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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
An object of the present invention is a method for the reconstruction of
images acquired by 3D experiments, especially in nuclear magnetic
resonance (NMR). The method of the invention is especially applicable to
NMR spectrometry or X-ray spectrometry. It can be transposed to image
reconstruction computations used in tomodensitometry. Among all the
reconstruction methods envisaged, the so-called 3 DFT reconstruction
method is particularly referred to herein. Imaging methods using 3D
acquisition, called 3D imaging methods, have many advantages as compared
with two-dimensional or 2D acquisition methods with the selection of
cross-sections in the bodies examined. In particular, they make it
possible to propose thin, contiguous cross-sections with contours that are
undistorted by supplementary steps in the method, which are required in
order to define this cross-section. However, as compared with 2D methods,
they have the disadvantage of requiring prohibitively lengthy periods for
the acquisition and reconstruction of images.
2. Description of the Prior Art
Recent improvements in methods for the excitation of the magnetic moments
of protons, known as steady state free precession (SSFP) methods, have
considerably reduced 3D acquisition means. The time taken to present
images then depends essentially on the time taken for reconstruction.
Typically, there are known ways of showing images with resolutions that
are substantially equal along two reference axes of the image. However,
for an axis oriented in a direction perpendicular to the images, along the
stack of these images, either a less efficient resolution is accepted (in
the final analysis relatively thick slices, for example 1 cm slices, are
chosen), or else the volume in which it is sought to make these images is
restricted. Assuming, for example, that the body of a patient is stretched
out in an NMR machine along an axis Z and that the aim is to make images
of cross-sections of this body with resolutions in each image of, for
example, 256.times.256 pixels, it is possible to accept, for example, a
depiction of only eight images superimposed along the axis Z. This typical
digital example shall be kept in the rest of the description of the
invention because it gives a clear picture of the subject. Of course, the
implications of the invention cannot be considered to be limited to this
digital example.
The implementation of a 3DFT type imaging method calls for the application
of excitation and measurement sequences which comprise, firstly, a
radiofrequency electromagnetic excitation of the body to be examined and
the measurement of a resulting NMR de-excitation signal and, secondly, the
application of additional magnetic field gradient pulses (superimposed on
the main magnetic field of the machine), for which the gradient directions
are pre-determined with respect to the directions of the images of the
sections to be obtained (in this case, cross-sections). It is known that,
during the measurement of the NMR signal, a so-called read gradient is
applied along a pre-determined axis of this type called a read axis. In
general, the read axis is called the X-axis. During the 3D experiment, the
field gradients applied to a so-called phase encoding axis (Y) and a
cross-section selection axis (Z) assume different values from one sequence
to another. For instance, there is a known method by which the
cross-section selection gradient is fixed at a given value and for a given
period during each sequence of a first series of sequences, while the
phase encoding gradient value changes step by step during the first series
of sequences. When the first series of sequences is acquired, the value of
the cross-section selection gradient is incremented and the entire series
of sequences is repeated. During the sequences of this other series, the
phase encoding gradient again assumes the same series of values as for the
first series of sequences. This series of frequencies is started again for
as many times as it is sought to obtain images counted in the direction of
stacking on the axis (Z). At the end of each series of sequences, 2D
Fourier transform is used to compute the contributions to the final
images. These contributions are thus acquired in each of these series of
sequences. When all the contributions to the images have been computed,
the image elements on all the images are computed by Fourier transform
from these contributions to the images. Typically, each contribution image
is defined on a space of 256.times.256 points. The computations of the
final images then require, in the example, the performing of 8
.times.256.times.256=524288 one-dimensional Fourier transforms (or
256.times.256=65536 Fourier transforms) for which the number of computing
points in each is small: it corresponds to a small number (eight) of
series of sequences which itself corresponds to the small number of images
sought to be depicted in the stack.
This method has many drawbacks. In particular, performing a very large
number of Fourier transforms, with a small number of computing points, is
ill suited to the vectorial processors used. For these processors are
normally optimized to perform greater numbers of computing points. In
practice, we thus arrive at an image reconstruction time of about 12
minutes in the example referred to above. Furthermore, the acquisition
mode is such that, during this reconstruction period, no intermediate
result is available: all the images are computed and available at the same
time. This means that this waiting time cannot be used to interpret images
which would be presented as and when they arise. Furthermore, in view of
the number of data to be processed simultaneously, the addressing problems
encountered to implement these reconstruction methods are great.
Finally, in the image, it is not always necessary to choose one and the
same resolution along both axes. For example, it might be decided to
produce images with 256.times.128 pixels. An additional problem would then
be encountered. For, this reduction in resolution along one of the axes of
the image, which reduces the measurements acquisition time by two, is
counterbalanced by the fact that there are no standard programs in the
vectorial processors used for reconstruction processing by 2D Fourier
transform of non-symmetrical sets. Since there is no pre-recorded program
available that works according to a fast algorithm, a specific algorithm
has to be programmed. This specific algorithm cannot be as well suited to
the machine as the fast algorithm for which the machine was itself
designed. The result of this is that the expected time gain is not
obtained.
An object of the invention is to remove the drawbacks referred to by
modifying the organization of the acquisition of sequences as well as the
organization of the computing of image reconstruction. In this
computation, advantage is taken of the fact that, in one of the
acquisition dimensions, the image resolution or the number of images is
small. In practice, instead of first performing symmetrical 2D Fourier
transforms (for example, 256.times.256) asymmetrical Fourier transforms
(for example 8.times.256) are performed. However, vectorial processors are
generally designed to work with a low-capacity fast memory and a
high-capacity slower memory. In the invention it has been observed that
the computation of highly asymmetrical 2D Fourier transforms makes it
possible, by using the entire useful volume of the fast memory, to use
vectorial processors to their maximum working speed. Subsequently, a third
one-dimensional Fourier transform is performed with a large number of
computing steps (256), and this large number too corresponds to a maximum
use of the computing power of the vector processor. The result of this is
that by making the processor work to its maximum capacity at all times,
images are produced faster than by burdening it with an excessively large
number of operations which, in particular, would be too simple for its
capacity. A large number of to and fro movements between the processor and
the slow memory are avoided.
SUMMARY OF THE INVENTION
An object of the invention, therefore, is a method for the reconstruction
of images acquired by a 3DFT type imaging method for which the resolution
M along one of the imaging axes is smaller than the resolutions N and P
along two other axes of the image, said method comprising a first
computation of N.M.P Fourier transforms with P computation steps followed
by a second computation of N.M.P. Fourier transforms with M computation
steps followed by a third computation of N.M.P. Fourier transforms with N
computation steps.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be better understood from the following description and
the accompanying figures which are given purely by way of example and in
no way restrict the scope of the invention. Of these figures:
FIG. 1 shows an NMR machine which can be used to implement the method
according to the invention;
FIGS. 2a to 2d show timing diagrams of gradient signals of encoding
magnetic fields used in the method according to the invention;
FIGS. 3a and 3b show the shape of the temporal distributions of various
phases of the method according to the invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
FIG. 1 shows an NMR machine for the application of the method of recording
in accordance with the invention. This machine essentially comprises a
magnet represented by a coil 1 for producing a uniform magnetic field
B.sub.o of high strength in a zone of examination. This zone of
examination is located in the region in which a patient's body 2 is placed
on a table 3. When subjected to this magnetic influence, the body 2 is
further subjected to a radiofrequency electromagnetic excitation
transmitted by an antenna consisting, for example, of radiating rods 4 to
7 and fed through an oscillating circuit 8 by an excitation generator 9.
An antenna 10 serves to collect the de-excitation signal of the magnetic
moments of the body's protons. In certain cases, the antenna 10 may be
identified with the excitation antenna. The detected signal is conveyed on
a reception and processing circuit 11 in order to depict images of the
sections I.sub.1 to I.sub.8 on a display screen 12. In order to implement
the 3DFT imaging method, the machine further has gradient coils symbolized
by the coils 13 powered by a gradient pulse generator 14. All these means
work under the control of a sequencer I.sub.5. FIG. 1 again shows axes
XYZ. It is seen that the images will be developed along the axes X and Y
and stacked on one another along the axis Z. Besides, the functions of
these axes may be inverted or even combined so as to produce images of any
particular orientation.
FIGS. 2a to 2d show the shape of the radiofrequency signal and the shape of
the field gradient pulses along each of the axes Z, X, Y, respectively,
during an excitation and measurement sequence used in the invention.
During a sequence of this type, a radiofrequency excitation 16 has the
effect of making the orientation of the magnetic moments of the particles
of the body flip over. If necessary, a radiofrequency pulse, called a spin
echo pulse 17, is also applied to make the NMR signal of the body reappear
at 18. At the end of a period Tr, a following sequence is undertaken. In
the invention, the sequences are brought together in macro-sequences and
all the macro-sequences constituting all the experimenting sequences.
A macro-sequence comprises a reduced number M of identical sequences in all
their elements except for the value of a selection encoding gradient
G.sub.z. In fact, from one sequence to another, on a read axis X the read
gradient G.sub.x is kept identical: it consists of a read encoding pulse
19 and a read pre-coding pulse 20. Throughout the experiment, this
gradient pulse is constant. During all the sequences of a macro-sequence,
the phase encoding gradient G.sub.y preserves a same value n.k.sub.2. This
macro-sequence is called the order n macro-sequence. In the experiment,
there are N macro-sequences (typically N is equal to 256), and n is equal
to -N/2 , to +N/2 (strictly speaking n should not assume values except
between -N/2 and N/2-1. To simplify the presentation, the -1 has been
omitted. Besides, the same applies to M and P). By contrast, during the
macro-sequence, at each of the sequences, the pulse 22 of a selection
encoding gradient changes from a value m.k.sub.3 to a following
(m+1).k.sub.3. In an imaging sequence there are M sequences (typically M
is equal to 8) and m can take the values of -M/2 to +M/2.
FIGS. 3a and 3b show the course of all the imaging sequences according to
the invention. There are N macro-sequences, the elementary duration of
which is M.Tr each time. After M sequences of a macro-sequence, a first
computation of the 2D Fourier transform 23 is done. It will be shown
further below that, because of the number of computing steps implied in
this 2D Fourier transform computation, this computation can be easily
completed before the end of the following macro-sequence. In practice,
with the values given in the example and taking a duration of about 50
milliseconds as the duration T.sub.r, a macro-sequence lasts 400
milliseconds (all the 256 macro-sequences then last about 2 min) while the
computation of the 2D transform with the fast memory of the vector
processors used, lasts about 40 milliseconds each time. In other words,
while the macro-sequence n is acquired, the 2D Fourier transform can be
computed on the results of the acquisition relating the macro-sequence
n-1. This leads, firstly, to work in effective real time, and, secondly, a
limit on addressing constraints: it is possible, if necessary, to re-use
same addresses of the fast memory during the 2D Fourier transform
computation in the macro-sequences.
Further below, we shall recall, albeit with some mathematical
simplifications, the theoretical architecture for the computing of image
reconstruction by 3D acquisition using the 3DFT method, as well as the
modification resulting therefrom through the invention. Since this is a
sequence where the phase encoding gradient is equal to n.k.sub.2, and
where the selection encoding gradient is equal to m.k.sub.3, the signal 18
given as a function of time can be converted into a sequence of samples,
evenly distributed in time and equivalent to a number P. P represents the
resolution of the images to be obtained developed along the axis X. In
these conditions, signal 18 is converted into a signal S(p,n.k.sub.2,
m.k.sub.3).
According to its principle, the computing of reconstruction by Fourier
transform requires three steps. The effect of the first step is to
transform S(p,n.k.sub.2,m.k.sub.3) into:
##EQU1##
Here, the Fourier transforms are transforms approximated by discrete
summations on the P samples. In the rest of the explanation as well as in
the claims, the term Fourier transform will designate the computation thus
relating to a summation, hence, in this case, for a value of x.sub.0. Each
Fourier transform has P computing points since p varies from -P/2 to +P/2.
In each macro-sequence, there are P.M Fourier transforms such as this one,
since there are P possible values of x.sub.0 and because there are M
values of m. At the end of the acquisition, when N macro-sequences have
been acquired, then N.M.P Fourier transforms such as this one have been
performed with P computing points. In fact, during each interval 23, the
second step of the Fourier transform computation, wherein S.sub.x0 becomes
S.sub.x0 z0, is performed. This computation is written as follows:
##EQU2##
These latter Fourier transforms are Fourier transforms with M computing
points. In the invention, M is notably smaller than M or P: in the example
indicated, M is equal to eight. Here again, a total of N.M.P
one-dimensional Fourier transforms have to be done.
In practice, it is not two computations of one-dimensional Fourier
transforms that are done as indicated, but one computation of 2D Fourier
transforms, each comprising M.P. computing points. This number M.P. of
computing points must be compared with the number N.P. in the prior art
where a series of sequences were acquired by varying the phase encoding
gradient and by keeping the selection encoding gradient constant. In view
of the low value of M, it becomes possible to compute N.M.P 2D Fourier
transforms with M.P computing points by using the fast memory of the
vectorial processors. A specific algorithm can be used successfully. It is
this computation of 2D Fourier transforms which is performed at each
macro-sequence during the interval 23.
To complete the image reconstruction computation, all that remains is to
calculate S.sub.x0 y0 z0 for all the coordinates x.sub.0, y.sub.0, z.sub.0
of the volume studied in the body with a computation of the following
form:
##EQU3##
In this latter computation there are M.N.P Fourier transforms with N
computing steps in each.
It can be seen, however, that the invention makes it easy to envisage the
reconstruction of images for which the resolution along one of the axes
(phase encoding axis) is less precise than along the read axis. For
example, if N equals 128, the acquisition will last two times less and the
time taken for computation of the third Fourier transforms will be
shorter. The computations that correspond to these third one-dimensional
transforms are illustrated by the dimensions of images I.sub.2 to I.sub.7
in FIG. 3b. In the invention, the computing time for an image is about 3
seconds (with a resolution of 256 phase encoding steps). The
reconstruction of the eight images I.sub.1 to I.sub.8 theoretically lasts
24 seconds.
The method of the invention has many advantages. Firstly, the total
acquisition and reconstruction time is about 21/2 minutes. Secondly, the
first image can be available 4 seconds after the end of the acquisition
and not 12 minutes after as in the prior art referred to. For the
computing of an image, which is defined by z.sub.0, can be organized by
computing the Fourier transforms on all the values of S.sub.x0z0
(n.k.sub.2) corresponding to one and the same particular z.sub.0 : for
example that of the image I.sub.1. It is enough to organize the addressing
S.sub.x0z0 to this end. Furthermore, by known phenomena related to
aliasing with respect to images, a part of the image I.sub.1 is recovered
in the image I.sub.8 and reciprocally. These images create interference.
It is therefore not necessary to compute them. In the invention, the
reconstruction computing of images which are known in principle to be
unusable is quite simply eliminated: neither I.sub.1 nor I.sub.8 are
computed. Finally, it can be seen that the invention can be used to choose
or to quite simply to first bring out the central image I.sub.5 or I.sub.4
in the part of the examined volume of the patient. For the central image
is most often worthwhile especially when the exploration setting of the
machine is centered on it. By computing all the images, it is then
possible alternately to produce images located on either side of the
central image every three seconds, while at the same time gradually moving
away. FIG. 3 shows a typical sequence: I.sub.5, I.sub.4, I.sub.6, I.sub.3,
I.sub.7, I.sub.2, the images I.sub.1 and I.sub.8, for example, being not
computed.
To cope with phenomena of aliasing in images, the precaution is also taken,
in the invention, of applying the excitation 16, as well as the spin echo
excitation 17 at the same time as the selection pulses 24, 25 of a
standard type in 2DFT methods. However, here this is done with a greater
exploration width so as to restrict the excitation of the phenomenon of
resonance at the volume where it is planned to make the images I.sub.1 to
I.sub.8 (FIG. 2b). Ultimately, the object of the selection pulses 24 and
25 is to select the macro-section in which all the images are made.
* * * * *
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Description |
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