Abstract:
In a method and apparatus for generating an image from magnetic resonance signals, two image matrices generated from magnetic resonance signals are added to or subtracted from one another pixel-by-pixel, to generate a further image therefrom. The magnitude added or subtracted for each picture element is formed by multiplication of a magnitude value of the second image matrix by a weighting factor. The weighting factor is dependent on the magnitude value of the second image matrix such that it is higher given a high magnitude value than for a low magnitude value. The magnitude noise is decreased compared to a linear addition or subtraction, and uncontrolled signal reductions are avoided. An exponent in the power of the magnitude value of the second image matrix a signal-dependent weighting factor can be set at an input device.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention is directed to a method for generating an image from magnetic resonance signals of the type wherein a first image matrix is generated from first magnetic resonance signals and a second image matrix is generated from second magnetic resonance signals, an overall magnitude is formed for each picture element by adding or subtract a magnitude dependent on the appertaining magnitude value of the second image matrix is to or from a magnitude that is dependent on the magnitude value of the corresponding picture element of the first image matrix, with the overall magnitudes being employed for generating the image.  
           [0003]    The present invention also is directed to a method for generating an image from magnetic resonance signals of the type wherein a first group of location coded magnetic resonance signals and a second group of location coded magnetic resonance signals different therefrom are received, overall signals are formed from the respective magnetic resonance signals with coinciding location coding of the first group and the second group, wherein the overall signal is formed by adding or subtracting a second magnitude dependent on the appertaining magnetic resonance signals of the second group to or from a first magnitude that is dependent on the magnetic resonance signals of the first group, and wherein the overall signals are utilized for reconstruction of the image.  
           [0004]    The invention also is directed to a magnetic resonance tomography apparatus for the implementation of the method and to a data processing system for a magnetic resonance tomography apparatus.  
           [0005]    2. Description of the Prior Art  
           [0006]    It is known in the field of magnetic resonance tomography to add or subtract two congruent images generated in different ways, i.e. images that constitute the same portion in the examination subject. The magnitude value of the appertaining picture element of the second image is added to or subtracted from a magnitude value of a picture element of the first image for each picture element. In this way, contrasts can be intensified, new contrasts can be generated or image artifacts can be avoided. The congruent images are generated from a common pulse sequence, i.e. they derive from a readout sequence with common phase coding.  
           [0007]    The picture elements are represented in the images as complex numbers, and the magnitude value of a complex number a+bi is (a 2 +b 2 ) ½  (also called the absolute value).  
           [0008]    An image addition is implemented, for example, in the DESS technique (Double Echo Steady State). A specific pulse sequence is generated with which a FISP echo as well as a PSIF echo can be read out within a readout train. The DESS method is disclosed, for example, in the article by W. Nitz in electromedica 65 (1997), No. 1. The FISP echo (Fast Imaging with Steady State Precession) is a gradient echo. In the preferred field of application of orthopedics, it supplies a T 1 /T 2  contrast typical of steady state techniques (SSFP pulse sequences). The PSIF echo arises from a FSIP pulse sequence that sequences backwards. This is also referred to as a quasi-spin echo. Dependent on the repetition time, it carries a strong T 2  contrast. The magnitude addition of the image resulting from the FISP echo with the image resulting from the PSIF echo supplies an image with good anatomy and very good emphasis of fluid, for example the synovil fluid, at pathological locations.  
           [0009]    An image subtraction is known, for example, from German OS 196 16 387. The HIRE method (high-intensity reduction sequence) is disclosed therein. After an excitation, two groups of magnetic resonance signals are acquired in two time spans at a different intervals from the excitation. An image is acquired on the basis of the signal differences of respective magnetic resonance signals of the first and second groups with coinciding location coding. The first group of magnetic resonance signals or echos, which is acquired shortly after the excitation, results in an image with normal T 2  weighting. The second group of magnetic resonance signals or echos, which is acquired later in a time span than the first group and wherein a tissue part having a longer T 2  time constant supplies the significant signal contribution, yields a highly T 2 -weighted image. A fluid such as, for example, the cerebral spinal fluid (CSF), leads to a very high signal contribution in a normally T 2 -weighted image, for example to a significantly higher signal contribution in the brain than the other brain areas. In the normally T 2 -weighted image acquired shortly after the excitation, a neighboring image region would be over-shadowed by this high signal contribution of the CSF and the resolution would thus be locally diminished. Moreover, artifacts referred to as CSF flux or pulsation artifacts also arise. When the highly T 2 -weighted image acquired at a later point in time is subtracted from the magnitude image acquired shortly after excitation, then an image results that is still T 2 -weighted and wherein the fluid, particularly CSF, is highly suppressed.  
           [0010]    One disadvantage of the known image subtraction or image addition methods is that the aggregate noise increases approximately by a factor of {square root}{square root over (2)}.  
         SUMMARY OF THE INVENTION  
         [0011]    An object of the present invention is to provide a method and a nuclear magnetic resonance tomography apparatus wherein this disadvantage is avoided.  
           [0012]    In a method of the type initially described, this object is inventively achieved in that the magnitude for each picture element of the second image matrix is formed by multiplication of the magnitude value of the second image matrix by a weighting factor, the weighting factor being dependent on the magnitude value of the second image matrix such that it is higher for a high magnitude value than for a low magnitude value.  
           [0013]    The second magnitude thus is formed for each picture element such that its contribution to the respective overall magnitude is lower given a low value of the magnitude value of the second image matrix than it would be given a linear addition or subtraction of the magnitude values of the two image matrices, and such that it is essentially as large as it would be given a linear addition or subtraction when the magnitude value of the second image matrix is high. In the described method, a self weighting of the magnitude value of the second image matrix employed for the correction or improvement of the image quality of the first image matrix is made. In other words: the second magnitude weights itself dependent on the local image conditions. This results in only those picture elements that have a high signal magnitude being superimposed with large contribution on the respective picture element of the first image matrix. Picture elements having a slight signal contribution lead to no significant influence on the magnitude value of the first image matrix. In other words, only the picture elements that are in fact useable for the correction or improvement of the first image matrix are filtered out of the second image matrix pixel-by-pixel. The remaining pixels remain essentially out of consideration, or at least are weighted less. This results in the advantage that the noise is lower in the resulting image then it would be given a linear addition or subtraction of the two images.  
           [0014]    Another advantage is that an uncontrolled signal reduction or reduction of the image quality is avoided in regions where there is actually nothing to correct or improve.  
           [0015]    Preferably, the first image matrix is reconstructed from a first group of location-coded nuclear magnetic resonance signals by means of Fourier transformation, and the second image matrix is likewise reconstructed by Fourier transformation from a second group of location-coded nuclear magnetic signals different from the first group. In particular, a magnitude formation occurs after the Fourier transformation. The method of the invention can be implemented not only with Fourier-transformed values or magnitude values but also can be implemented using raw data acquired directly from the magnetic resonance signals. This is explained in greater detail below in conjunction with the method according to the second embodiment.  
           [0016]    The weighting factor can be realized, for example, by a mathematical step function that sets the weighting factor to a low value or to zero below a defined threshold of the magnitude value of the second image matrix.  
           [0017]    In a preferred version of the first embodiment of the method, the second magnitude is formed such for every picture element such that it is dependent on the magnitude value of the second image matrix in non-linear fashion, particularly steadily non-linear, with the same non-linear mathematical function being employed for the formation of the overall magnitudes of all picture elements.  
           [0018]    Preferably, the second magnitude for every picture element is formed such that it is dependent on a power of the magnitude value of the second image matrix, with the exponent being the same for all picture elements and is greater then 1 (one), particularly greater than or equal to 2. A steady non-linear dependency of the weighting factor on the magnitude value of the second image matrix is used for this purpose. Compared to a step function, this version has the advantage that image artifacts are avoided.  
           [0019]    In a preferred embodiment, the exponent in the power of the magnitude value of the second image matrix is varied, particularly in order to achieve an optimally high contrast in the image and/or an optimum correction of the first image matrix with the second image matrix. The variation of the exponent is undertaken, for example, by a computer program or manually by an operator.  
           [0020]    Preferably, the exponent in the power of the magnitude value of the second image matrix is greater in the second magnitude than an exponent of a power of the magnitude value of the first image matrix. The self-weighting is further intensified as a result.  
           [0021]    The method is not limited to the superimposition of two image matrices. One or more further image matrices can be employed for generating the image in the same way as the first image matrix or as the second image matrix. This has the advantage that the advantageous regions of a number of image matrices are imported into the first image matrix by the described self-weighting. The two image matrices and the further image matrices that are possibly employed, are congruent at least in a sub-region and preferably result from a pulse sequence deriving from a common radio-frequency excitation pulse.  
           [0022]    In another preferred embodiment of the method, the first image matrix is more signal-intensive, particularly more signal-intensive on average, than the second image matrix. In particular, the first image matrix is the most signal-intensive image matrix that can be generated from a pulse sequence, i.e. from a common readout train.  
           [0023]    The method of the invention is preferably applied to the initially described HIRE method or to the initially described DESS method, so that these two known, linearly functioning superimposition methods are provided with a self-weighting.  
           [0024]    For realizing a self-weighting HIRE method, the overall magnitudes are formed by subtraction of the second magnitude from the first magnitude, with those magnetic resonance signals that would be subtracted from one another given application of a high-intensity reduction pulse sequence being employed for generating the two image matrices.  
           [0025]    As initially set forth, the HIRE method is especially suited for the examination of a subject that contains a first tissue having a first T 2  time constant as well as a second tissue having a significantly longer, second T 2  time constant. For such a tissue, the magnetic resonance signals in the method of the invention preferably are acquired for both image matrices during the time span wherein the cross-magnetization that has arisen after an excitation decreases with the respective T 2  time constant, and the magnetic resonance signal for the first image matrix is acquired soon after the excitation, and the magnetic resonance signal for the second image matrix is acquired in a time interval wherein the second tissue supplies the significant signal contribution.  
           [0026]    With application of the method of the invention to the HIRE pulse sequence, the advantage is achieved that a determinant image subtraction only occurs in those regions of the first image matrix wherein the magnitude of the second image matrix is large. In the examination of the brain, for example, this applies to the aforementioned cerebral spinal fluid (CSF). By contrast, only a slight magnitude is subtracted in the region of an edema (seat of a disease with surrounding accumulation of fluid) or in the region of normal tissue (for example, muscle tissue as well), so that the signal-to-noise ration (S/N) of these regions is not unnecessarily deteriorated. With a summary image subtraction, regions would also have their signal value reduced dependent on their local T 2  values, so that, for example, an edema would disadvantageously have a SN similar to the normal, surrounding tissue.  
           [0027]    In another preferred embodiment, the method of the invention is applied to the known DESS method. To this end, the overall magnitudes are formed by addition of the first magnitude and of the second magnitude, with those magnetic resonance signals being employed for generating the two image matrices that would in a double echo steady-state pulse sequence (DESS method).  
           [0028]    Specifically, the magnetic resonance signal for the first image matrix is generated from a gradient echo, particularly from a fast imaging with steady state precession echo (FISP echo), and the magnetic resonance signal for the second image matrix is generated from a quasi-spin echo, particularly from a PSIF echo, as would arise given an inverse FISP pulse sequence (PSIF pulse sequence), so that the two magnetic resonance signals derive from the same DESS pulse sequence.  
           [0029]    In the weighted image addition compared to linear, summary image addition, only those image regions are added wherein the second image has a strong signal and, in particular, a higher contrast than the first image. By contrast thereto, only a very slight portion of the second image is added to the first image in image regions having low signal-to-noise ratio (SN), for example in muscle tissue. The resulting image quality is therefore improved compared to a linear image addition.  
           [0030]    In a summary image addition, regions, for example muscle tissue, having a very low SN would also be added, so that the resulting image quality would be diminished.  
           [0031]    In the method of the invention, the overall magnitude of a picture element is particularly formed using an expression having the form  
           
         X 
         i 
         f 
         ±P·Y 
         i 
         e  
       
           [0032]    wherein X i , is the magnitude value of a picture element of the first image matrix, Y i  is the corresponding magnitude value of the second image matrix, and f and e are the exponents of the power of the appertaining magnitude values and P is a proportionality factor, and wherein e is greater than 1 (e&gt;1) and, preferably, e is greater than f (e&gt;f). Such a calculating rule can be programmed in a computer in a simple way without significant image artifacts being generated.  
           [0033]    In another preferred development, a scaling factor is employed for forming the second magnitude such that the value of the second magnitude is not greater for any picture element than the magnitude value of the second image matrix. The scaling factor thus normalizes the second magnitude such that the maximum case would add or subtract no more than would be the case given a linear addition or subtraction. In the maximum case, i.e. given a high magnitude value in the second image matrix, the method of the invention accordingly leads to a mathematical operation that is comparable to the described, linear procedure. By contrast, the magnitude of the second image matrix in the resulting overall image is suppressed in comparison to the linear operation in the case of low magnitude values of the second image matrix.  
           [0034]    Preferably, the scaling factor is formed from a maximum value of the magnitude values of the picture elements of the first image matrix.  
           [0035]    In a preferred embodiment the scaling factor is determined from a maximum value of the magnitude values of the picture elements of a number of image matrices, whereby the image matrices being generated from pulse sequences of the same type and, in particular, derived from a common three-dimensional image. As a result, it is easier to view a series of 2D images.  
           [0036]    For calculating the second magnitude, a weighting factor that is identical for all picture elements can be additionally employed that does not exhibit the value 1, particularly a value greater than 1.  
           [0037]    This weighting factor is varied in a preferred version of the method, in order to achieve an optimally high contrast in the image and/or an optimum correction of the first image matrix by the second image matrix. The variation ensues either manually or automatically by computer.  
           [0038]    The object directed to a magnetic resonance tomography apparatus is inventively achieved in a nuclear magnetic resonance tomography apparatus in which a computer program for the implementation of the method is loaded.  
           [0039]    The magnetic resonance tomography apparatus preferably is equipped with an input device with which the exponent in the power of the magnitude value of the second image matrix and/or the weighting factor can be set.  
           [0040]    As already mentioned, the weighted addition or subtraction as implemented in the first embodiment of the method of the invention can be accomplished not only at the magnitude values of image matrices but can also be accomplished at the magnetic resonance signals per se, i.e. at the raw data.  
           [0041]    With the initially cited, second embodiment of the invention, the method-related object is achieved by the second magnitude being formed by multiplication of the corresponding magnetic resonance signal of the second group with a weighting factor, the weighting factor being dependent on the magnetic resonance signal of the second group such that it is higher for a high magnetic resonance signal than for a low magnetic resonance signal.  
           [0042]    The second magnitude thus is formed such that its contribution to the overall signal is lower given a small value of the magnetic resonance signal of the second group than it would be given a linear addition or subtraction of the magnetic resonance signals of the two groups, and such that it would be essentially of the same size as in the linear addition or subtraction given a high value of the magnetic resonance signal of the second group.  
           [0043]    Preferably, the second magnitude is formed such that it is dependent on the magnetic resonance signal of the second group in non-linear fashion, particularly steadily non-linear, with the same non-linear function being employed for the formation of all overall signals.  
           [0044]    In particular, the second magnitude is formed such that it is dependent on a power of the magnetic resonance signal of the second group, the exponent being of the same size for all overall signals and is greater than 1, particularly greater than or equal to 2.  
           [0045]    Particularly good results are achieved when the exponent in the power of the magnetic resonance signal of the second group is higher in the second magnitude than in exponent in a power of the magnetic resonance signal of the first group in the first magnitude.  
           [0046]    A raw data matrix can be formed from the overall signals determined in this way, a matrix yielding the image being generated therefrom from Fourier transformation. 
       
    
    
     DESCRIPTION OF THE DRAWINGS  
       [0047]    [0047]FIG. 1 is a flowchart of an exemplary first embodiment of the inventive method.  
         [0048]    [0048]FIG. 2 illustrates a simulation of the method according to FIG. 1 employed in a DESS method;  
         [0049]    [0049]FIG. 3 illustrates a simulation of the method according to FIG. 1 employed in a HIRE method.  
         [0050]    [0050]FIG. 4 is a flowchart of an exemplary second embodiment of the inventive method. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0051]    [0051]FIG. 1 schematically shows the executive sequence of the method and the required components as well. In a magnetic resonance tomography apparatus  1  having a conventional magnet and gradient system (not explicitly shown), radio-frequency pulses are emitted into an examination subject  7  with a radio-frequency transmitter  3  and the magnetic resonance signals SG 1 , SG 2 , SG 3  . . . and SG 1 ′, SG 2 ′, SG 3 ′ . . . are received with a radio-frequency receiver  5 . The magnetic resonance signals SG 1  through SG 3  are sampled in an evaluation unit  9 , digitized, and the digital values are entered row-by-row into a raw data matrix. The magnetic resonance signals SG 1 ′ through SG 3 ′ are processed in the same way in an evaluation unit  11  and are entered into a second raw data matrix. Both raw data matrices are subjected to a two-dimensional Fourier transformation (2D FFT), and magnitude values X 1  and Y i  are calculated from the complex values acquired in this way. Two image matrices BM 1  and BM 2  having a number of picture elements i are thus obtained, whereby X i  references the magnitude value of a picture element i of the first image matrix BM 1  and Y i  references the magnitude value of a picture element i of the second image matrix BM 2 .  
         [0052]    The two image matrices BM 1  and BM 2  are supplied to a calculating unit  13  that is in communication with an input unit  15 . In the calculating unit  13 , the final image or image B that can be viewed by the user and that is displayed in a display unit  17  is calculated. The individual picture elements i of the image B are respectively calculated as follows as overall magnitude G i  from a first magnitude B 1  and from a second magnitude B 2   i :  
           G   i   =B 1 i   ±B 2 i   (Eq. 1)  
         [0053]    i.e., either the second magnitude B 2   i  is subtracted from the first magnitude B 1   i  or the two magnitudes B 1   i , B 2   i  are added.  
         [0054]    The first magnitude B 1   1  is dependent on the magnitude value X i  of the corresponding picture elements i of the first image matrix BM 1  and, in particular, is identical thereto. According to the invention, the second magnitude B 2   i  for each picture element i is formed by multiplication of the corresponding magnitude value Y i  of the second image matrix BM 2  by a weighting factor F, the weighting factor F being dependent on the magnitude value Y i  of the second image matrix BM 2 :  
           G   i   =X   i   ±F ( Y   i )· Y   (Eq. 2)  
         [0055]    The weighting factor F can, for example, be formed by a mathematical step function that has a lower constant value as result below a specific threshold than above the threshold. In the preferred embodiment shown here, the weighting factor F is dependent via a power&#39;s law on the magnitude value Y i , of the second image matrix BM 2 , so that, for example, the following dependency exists:  
           G   1   =X   i   f   ±P·Y   i   e   (Eq. 3)  
         [0056]    wherein P is a location-independent or pixel-independent proportionality factor that is not dependent on any of the magnitude values X i , Y i , and e and f are the exponents of the powers of the appertaining magnitude values X i , Y i .  
         [0057]    For explaining the function of the calculating rule for the overall magnitudes G i , Equation 3 is subsequently brought into a different form for the case f=1:  
               G   i     =       X   i     ±     W   ·       (       Y   i       X   max       )     λ     ·     Y   i                 (     Eq   .              4     )                               
 
         [0058]    wherein, W is a location-independent or pixel-independent weighting factor and the term with the exponent references a scaling factor S according to:  
             S   =       (       Y   i       X   max       )     λ             (     Eq                 5     )                               
 
         [0059]    In particular, the weighting factor lies in the range from 0.5 through 10.  
         [0060]    The exponent λ in the scaling factor S is related via the relationship  
         λ= e− 1  (Eq. 6)  
         [0061]    with the exponents e from Equation 3. The exponent λ can assume an arbitrary value that is greater than 0 and is preferably greater than 1.  
         [0062]    The quantity X max  is a maximum value of the magnitude values X i  of the picture elements i of the first image matrix BM 1 . In that case wherein, given the assistance of the gradient coil, a plurality of slices or partitions were successively excited in the direction of their gradients, in that case wherein data for a three-dimensional image are thus present, the maximum value X max  is formed as maximum of the magnitude values of all picture elements of the three-dimensional image. In other words: X max  is the global maximum image intensity of all n*m*N pixels (n*m: in-plane matrix resolution; N: number of slices or partitions, for example n=m=256, N=64).  
         [0063]    The first image matrix BM 1  was selected such that it is more signal-intense than the second image matrix BM 2 . The following therefore applies for all picture elements i: Y i ≦X i . It follows therefrom that the scaling factor S for all picture elements i is smaller than 1. The scaling factor S is such that the weighted, second magnitude B 2   i  is lower, the lower a magnitude value Y i  of the second image matrix BM 2  becomes lower.  
         [0064]    For forming the overall magnitudes G i , other mathematical operations can be additionally utilized in additional to a subtraction or/and an addition, insofar as a self-weighting of the magnitude value Y i  of the second image matrix BM 2  is merely present. For example, the following mathematical operations have proven especially suitable:  
               G   1     =       [       X   i     r     +   1         ±       X   i   r     ·   W   ·       (       Y   i       X   max       )     λ     ·     Y   i         ]       1     r   /   1                 (     Eq   .              7     )                               
 
         [0065]    when r is an arbitrary real number  
         [0066]    For the case r=1 and for the case of addition of the two magnitudes B 1   i , B 2   i , the following weighting is obtained:  
               G   i     =         X   1   2     +       X   i     ·   W   ·       (       Y   i       X   max       )     λ     ·     Y   i                   (     Eq   .              8     )                               
 
         [0067]    This calculating rule is especially suited for self-weighting in a DESS method. In this case, the FISP signal is respectively utilized for the magnitude value X i  of the first image matrix BM 1  and the PSIF signal is utilized for the magnitude value Y i  of the second image matrix BM 2 . In a region I (see FIG. 2) of the examination subject  7  having relatively high PSIF signal, for example in the region of fluid, water or CSF, the signal magnitude of the PSIF signal is added to the FISP signal with the scaling factor S that is then approximately equal to 1. In a region II, for example in musculature, the scaling factor S magnitudes to only approximately (1/10)) 2 =0.01, i.e. the signal contribution of the PSIF signal remains below the magnitude noise limit.  
         [0068]    [0068]FIG. 2 shows the result of the addition of the magnitudes of the PSIF signal and of the FISP signal to form the respective overall magnitude G i  for specific T 2  values in msec. The curve  21  represents the result of the linear addition of the FISP signal and of the PSIF signal according to the traditional DESS method. The curve  23  shows the result of an addition according to Equation [Eq. 8]. W=3 and λ=2 were selected for the calculation. In the region  1 , the overall magnitude G i  according to the method of the invention is comparable to the corresponding, traditional DESS value. The PSIF signal and the FISP signal are added essentially equally weighted. By contrast, for low T 2  values in region  11 , the PSIF signal contribution is essentially suppressed, so that the overall magnitude G i  is essentially identical to the FISP signal.  
         [0069]    For r=0 and for the case of a magnitude subtraction, the following equation is obtained, this being particularly suited for weighting the known HIRE method:  
               G   i     =       X   i     -     W   ·       (       Y   i       X   max       )     λ     ·     Y   i                 (     Eq   .              9     )                               
 
         [0070]    The T 2 -weighted, diagnostic signal is respectively employed as magnitude value X i  of the picture elements i of the first image matrix BM 1 . The highly T 2 -weighted signal that, in particular, supplies a very high magnitude in CSF, is utilized as magnitude value Y i  of a picture element i of the second matrix BM 2 . The result of such a calculation is shown in FIG. 3 as curve  27  for various T 2  values (in msec), particularly for two different regions III, IV of the examination subject  7 , respectively compared to a linear image subtraction (“HIRE (Standard)”, curve  25 ). Curve  27  represents the overall magnitudes G i  for various T 2  values according to Equation [Eq. 9]. λ=2 and W=3 were again utilized. In region III, the same image subtraction essentially occurs in the method of the invention as in the traditional HIRE method. By contrast, no determining subtraction occurs in region IV.  
         [0071]    Using the input unit  15  (see FIG. 1), the weighting factor W as well as the exponents e, f of the power of the appertaining magnitude values X i , Y i  or the exponent λ substituting for the exponent e can be varied or set by an operator. The proportionality factor P can also be variable. There is thus the possibility of optimizing the self-weighting with empirical knowledge.  
         [0072]    The explained, weighted addition or subtraction is capable of being implemented not only with magnitude values of image matrices BM 1 , BM 2  but also with the original magnetic resonance signals SG 1  through SG 3  . . . or, respectively, SG 1 ′ through SG 3 ′ . . . This is schematically illustrated in FIG. 4. The magnetic resonance signals SG 1  through SG 3  of the first group and the magnetic resonance signals SG 1 ′ through SG 3 ′ of the second group are subtracted or added weighted in the calculating unit  13 , whereby the exponents e, f and the weighting factor W can be set via the input unit  15 . The result of the addition or subtraction, which is preferably undertaken corresponding to Equations 1 through 9, is the respective overall G 1 , G 2 , G 3  . . . The result of the calculating procedure of the calculating unit  13  is a raw data matrix RDM that contains the overall signals G 1 , G 2 , G 3  . . . as rows and that, following a Fourier transformation and magnitude formation, is converted into a matrix that generates the image B. This matrix is presented on the display unit  17 .  
         [0073]    The evaluation units  9 ,  11 , the calculating unit  13  and/or the display unit  17  can be part of a data processing system  31  or of a computer.  
         [0074]    Although modifications and changes may be suggested by those skilled in the art, it is in the intention of the inventor to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of his contribution to the art.