Method of and device for automatic phase correction of complex NMR spectra

A method is proposed for the automatic correction of phase errors in NMR spectra. The phase errors are interalia due to deficiencies of the NMR hardware, the time-shifted sampling of a magnetic resonance signal after the appearance thereof. The phase correction is performed by first determining peak locations in a modulus spectrum determined from the complex spectrum and by determining the phases in the peak locations, after which the phase in the peak locations are fitted to a predetermined polynomial by means of a least-squares optimization procedure. The coefficients of the polynomial are thus defined. Subsequently, the NMR spectrum is point-wise corrected by means of the phase polynomial determined. The proposed method can be simply implemented in a NMR device; no severe requirements are imposed as regards the signal-to-noise ratio and the resolution of the spectrum. In practical situations an NMR spectrum usually comprises many spectral lines. Therefore, the method is not susceptible to the effects of overlapping spectral lines.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates to a method of correcting a complex resonance 
spectrum obtained from sampling values of at least one resonance signal by 
Fourier transformation, which resonance signals are generated by means of 
R.F. electromagnetic pulses in an object situated in a steady, uniform 
magnetic field, there being determined peak locations in the complex 
spectrum and phase values in the peak locations. 
The invention also relates to a device for determining a complex magnetic 
resonance spectrum of at least a part of an object, which device comprises 
means for generating a steady magnetic field, means for applying magnetic 
field gradients on the steady, uniform magnetic field, means for 
transmitting R.F. electromagnetic pulses in order to excite resonance 
signals in the object, means for receiving and detecting the excited 
resonance signals and means for generating sampling values from the 
detected resonance signals, and also comprises programmed means for 
determining, using Fourier transformation, the complex magnetic resonance 
spectrum from the sampling values, which programmed means are also 
suitable for determining peak locations in the complex spectrum and phase 
values in the peak locations. 
2. Description of the Prior Art 
A method of this kind is known from the article by C. H. Sotak et al. in 
"Journal of Magnetic Resonance", Vol. 57, pp. 453-462, 1984. Said article 
describes a non-iterative automatic phase correction for a complex 
magnetic resonance spectrum containing phase errors. The phase errors are 
due inter alia to deficiencies of the NMR device, for example 
misadjustment of the means for receiving and detecting the resonance 
signals or the finite width of the R.F. electromagnetic pulses; phase 
errors occur notably also due to incorrect timing. For example, when the 
resonance signal (the so-called FID signal) which occurs immediately after 
the R.F. electromagnetic pulse is sampled, in practice the instant at 
which the FID signal commences will hardly ever coincide with the instant 
at which a first sampling value is obtained. Across the complex spectrum, 
therefore, frequency-independent (zero-order) as well as 
frequency-dependent (first order and higher order) phase errors will 
occur. In said article a method is proposed for correcting zero-order and 
first-order phase errors by way of a linear phase correction across the 
complex spectrum. The complex spectrum can be considered to be a real and 
an imaginary spectrum (absorption mode and dispersion mode, respectively). 
Using a so-called DISPA (plot of dispersion versus absorption), an image 
is indicated for a single Lorentzian spectral line. When the Lorentzian 
spectral line is ideal (i.e. when there is no phase shift), an image is 
produced in the form of a circle which serves as a reference image for 
non-ideal Lorentzian lines. Using a DISPA, in principle the phase error of 
non-ideal Lorentzian lines can be determined with respect to an ideal 
Lorentzian line. The linear phase correction disclosed in the cited 
article utilizes this phenomenon in order to determine the 
frequency-dependent phase error. First a power spectrum is determined from 
the complex spectrum and peak locations of suitable resonance lines are 
determined from said power spectrum. Subsequently, the phase of a peak 
nearest to the centre of the spectrum is determined by means of DISPA. 
Using this phase, the zero-order phase error is corrected. Subsequently, 
the phase of the other peaks is determined by means of DISPA and, using 
the phases of the other peaks determined, a linear phase variation is 
estimated as well as possible in order to approximate the first-order 
phase error. Using the approximation found for the zero-order and 
first-order phase error, the complex spectrum is ultimately 
phase-corrected point by point. The known method imposes requirements as 
regards peak separation; peaks in the spectrum which are comparatively 
near to one another cannot be used. Furthermore, there must be at least 
two peaks which are comparatively remote from one another in the spectrum; 
if this is not the case, it will be necessary to create two remote peaks 
in the spectrum by the addition of an agent. By using linear phase 
correction in the known method, for example only phase shifts will be 
compensated for which are caused by the time shifted measurement of the 
resonance signals. Inevitably present phase errors due to other causes, 
will not be covered. 
It is an object of the invention to provide a method which does not have 
the described drawbacks. 
To achieve this, a method in accordance with the invention is characterized 
in that coefficients of a frequency-dependent phase function extending 
across the complex spectrum are approximated from the phase values in the 
peak locations in accordance with a predetermined criterion, after which 
the complex spectrum is corrected by means of the frequency-dependent 
phase function determined. The frequency-dependent phase function may be a 
polynomial whose degree may be predetermined. It is alternatively possible 
to define the power of the polynomial during the approximation. As a 
result, any phase-dependency can be approximated. The method in accordance 
with the invention is based on the recognition of the fact that the phases 
in the peak locations of the complex spectrum must be zero in the absence 
of phase errors; the absorption mode signal is then maximum and the 
dispersion mode signal is zero. When the coefficients of the 
frequency-dependent phase function have been determined, the complex 
spectrum can be corrected by means of the frequency-dependent phase 
function determined by point-wise correcting the real and the imaginary 
part thereof as a function of the frequency. 
A version of a method in accordance with the invention is characterized in 
that the peak locations are derived from a modulus spectrum which is 
determined from the complex spectrum. The peak locations can be suitably 
determined from the modulus spectrum because this spectrum is not 
influenced by the phase errors occurring. 
A version of a method in accordance with the invention in which peak 
parameters are determined in the peak locations during the determination 
of the peak locations is characterized in that in the case of overlapping 
peaks the overlapping peaks are corrected by means of the peak parameters 
determined. The peak parameters determined for overlapping peaks can be 
used for correcting neighbouring overlapping peaks by utilizing the fact 
that the real and the imaginary part must satisfy Lorentzian formulas; an 
excessive contribution to a line can be subtracted from a neighbouring 
line. If such a correction were not performed, ultimately a spectrum which 
has not been completely corrected could be obtained. It is to be noted 
that such a correction can be dispensed with in the case of spectra 
comprising numerous lines. When a wide background is present in the 
spectrum, the parameters of the wide background (which may be considered 
to be a wide spectral line) can be determined; using the method described 
for correcting overlapping lines, the parameters determined for the wide 
background can be used to eliminate the effect of the wide background. 
Moreover, a model of the complex spectrum can be calculated on the basis of 
the peak locations and peak parameters determined. The phase of the 
complex spectrum can then be corrected in the peak locations by means of 
the frequency-dependent phase function determined and in frequencies 
outside the peak locations by means of a weighted phase from the phases of 
the peak locations. Using the model, the degree of contribution of the 
peaks to a frequency outside the peak locations is determined in order to 
determine weighting factors for the weighted phase. Notably when a very 
strong peak is present in the spectrum, for example a water peak in proton 
spectra, it may be necessary to use such a somewhat refined correction. 
The invention will be described in detail hereinafter whith reference to a 
drawing; therein:

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 diagrammatically shows a device 1 in accordance with the invention 
which comprises, arranged within a shielded space 2, magnet coils 3 for 
generating a steady, uniform magnetic field (the means for generating a 
steady magnetic field), gradient coils 5 (the means for applying magnetic 
field gradients), and a transmitter and receiver coil system 6, comprising 
a transmitter coil 7 and a receiver coil 8 (the means for transmission and 
reception). When the magnet coils 3 are formed by a resistance magnet, 
they are powered by a DC power supply source 4. When the magnet coils are 
formed by a permanent magnet, the DC power supply source 4 will of course 
be absent. The magnet coils can also be formed by a superconducting 
magnet. The transmitter coil 7 is coupled, via an R.F. power amplifier 9 
and an R.F. generator 10, to a reference generator 11. The R.F. generator 
10 serves to generate an R.F. electro-magnetic pulse for the excitation of 
nuclear spins in the object situated within the magnet coils 3. The 
gradient coils 5, are controlled by a gradient coil control device 12 and 
serve to generate magnetic field gradients which are superposed on the 
steady, uniform magnetic field. Generally three gradients can be generated 
their field direction coincides with the direction of the steady, uniform 
magnetic field and their respective gradient directions z, y and x extend 
mutually perpendicularly. The receiver coil 8 serves to receive magnetic 
resonance signals of nuclear spins generated in the object by the 
transmitter coil 7 and is coupled to a detector 13 (the means for 
detection) for detecting the magnetic resonance signals 14 in quadrature 
detection. The detector 13 is coupled to the reference generator 11 and 
comprises low-pass filters and analog-to-digital converters (the means for 
generating sampling values) for digitizing the resonance signals received 
and detected. Control means 15 serve for the control and timing of the 
R.F. generator 10 and the gradient coil control device 12. The device 1 
also comprises processing means 16 for processing the digitized resonance 
signals 17. The processing means 16 are coupled to the control means 15. 
For the display of spectra formed by means of programmed means in the 
processing means 16, the processing means are also coupled to a display 
unit 18. The processing means 16 comprise a memory 19 for the storage of 
the programmed means and for the storage of the non-corrected and 
corrected spectra and other data formed by means of the programmed means. 
The processing means 16 are generally formed by a complex computer system 
comprising a variety of many facilities for coupling to peripheral 
equipment. 
FIG. 2A shows a Lorentzian spectral line. An absorption line a1 is plotted 
as a function of the frequency .omega. in the upper graph and a dispersion 
line d1 is plotted as a function of the frequency .omega. in the lower 
graph of FIG. 2A. An object (not shown) is arranged within the magnet 
coils 3 so as to be exposed to a steady, uniform magnetic field B.sub.o 
generated in the magnet coils. Under the influence of the field B.sub.o a 
small excess of nuclear spins present in the object will be directed in 
the direction of the field B.sub.o. From a macroscopic point of view the 
small excess of nuclear spins directed in the direction of the field 
B.sub.o is considered as a magnetization M of the object or as a slight 
polarization of the nuclear spins present in the object. With respect to a 
coordinate system which is stationary to an observer, the magnetization M 
performs a precessional motion about the magnetic field B.sub.o 
:.omega..sub.o =gamma. B.sub.o, where gamma is the gyromagnetic ratio and 
.omega..sub.o is the resonance frequency of the nuclear spins. The object 
arranged in the magnetic field B.sub.o is subsequently irradiated with an 
R.F. electromagnetic pulse generated in the transmitter coil 7 by the R.F. 
generator 10. The steady magnetic field B.sub.o defines a z-axis of an xyz 
cartesian coordinate system which rotates about the z-axis thereof at the 
angular frequency .omega..sub.o of the R.F. electromagnetic pulse (a 
coordinate system rotating in the same direction). Nuclear spins having a 
Larmor frequency equal to the angular frequency .omega..sub.0 will be 
synchronized with the rotating coordinate system. Before and after the 
application of the R.F. electro-magnetic pulse the magnetization M will be 
stationary in the rotating coordinate system. The rotation in the rotating 
coordinate system of the magnetization M will be proportional to the pulse 
duration and the pulse amplitude of the R.F. electromagnetic pulse. A 
component of the magnetization M projected onto the xy plane of the 
rotating coordinate system, being coincident with the x axis, forms the 
dispersion component and a component which coincides with the y axis of 
the rotating coordinate system forms the absorption component of the 
magnetization M. When the power of the applied R.F. electromagnetic pulse 
is so small that no saturation occurs, the description of the absorption 
component as a function of the frequency is in conformity with the 
Lorentzian spectral line a1, a Fourier transform of an exponential 
function. The dispersion component is the associated component. The 
absorption line a1 and the dispersion line d1 are related via a Hilbert 
transformation: d1=a1 (2.pi./.omega.), where represents the convolution 
operation (for a detailed description of absorption and dispersion, see: 
Fourier Transform NMR Spectroscopy, D. Shaw, published by Elsevier, 1976, 
pp. 33). The exponential function describes the decreasing of the 
magnetization M projected onto the xy plane (the so-called transverse 
magnetization). This generally known relaxation phenomenon is also 
described in said manual. The absorption line a1 (being out of phase with 
respect to the excitation frequency) is of most interest to a 
spectroscopist: the absorption of energy by the system of nuclear spins 
(object), the behaviour of the magnetization as a function of the 
frequency. When the object contains not only water-bound protons (with 
which synchronization takes place) but also fat-bound protons which are 
present in a different chemical environment, a water and fat spectrum will 
be obtained after Fourier transformation of an NMR resonance signal. In 
the absorption spectrum thereof two (dominant) resonance lines occur. It 
will be evident that when the object also contains protons situated in 
other chemical environments, the spectrum will exhibit more resonance 
peaks. For example, when double phase-sensitive detection is used, in 
which case the detector comprises a first phase-sensitive detector (not 
shown in detail) whereto the reference signal generated by means of the 
reference generator 11 is applied as a reference signal and a second 
phase-sensitive detector whereto the 90.degree. phase-shifted reference 
signal is applied, the two digital signals 17 will become available after 
signal sampling by the analog-to-digital converters in the detector 13, 
which signals serve to determine the absorption mode spectrum and the 
dispersion mode spectrum therefrom by Fourier transformation in the 
processing means 16. The dispersion mode spectrum can be considered to be 
the real part of the transverse magnetization as a function of the 
frequency and the absorption mode spectrum can be considered to be the 
imaginary part thereof. The NMR spectrum can be considered to be the pulse 
response of the nuclear spin system (object). When phase errors occur in 
the NMR device 1, they will have an effect on the spectrum. Broken lines 
in FIG. 2A indicate the effect of a 90.degree. phase shift on the 
absorption line a1 and on the dispersion line d1; it can be simply 
established that: a2=d1 and d2=-a1. In said article by Sotak correction 
formules are given for the linear correction of spectra containing phase 
errors (on page 453 of the Sotak article). 
FIG. 2B shows a so-called DISPA of a Lorentzian spectral line. Pages 
453-454 of said article by Sotak describe that the plotting of the 
dispersion d as a function of the absorption a results in a circle c in 
the case of an ideal Lorentzian spectral line. The diameter of the circle 
c is equal to the absorption peak of the absorption line a1. The article 
also describes the effect of a phase error on the circle c. In FIG. 2B the 
reference c' denotes a DISPA circle where a 90.degree. phase shift has 
occurred. Sotak demonstrates that the circle c is rotated with respect to 
the origin 0 for arbitrary phase errors. 
FIG. 3 shows a decomposition of two resonance lines from a magnetic 
resonance spectrum. It is assumed that the object to be measured contains 
water and other materials containing protons (in this case one material, 
for example fat). The upper graph of FIG. 3 shows a disturbed absorption 
spectrum and the lower graph shows a disturbed dispersion spectrum. 
Therein, a3 is the absorption peak of the water (the reference generator 
11 is tuned to the Larmor frequency of protons in water) and a4 denotes 
the disturbed absorption peak of fat. The references d3 and d4 denote the 
corresponding respective dispersion peaks. The Larmor frequency of protons 
in fat deviates from that of protons in water; in this respect: 
.omega.=gamma. (1-.sigma.). B.sub.o, where .sigma. is a shielding constant 
(the effect of the so-called chemical shift due to the difference in 
shielding of protons by electrons). The phase error for fat (-90.degree. 
in the example shown) is caused, for example in that the resonance signal 
is sampled only some time after t=0 (centre of the R.F. electromagnetic 
pulse); this often occurs due to instrumental deficiencies; this effect 
can occur also in the case of so-called spin echo measurements and other 
measurements, but in that case it will be due, for example to the 
non-coincidence of a first signal sample and the maximum of an echo 
signal. This shifted measurement has no effect on the water peak in the 
present example (is synchronized with the rotating coordinate system and 
with the frequency of the reference generator 11); however, it has an 
effect on the fat peak (in this case a 90.degree. phase shift). It will be 
evident that the absorption spectrum is disturbed thereby. From the 
absorption and dispersion spectrum measured, Sotak determines a power 
spectrum and peak locations therefrom. DISPA is used to determine the 
phase of a peak in order to execute a zero order phase correction. Sotak 
subsequently determines the phase of the other peaks by means of DISPA and 
estimates a linear phase variation therefrom. Finally, Sotak performs a 
linear phase correction by means of the formules stated on page 453 of the 
cited article. In FIG. 3 the line 1 represents a linear phase variation 
across the spectrum; the phase error is zero for .omega.= .omega..sub.0. 
When there are a number of causes of phase errors, other than the shifted 
measurement (for example, hardware causes), the phase error will not vary 
linearly across the spectrum. In the case of a wide background in the 
spectrum, the method in accordance with Sotak will require a separate 
correction. In accordance with the invention, using the programmed means 
stored in the memory 19, the processing means 16 first determine a modulus 
spectrum from the absorption spectrum and the dispersion spectrum measured 
by means of the NMR device 1. From the modulus spectrum there are 
determined peak locations with associated parameters, such as: peak 
amplitude, peak width at half amplitude and peak position. In a number of 
peak locations the phase is determined according to: 
EQU .phi..sub.i =arctg Im/Re, 
where .phi..sub.i is the phase of the peak having the frequency 
.omega.=.omega..sub.i, and Re and Im are the real part and the imaginary 
part, respectively, of the complex magnetic resonance spectrum in 
.omega.=.omega..sub.i. Subsequently, a polynomial approximation is 
executed: 
EQU .phi.=.phi..sub.o +.phi..sub.1.f.sub.i +.phi..sub.2.(f.sub.i).sup.2 + 
where f.sub.i is the frequency in the peak i and where .phi..sub.0, 
.phi..sub.1, .phi..sub.2, . . . are the coefficients to be determined. The 
polynomial is adapted as well as possible, for example by means of a 
least-squares optimization procedure (for example, as described on page 
817-819 of Advanced Engineering Mathematics, E. Kreyszig, 4th Edition, 
Wiley 1979), to the phases .phi..sub.i in the peaks. Alternatively, an as 
correct as possible phase polynomial can be determined by iteration of 
coefficients. Finally, using the polynomial determined the complex 
spectrum (absorption spectrum and dispersion spectrum) will be point-wise 
corrected (i.e. for a number of data points in the frequency domain) by 
means of the formules stored in the programmed means: 
EQU Re'(f)=Re(f).cos(.phi.[f]+Im(f).sin(.phi.[f]) and 
Im'(f)=-Re(f).sin(.phi.[f]+Im(f).cos(.phi.[f] 
where Re'(f) is the corrected real part of the complex spectrum, Im'(f) is 
the corrected imaginary part of the spectrum, Re(f) is the real part and 
Im(f) is the imaginary part of the non-corrected complex spectrum. The 
above correction with the determined frequency-dependent phase function 
can also be performed only in the peak locations and a different strategy 
can be adopted for intermediate points. A model of the spectrum is formed 
on the basis of the peak locations and the peak parameters. In an 
intermediate point in the model the contribution of various peaks is 
calculated and the phase is corrected thereby in a weighted manner. For 
example, when a contribution of a first peak amounts to 80% and that of a 
second peak to 20%, phase correction in the intermediate point is realized 
with 80% of the phase according to the frequency-dependent phase function 
determined in the first peak and with 20% of the phase according to the 
frequency-dependent phase function determined in the second peak. 
FIG. 4 shows a decomposition of two overlapping resonance lines from a 
magnetic resonance spectrum. For a clear description of the effect of 
overlapping in relation to the invention it is assumed that no phase 
errors are involved. In the upper graph of FIG. 4 two absorption lines a5 
and a6 are shown as a function of the frequency .omega.. In the graphs 
therebelow two associated dispersion lines d5 and d6 are shown and a 
modulus graph M which is determined from the absorption lines a5 and a6 
and from the dispersion lines d5 and d6 by means of the programmed means. 
Below the modulus graph M the associated phase in the peak locations 
.omega..sub.1 and .omega..sub.2 is determined, i.e. .phi.[.omega..sub.1 ] 
and .phi.[.omega..sub.2 ], respectively. In the absence of overlapping, 
.phi.[.omega..sub.1 ] and .phi.[.omega..sub.2 ] will be zero when no phase 
errors are present. If a phase correction were still performed, of course 
it would be uncalled for. Using further parameters determined in the 
overlapping peaks, such as peak amplitudes M[ .omega..sub.1 ], 
M[.omega..sub.2 ] and pulse widths at half amplitude, B1 and B2, the 
effect of (strongly) overlapping lines can be eliminated prior to the 
execution of the phase correction. Using the parameters of a neighbouring 
line, the phase of the adjacent line determined is corrected. When the 
spectrum contains many spectral lines (a situation which frequently occurs 
in practice), the correction for overlapping lines can usually be omitted. 
In that case phase contributions in the peak positions are averaged out. 
In the case of a poor signal-to-noise ratio, an excessively large number 
of peaks (also a number due to noise) would probably be involved in the 
phase correction. Because of the random nature of noise, noise effects 
would be averaged out. In that case it is not necessary to take it into 
account noise (this is the case for most measurements; by repeating the 
measurement, at the expense of the overall measuring time, and averaging 
the resonance signals, the signal-to-noise ratio can be improved). The 
execution of the phase correction can also be preceded by filtering in the 
time domain in order to reduce the effect of noise on the phase correction 
and to facilitate the determination of spectral peaks in a modulous graph 
determined from the filtered signal. 
FIG. 5 shows a flow chart illustrating the method in accordance with the 
invention. The method in accordance with the invention is stored in the 
form of programmed means in the memory 19 and is executed in the 
processing means 16. It is assumed hereinafter that a magnetic resonance 
measurement has been performed by means of the NMR device 1 (magnetic 
resonance measurements are generally known and are described in many 
publications: in chapter 5 and chapter 6 of said book by Shaw). As from F1 
the programmed means will be described hereinafter. In F2 a real spectrum 
Re(.omega.) (u mode) and an imaginary spectrum Im(.omega.) (v mode) are 
determined by Fourier transformation by means of the programmed means. In 
F3 a choice can be made as regards the filtering in advance or not of the 
complex spectrum obtained. When a filtering operation F4 is performed, the 
programmed means execute an inverse Fourier transformation on the complex 
spectrum Re(.omega.) and Im(.omega.), filter the result obtained by means 
of inverse Fourier transformation, using (for example) an exponential 
digital filter, and finally perform a Fourier transformation on the 
filtered result. The filtered spectrum is stored in the memory 19. 
Subsequently, in F5 the modulus spectrum is determined from the complex 
spectrum, filtered or not. In F6 peak positions .omega..sub.i are 
determined and also the phases .phi..sub.i therein, and possibly further 
peak parameters such as peak amplitudes M(.omega..sub.i) and peak widths 
at half amplitude Bi. In F7 it can be decided whether or not a correction 
will be performed in advance for overlapping spectral lines. When a 
correction is performed in advance, it takes place in F8 on the basis of 
.omega..sub.i, M(.omega..sub.i) and Bi for neighbouring peaks. In F9 the 
polynomial is defined whereby the least-squares optimization procedure is 
performed. In F10 the coefficients .phi..sub.0, .phi..sub.1, .phi..sub.2, 
. . . of the polynomial are determined by means of the least-squares 
optimization procedure. In F11 the real spectrum Re(.omega.) and the 
imaginary spectrum Im(.omega.) are corrected with the phase .phi.(.omega.) 
determined from the polynomial. In F12 the corrected and the non-corrected 
spectrum are displayed on the display unit 18. In F13 the programmed means 
continue with other tasks to be performed by means of the NMR device 1. 
The blocks in FIG. 5 are designated as follows: 
F1 Start 
F2 Fourier transformation 
F3 Filtering (yes/no)? 
F4 Filtering 
F5 Determination of modulus spectrum 
F6 Determination of peak locations and peak parameters 
F7 Correction for overlapping peaks (yes/no)? 
F8 Correction for overlapping peaks 
F9 Determination of polynomial 
F10 Determination of coefficients of polynomial 
F11 Correction of complex resonance spectrum 
F12 Display of corrected spectrum 
F13 Stop 
Not all nuclear spins in the object need be excited. For example, a part of 
the object (volume of interest) can be excited in order to display a 
corrected spectrum thereof. In that case so-called volume-selective 
excitation will take place. This is realized by exciting the gradient 
coils 5 (G.sub.x, G.sub.y and G.sub.z) in a given sequence by means of the 
gradient coil control device 12 and by transmitting an R.F. 
electromagnetic pulse by means of the transmitter coil 7. For a detailed 
description of volume-selective excitation reference is made to, for 
example an article by Luyten and Den Hollander "1H MR Spatially Resolved 
Spectroscopy", Magnetic Resonance Imaging, Vol. 4, pp. 237-239, 1986. It 
will be evident that the described method is not restricted to proton 
spectra and that, for example .sup.13.sub.C, .sup.31.sub.p, etc. spectra, 
high-resolution spectra, etc. can also be corrected. Spectra of organic 
and/or anorganic materials can be corrected. The method can be combined 
with many known NMR pulse sequences for spectroscopy.