Method for magnetic resonance image acquisition and reconstruction of the basic of wavelet encoding

For obtaining image information from a subject, in an excitation phase nuclear resonance signals are excited with wavelet-encoding by emitting a radio-frequency pulse under the influence of a gradient in a first direction, the pulse having an envelope that corresponds to the Fourier transforms of a wavelet function. In addition, a layer selection is achieved by the application of an oscillating gradient in a second direction. In a readout phase, a gradient echo signal is sampled under the influence of a readout gradient in a third direction. The pulse sequence can be repeated with a repetition time that is shorter than the longitudinal and transverse relaxation time, so that a steady state arises.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention is directed to a method for the acquisition of image 
data from nuclear magnetic resonance signals. 
2. Description of the Prior Art 
Despite considerable progress in shortening data acquisition time for MR 
imaging, for real-time exposures of dynamic (motion-containing) processes 
MR imaging remains limited, in particular if at the same time a good local 
resolution is required. In many cases, however, it is known from the 
outset that motions are to be expected substantially only in narrowly 
limited regions of the subject, or motions are of interest only in such a 
narrowly limited region. This is the case, e.g., in interventional nuclear 
spin tomography. 
With certain magnetic systems for nuclear spin tomographic devices, such as 
are marketed e.g. by Siemens under the designation "MAGNETOM OPEN.RTM.," a 
relatively good accessibility to the patient is offered during the 
examination. This allows interaction with the patient using interventional 
instruments during the MR imaging. Typical applications are e.g. surgery 
and biopsy, whereby the respective position of the instrument can be 
observed on a screen. Of course, chronologically and spatially precise 
information about the respective position of the instrument in the body is 
required for these procedures. A real-time monitoring of the instrument 
position at the required spatial resolution and at a sufficiently large 
contrast-noise ratio, however, places extreme demands on the speed of the 
data acquisition and processing, if the entire raw data set is to be 
updated. 
From the article "Keyhole Imaging Offers Short Cut to Fast MR-Scans," in 
Diagnostic Imaging, February 1993, page 36, it is known to improve the 
time resolution in MR imaging by intentionally obtaining a less than 
complete data set during each individual sequence repetition. Rather, in 
the context of this keyhole technique, as it is called, only a fast update 
of the average k-space lines ensues. A conventional Fourier transformation 
technique is used, in which these average k-space lines substantially 
determine the signal-noise ratio. Similar techniques for time-resolved MR 
imaging are known from the U.S. Pat. No. 5,168,226 and from the German 
letters patent DE 43 27 325. In obtaining several raw data matrices at 
different time points of a motion sequence, signals for two 
chronologically successive raw data matrices are thereby used, i.e. for 
each image obtained only a part of the raw data lines are updated. The 
time advantage is proportional to the non-updated raw data lines. The 
above-named techniques have the disadvantage that the resolution decreases 
for the representation of moving subjects, to an extent governed by the 
percentage of the raw data which is non-updated. 
From the articles L. P. Panych et al., "A Dynamically Adaptive Imaging 
Algorithm for Wavelet-Encoded MRI," in Magnetic Resonance in Medicine 32, 
pages 738 to 748 (1994), and L. P. Panych et al., "Implementation of 
Wavelet-Encoded MR Imaging," in Journal of Magnetic Resonance Imaging, 
1993, 3, pages 649 to 655, it is known to use wavelet transformations as 
an alternative to phase encoding and to conventional Fourier 
transformation. In contrast to conventional Fourier transformation, 
wavelet functions are spatially localized, i.e. wavelet profiles are 
generated at different places via the observation window. In contrast, the 
discrete Fourier transformation always covers the entire field of 
observation. The discrete Fourier transformation converts a periodic 
signal from the locus space into the frequency space, but does not supply 
information about the time and place at which a particular frequency has 
occurred. 
In the above-identified article "A Dynamically Adaptive Imaging Algorithm 
for Wavelet-Encoded MRI," the spatially selective characteristic of the 
wavelet transformation is used to acquire motions in the observation 
window and to update only the raw data for the regions in which a motion 
actually occurs. A motion of direction in the direction of the wavelet 
encoding is thereby assumed. 
With the use of interventional instruments in a body, the motion direction 
is usually known from the outset. Often it need only be determined how far 
the interventional instrument has been inserted into the body, e.g. in 
order to contact particular organs for the surgery or biopsy and to avoid 
damage to other organs during the insertion of the interventional 
instrument. 
In prior German patent application 195 28 436, it was thus proposed to 
provide the raw data sets with a frequency encoding in the direction of 
the path of motion and with a wavelet encoding in a direction 
perpendicular thereto, and to update only wave encodings allocated to the 
region of the path of motion. 
Since the path of motion is relatively well known, only a small part of the 
nuclear resonance signals need be updated, so that the data acquisition 
time is reduced correspondingly and the time resolution increases. In 
contrast to the above-named method according to Panych, here the data set 
for the entire region of the path of motion is always updated, so that the 
entire instrument inside the subject of examination is represented with 
good local resolution due to the averaging over several measurements. In 
the method according to Panych, however, data sets are updated only for 
the regions in which a change occurs. In the present case, this is the 
case only in the region of the tip of the instrument. 
In contrast to the known keyhole technique or the use of data lines for 
several temporally successive images, here the spatial localization of the 
wavelet function is exploited. 
The above-named techniques have in common that the nuclear resonance 
signals are read out as spin echoes, i.e. after a refocussing through a 
180.degree. radio frequency pulse. This is due to the fact that the 
required layer selection is achieved by means of layer-selective 
refocussing. The layer selection used in the standard phase and frequency 
encoding through activation of a constant gradient cannot be used for the 
wavelet encoding. 
Spin echo sequences, however, are relatively slow. The time advantage 
gained by updating of a partial region of the raw data matrix using the 
local selectivity of the wavelet encoding is thus partly lost again. 
In the article "Adapted WaveForm Encoding For Magnetic Resonance Imaging" 
by Healy et al in IEEE Engineering in Medicine and Biology, 
September/October 1995, pp. 621-638, wavelet encoding possibilities are 
likewise explained. A local resolution is thereby achieved in a first 
direction by means of a (layer-selective) wavelet encoding, a local 
resolution is achieved in a second direction by means of a phase encoding, 
and in a third direction by means of a frequency encoding. It is true that 
one can produce three-dimensional image data sets in this way, but the 
data acquisition time is relatively long due to the large number of phase 
encoding steps required. 
SUMMARY OF THE INVENTION 
An object of the present invention is to achieve faster pulse sequences 
using wavelet encoding. 
The above object is achieved in accordance with the principles of the 
present invention in a method for obtaining image information from a 
subject including the steps of, in an excitation phase, generating an RF 
pulse in a homogenous magnetic field, the RF pulse having an envelope 
corresponding to the Fourier transforms (dilation and translation) of a 
wavelet function, generating a constant magnetic field gradient in a first 
direction during emission of the radio frequency pulse, and also 
generating a further magnetic field gradient, having a time-varying 
amplitude and a linear local dependency, in a second direction. In a 
readout phase, a gradient echo signal, produced during the excitation 
phase, is sampled, digitized and entered into a line of a raw data matrix 
under a readout gradient in a third direction. The steps respectively 
constituting the excitation phase and the readout phase are repeated N 
times with a different wavelet encoding for each repetition, thereby 
generating a raw data matrix with N lines. An image matrix is produced by 
Fourier transformation of the raw data matrix in the third direction and 
wavelet transformation of the raw data matrix in the first direction. 
The invention makes use of a gradient echo sequence which, as is generally 
known, can be carried out with considerably shorter repetition times than 
spin echo sequence.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 schematically shows a known pole shoe magnet of a nuclear spin 
tomography apparatus with a C-shaped yoke, as is disclosed in U.S. Pat. 
No. 5,200,701. The magnetic drive ensues in the exemplary embodiment 
according to FIG. 1 through normally conductive magnetic coils 5. Gradient 
coil assemblies 7 and radio-frequency antennas 4 are respectively attached 
in the region of pole shoes 1 and 2. In the exemplary embodiment, the 
radio-frequency antennas 4 serve both for the transmission and the 
reception of signals. An examination subject 6 is positioned in the 
magnet. 
The magnetic coils 5 are fed by a magnet power supply 8, and the gradient 
coil assemblies 7 are fed by a gradient power supply 9. The antennas 4 are 
connected with a radio frequency unit 10. Using an image computer 12, an 
image is reconstructed from the signals obtained by the radio frequency 
unit 10, which image is shown on a monitor 13. The magnet power supply 8, 
the gradient power supply 9, the radio frequency unit 10 and the image 
computer 12 are controlled by a control computer 11. 
The foundations of wavelet transformation are explained in detail in the 
references identified above, and are presented here only in outline. The 
integral wavelet transformation F.sub.g(a,b) of a real-valued, 
energy-limited function f(x) is given by: 
##EQU1## 
A wavelet function g(a,b) arises through dilation and translation of a 
base wavelet function, i.e., in contrast to the Fourier transformation, 
the wavelet transformation maps on two parameters. The dilation "a" 
thereby influences the width of a wavelet function g(a,b) and the 
translation "b" of its position in the subject space. A series of 
functions are known that can be used as base wavelet functions. 
Battle-Lemarie wavelets are used in an exemplary embodiment. The wavelet 
function that arises is schematically shown in FIGS. 2 and 3. The index j 
thereby designates the dilation and the index k designates the translation 
of the base wavelet function. FIG. 2 shows the dilation of the base 
wavelet function .PSI..sub.j,k for three different dilatations a. In each 
dilatation, according to FIG. 3 the wavelets are pushed over the subject 
in a spatial direction. Of the translations, which run from 0 to 64, only 
every sixteenth translation is drawn. The other translations are indicated 
by points. Corresponding to the dilation parameters, arbitrarily broad 
subject windows can be produced, from which the raw data are then read 
out. A broad windowing (equivalent to small a) of the subject region 
corresponds to a lowpass filtering, while the wavelet function becomes 
narrower as a increases, and thereby increasingly takes on a high-pass 
characteristic. 
FIGS. 4 to 8 show the application of the wavelet encoding in a gradient 
echo pulse sequence. For the wavelet encoding of the signals, first a 
radio frequency pulse RF1 is emitted under the influence of a gradient Gx. 
The frequency spectrum of the radio frequency pulse RF1 thereby defines 
the dilation and translation of the wavelet function in connection with 
the gradient Gx. A strip profile perpendicular to the direction of the 
gradient Gx can thereby be purposely chosen. For small flip angles of the 
radio frequency pulse RF1, the envelopes of these radio frequency pulses 
and the strip profile required here are a Fourier-transform pair. The 
dilation a and the strength of the gradient Gx are related proportionally 
to one another. By means of amplification of the gradient Gx, a is thus 
enlarged, and the strip width is thereby reduced. The desired translation 
b can be achieved by displacement of the center frequency of the radio 
frequency pulse RF1 or by means of an offset of the gradient Gx. The 
gradient Gx is subsequently inverted in order to cancel the dephasing 
caused by the positive partial pulse. At the same time, a pre-phasing is 
achieved emitting a first gradient pulse Gz in the negative z direction. 
In contrast to known wavelet-based methods, in the exemplary embodiment a 
layer selection is already carried out during the excitation, and thus 
does not take place for the first time during a subsequent refocussing. 
For this purpose, during the emission of the radio frequency pulse RF1, in 
addition to the gradient Gx in the first direction a second gradient Gy is 
emitted in a second direction perpendicular to the first. The strength of 
this gradient Gy oscillates about a zero line. In the present exemplary 
embodiment, the gradient Gy has a sinusoidal shape, since the high 
gradient amplitudes and oscillation frequencies required here are most 
easily achieved by means of a resonant circuit in which the gradient coil 
functions as an inductance. The effect of this gradient Gy is illustrated 
on the basis of FIG. 10. FIG. 10 shows the magnetic field curve B in the 
y-direction for six different times in which the gradient Gy has six 
different strengths. With the time-dependent Gy gradient, a local and time 
dependency is thereby impressed on the homogeneous basic magnetic field in 
the second direction. 
As is well known, the nuclear spins are excited only when an excitation 
occurs at the Larmor frequency associated therewith. Since this Larmor 
frequency is dependent on time and on the prevailing local magnetic field, 
in the present case a time- and locus-dependent excitation of the nuclear 
spins ensues. 
The nuclear spins experience an excitation over the entire length of the 
radio frequency pulse RF1 only in a region around the location of the zero 
crossing of the magnetic field gradient Gy, thus defining a layer 
perpendicular to the y axis. Outside this layer, the resonance condition 
is indeed briefly fulfilled with each zero crossing of the oscillation of 
the gradient Gy. In these short time segments, no appreciable 
cross-magnetization can be produced, i.e. the flip angle outside the layer 
remains very small. 
The thickness d of the layer in which an appreciable excitation of the 
nuclear spins ensues is determined by the following factors: 
First, the extent to which an excitation also occurs at particular local 
magnetic field deviations from the basic magnetic field depends on the 
bandwidth of the excitation pulse RF. Second, the thickness d of the 
selected layer is determined by the frequency and the amplitude of the 
oscillating gradient Gy. The higher the amplitude of this gradient, the 
thinner the thickness d becomes. The thickness d of the layer also becomes 
narrower given a higher frequency of the oscillations of the gradient Gy. 
More precise statements concerning the connection between the selectivity 
of an excitation under the effect of an oscillating gradient are to be 
found in the article by W. S. Hinshaw, "The Sensitive Point Method," 
Journal of Applied Physics, vol. 47, no. 8, August 1976. A series of 
parameters are thus available for the setting the desired layer thickness 
d in the y direction. The position can be defined through the position of 
the zero crossing of the straight bundle according to FIG. 10. 
In the following readout phase, a positive gradient pulse Gz is activated. 
The dephasing caused by the negative gradient pulse Gzv is thereby 
canceled. In a known way, there arises a nuclear resonance signal in the 
form of a gradient echo, which is sampled M times in an acquisition window 
ADC under the influence of the gradient Gz. The gradient echo signal is 
thereby frequency-coded in the z-direction in a conventional manner. The 
signal is entered into a line of a raw data matrix RD according to FIG. 
11, in a way similar to conventional Fourier transformation methods. 
The wavelet encoding here replaces the otherwise standard phase encoding of 
the nuclear resonance signals. As in the phase encoding, in the wavelet 
encoding N measurements with different wavelet encoding must be carried 
out in order to fill N fully resolved lines of the image matrix. As 
already stated above, these N measurements are carried out with different 
dilations and translations of the base wavelet function. For the following 
application, a special feature of the wavelet coefficients in comparison 
with the Fourier coefficients is important: the wavelet coefficients 
correlate with a defined segment of the subject space, corresponding to 
their dilation and translation. 
From the raw data matrix RD obtained in this way, with M.times.N 
measurement values, an image can now be reconstructed according to methods 
explained in the references indicated in the introduction to the 
specification. 
By the use of gradient echoes in place of the spin echoes known in 
connection with wavelet encoding, a considerable reduction of the data 
acquisition time can be achieved. In particular, as in the FLASH method 
known from European Application 0 191 431, the repetition time can be 
selected shorter than the longitudinal and transverse relaxation time of 
the excited nuclear spins, so that a steady state becomes established. As 
in the FLASH method, the flip angle of the excitation pulse RF1 is 
selected smaller than 90.degree.. 
In order to create the same preconditions for each excitation in a sequence 
with a faster repetition rate, after the readout phase, residual phase 
coherences can be prevented by spoiler gradients GSPx, GSPy, GSPz in the 
x, y and z directions, respectively. 
With the use of wavelet encoding with a rapidly repeated gradient echo 
sequence, acquisition times of 10 seconds are achieved for a complete 
image from a layer. The particular advantage of the local selectivity of 
the wavelet encoding comes to bear when only a small part of the image 
data matrix is updated. Acquisition times of less than half a second can 
thereby be achieved, so that the method is particularly suited for 
real-time exposures in interventional MR examinations. 
A precise local resolution in three dimensions is often required precisely 
in interventional techniques. The design shown also enables another local 
resolution inside the selected layer, if, as shown in to FIG. 9, another 
phase encoding gradient Gyp is activated in the y direction after the 
excitation phase. In the exemplary embodiment, this phase encoding 
gradient can be activated in four levels, so that a three-dimensional raw 
data matrix 4.multidot.N.multidot.M of four raw data sets is obtained 
(i.e, a three-dimensional arrangement of at least two raw data sets). As 
in standard three-dimensional methods, a local resolution is achieved in 
the third dimension by means of Fourier transformation in the third 
direction that arises in this way. For a three-dimensional method of this 
sort, the thickness of the excited layer will be chosen broader, 
corresponding to the requirements. The resolution inside the layer 
thickness depends on the number of phase encoding steps in the y 
direction. 
For small subjects, e.g. in the knee region, under certain circumstances 
the layer selection during excitation could also be forgone, i.e., the 
oscillating gradient G.sub.y would be omitted. In this case, the 
above-explained resolution of the subject in the y direction would then 
usefully be executed by the above-identified phase encoding. 
An exemplary embodiment for the application of the wavelet encoding to the 
task of following the motion of an interventional instrument is explained 
in the following on the basis of FIGS. 12 and 13. A biopsy needle is used 
in the exemplary embodiment as an interventional instrument, but other 
instruments, e.g. surgical instrument, are also possible, as long as the 
path of motion is at least roughly defined. 
For the physician, the important thing is to determine the position of the 
biopsy needle 15 in the examination subject with good time and local 
(spatial) resolution. For this purpose, first a reference image of the 
overall subject space 19, with the subject of examination 6, is obtained. 
This is shown schematically in FIG. 12. Of course, this reference image 
could be obtained with the specified wavelet encoding, i.e. with 
wavelet-coded excitation of the nuclear resonance signals. In comparison 
with phase encoding, however, wavelet-coded excitation causes a worse 
signal-noise ratio. This is due to the fact that during phase encoding 
signals are always acquired from the overall subject region; in 
wavelet-coded excitation, in contrast, signals are acquired only from 
individual strips. In addition, in wavelet encoding small flip angles are 
used. It is thus advisable first to use standard phase encoding for 
obtaining the reference image, since here the advantage of wavelet 
encoding (i.e., the limitation to a region of the subject) is not a factor 
anyway. In order to make the data set of the reference image (as will be 
necessary later) compatible with updated, wavelet-coded data sets, the 
obtained digital raw data matrix is inversely Fourier-transformed for 
subsequent processing in the phase encoding direction and is subsequently 
wavelet-coded. The image is thereby partitioned into N strips, 
corresponding to the factors a and b of the wavelet encoding. After the 
complete reconstruction (inverse Fourier transformation in the direction 
of the readout gradient and inverse wavelet encoding in the wavelet 
encoding direction), a wavelet-coded image is present, whose signal-noise 
ratio substantially corresponds to a standard spin echo image. 
As already mentioned, with conventional Fourier transformation methods it 
would hardly be possible to achieve a sufficient time resolution for 
following the motion of the biopsy needle. Since the path of motion of the 
biopsy needle is, however, already known relatively well, it is sufficient 
to update only the data sets that lie in the region of the known path of 
motion 16 of the biopsy needle 15. In FIG. 13, the region 16 of the path 
of motion to be acquired is shown with cross-hatching, and the target to 
be reached with the biopsy needle 15 is designated 18. With wavelet 
encoding it is possible, as described above, to selectively record the 
region 16. The frequency encoding direction y thereby lies parallel to the 
direction of motion of the biopsy needle 15, and the wavelet encoding 
direction x is orthogonal thereto. 
Since, for the updating of the raw data, considerably fewer data samples 
must be acquired from the region 16 in comparison with the subject space 
19, this can ensue with correspondingly improved time resolution. If, for 
example, one proceeds on the basis of an image of size 30.times.30 cm, 
with a resolution of 128.times.128 pixels, updating the overall image 
requires 128 sequences according to FIGS. 4 to 8. If the region of motion 
16 can be limited, however, to for example 20 mm, then only twelve 
sequences are required for the same local resolution, i.e., the data 
required for updating can be obtained approximately ten times as quickly. 
During the intervention, only twelve lines need be updated respectively in 
the original raw data set comprising the overall reference image. Since, 
for the reasons named above, the data sets obtained with wavelet encoding 
have a smaller signal amplitude than the signals of the reference image 
obtained on the basis of phase encoding, the updated wavelet-coded data 
sets must be correspondingly normalized. 
The image obtained from the raw data sets obtained in this way thus shows 
the overall subject of examination in good spatial resolution, and also 
the motion of the biopsy needle 15 in good time resolution. Since the 
signals from the biopsy needle 15 change between the individual data set 
updatings only with respect to its tip, the signals from the rest of the 
biopsy needle are constantly averaged. Despite the low signal intensity 
due to the wavelet encoding, the biopsy needle 15 is thus shown with a 
good signal-noise ratio due to the averaging of the signals (with the 
exception of signals from the moved tip of the biopsy needle). 
In the previous discussion, it was assumed that in the region of 
examination only the biopsy needle 15 moves, while the rest of the subject 
of examination 6 is immobile. Of course, during a motion of the overall 
subject of examination 6, the spatial allocation between the updated 
region 16 and the rest of the subject of examination 6, which was acquired 
only at the beginning of the measurement in the form of a reference image, 
is no longer correct. The physician often no longer needs the information 
from the rest of the subject of examination, since he or she still 
remembers it during the interventional process. In order to avoid 
displaying false information, however, it is recommended to remove the 
reference image as soon as a motion of the subject occurs, and to continue 
to show only the region 16 of the path of motion. 
In order to determine a motion of the subject 6, it is possible to attach, 
for example, an MR-sensitive marker 17 to the subject. In this case, one 
can then likewise obtain, e.g. in an additional region 20, wavelet-coded 
data sets, and can acquire the motion of the marker 17 on the basis of 
these data sets. As soon as the motion of the marker 17 exceeds a certain 
threshold value, the reference image is removed. 
An alternative it is also possible to update the reference image, i.e. the 
data set for the complete subject of examination 6, as soon as a larger 
motion of the subject 6 has seen determined. 
In the previous display, the path of motion was in the y direction, and 
wavelet encoding of the nuclear resonance signals was undertaken in the 
x-direction and frequency encoding the nuclear magnetic resonance signals 
was undertaken in the y-direction. The method is not limited to a rigid 
coordinate system, however, since in MR equipment, by means of 
simultaneous activation of several gradients, resulting gradients can be 
realized in arbitrary directions. 
In order to show the biopsy needle in the image with good contrast, it can 
advantageously be filled with a negative contrast means, e.g. iron oxide. 
It is then displayed in black in the image. 
With the above-identified method, it is thus possible to follow the motion 
of an interventional instrument with good time resolution, since at all 
times only a small part of the overall data set is updated, and since 
short data acquisition times are possible. By the use of a gradient echo 
sequence with rapid repetition, the data acquisition time is further 
reduced. The characteristic of the wavelet function of allowing the data 
recording to be localized, in comparison with phase encoding, which always 
extends over the entire subject of measurement, thereby has a particularly 
positive effect. At the same time, the method also however delivers a high 
local resolution. During the acquisition of the reference image with the 
standard phase encoding, a high-quality image can be produced by means of 
the high signal-noise ratio that is thereby achievable. In the region of 
the path of motion, the less favorable signal-noise ratio, associated with 
the wavelet encoding, is further improved by averaging the sequentially 
obtained data. 
Understandably, various changes and modifications to the presently 
preferred embodiments described herein will be apparent to those skilled 
in the art. Such changes and modifications can be made without departing 
from the spirit and scope of the present invention and without diminishing 
its attendant advantages. Therefore, the appended claims are intended to 
cover such changes and modifications.