampled views. 
The invention has been described with reference to a preferred cardiac 
imaging embodiment. It is to be appreciated that the invention not only 
finds application in other diagnostic imaging applications but in other 
imaging and signal processing areas that have roll-over type aliasing. 
Numerous alterations, modifications and further applications will occur to 
others upon reading and understanding the preceding detailed description. 
It is intended that the invention be construed as including all such 
alterations and modifications insofar as they come within the scope of the 
appended claims or the equivalents thereof.