Abstract:
A method and apparatus for increasing the signal-to-noise ratio in a magnetic resonance image generated with a system including at least two receiver coils where the data acquisition period is reduced by increasing the space between k-space raster data rows such that image wrapping occurs and an unwrapping algorithm is required, the method including identifying a sensitivities matrix corresponding to the receiver coils, acquiring NMR signals and converting those signals to image pixel intensities, defining a correction matrix, altering the sensitivities matrix as a function of the correction matrix, combining the altered sensitivities matrix and the intensity matrix to generate an estimated spin density matrix and using a spin density matrix to generate the final image.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
         [0001]    Not applicable.  
         STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
         [0002]    Not applicable.  
         BACKGROUND OF THE INVENTION  
         [0003]    The field of the invention is nuclear magnetic resonance imaging (“MRI”) methods and systems. More particularly, the invention relates to systems and methods for increasing the signal to noise ratio in MRI images where image data has to be unwrapped during data processing.  
           [0004]    When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B 0 ), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B 1 ) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M z , may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment M t . A signal is emitted by the excited spins after the excitation signal B 1  is terminated, this signal may be received by receiver coils and processed to form an image.  
           [0005]    When utilizing these signals to produce images, magnetic field gradients (G x  G y  and G z ) are employed to select locations within the tissue for excitation. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which gradients G x  G y  and G z  vary according to the particular localization method being used. Herein it will be assumed that gradient G y  is used to adjust the phase of signals along a phase encoding axis Y. The resulting set of received nuclear magnetic resonance (NMR) signals are digitized and stored in a k-space raster format. An exemplary k-space raster  10  is illustrated in FIG. 2 and includes a plurality of rows  12  of data. After all of the k-space data has been acquired, the data is typically subjected to a two-dimensional Fourier transform and the resulting data is then used to reconstruct an image using one of several different reconstruction techniques. An exemplary resulting image  14  is also illustrated in FIG. 2.  
           [0006]    Thus, the intensity of each pixel in an MR image is generally a function of two factors. First, pixel signal intensity is a function of the spin density m at a point in an object slice being imaged that corresponds to the particular pixel in the image. Second, pixel signal intensity is also a function of the operating characteristics of the receiving coil that receives the NMR signal and converts the signal to an analog signal and then to a digital signal for storage in k-space. Specifically, the coil operating characteristic that affects the end pixel intensity the most is referred to as coil sensitivity s. Thus, intensity i for a pixel y can be expressed by the following Equation:  
             i ( y )= s ( y ) m ( y )  Equation 1  
           [0007]    There are several different factors that can be used to judge the value of any imaging system but two of the most important factors are the quality of the resulting images and the speed with which imaging data can be acquired. Higher quality images increase diagnostic value. Acquisition speed increases system throughput (i.e., the number of imaging sessions that can be performed in a given period) and can also increase image quality as patient movement is reduced when the acquisition period is chortened (i.e., patient movement is less likely during a shorter period than during a longer period. With MRI systems, throughput is extremely important as MRI systems are relatively expensive and the expense is in part justified by the amount of use a system receives.  
           [0008]    One way to increase system throughput is to reduce the amount of data collected during an imaging session. For example, one way to reduce the amount of collected data is to increase the space between phase encoding lines in k-space. Referring to FIG. 3, an exemplary k-space raster  20  having half as many k-space lines as the raster  10  of FIG. 2 is illustrated. The time required to collect the data in raster  20  would be approximately half the time required to collect the data in raster  10 .  
           [0009]    By reducing the number of phase encoding lines employed during data acquisition, the field of view (FOV) along the phase encoding axis Y of the resulting image is also reduced. Referring again to FIG. 3, the FOV for the image  15  in FIG. 3 is shown as being approximately {fraction (1/2)} the FOV in the image of FIG. 2 along the phase encoding axis Y. Where the object being imaged fits within the reduced FOV, the reduced FOV does not affect the resulting image. Because reducing the k-space phase encoded lines reduces the FOV, the factor by which the k space phase encoding lines are reduced is referred to as the reduction factor R.  
           [0010]    Unfortunately, where the object being imaged extends outside the reduced FOV, the image sections that correspond to the out-of-FOV object sections “wrap around” on the image and are overlaid on other image sections. Thus, in FIG. 3, out-of-FOV image sections  22  and  24  wrap around and are overlaid on in-FOV image section  25  thereby generating wrapped sections  28  and  26 , respectively. Each wrapped section (e.g.,  22 ) includes pixel intensities that are the sum of two intensities corresponding to two different pixels in a non-wrapped image (i.e., in an image like that of FIG. 2). The two intensities that combine to produce each wrapped pixel intensity include one intensity corresponding to an in-FOV pixel and one intensity corresponding to an out-of-FOV pixel. For example, referring to FIGS. 2 and 3, the FOV of FIG. 3 is also illustrated in FIG. 2 by the space between lines  36  and  38  and thus when the FOV is reduced as in FIG. 3, pixel  30  is an in-FOV pixel and pixel  40  is an out-of-FOV pixel. Thus the pixel intensity of pixel  40  wraps as indicated by arrow  41  and is laid over pixel  30  intensity. Together the intensities of pixels  30  and  40  add to generate the intensity of pixel  42  upon wrapping.  
           [0011]    Where the reduction factor R is greater than 2 additional image wrapping can occur thereby causing wrapped image pixels to include intensity corresponding to more than two (e.g., 3, 4, etc.) unwrapped pixels. This additional wrapping further reduces the diagnostic value of the resulting image.  
           [0012]    The industry has devised ways to effectively “unwrap” wrapped images like the exemplary image in FIG. 3. It has been recognized that by providing several NMR signal receiving coils where the sensitivities of each coil are known, a permutation of Equation 1 above can be used to separate the intensity of a wrapped pixel into the in-FOV intensity and the out-of-FOV intensity. To this end, along a phase encoding axis the intensity of a wrapped pixel y corresponding to first and second receiver coils can be expressed as:  
             i   1 ( y )= s   1 ( y ) m ( y )+ s   1 ( y+D ) m ( y+D )  Equation 2  
             i   2 ( y )= s   2 ( y ) m ( y )+ s   2 ( y+D ) m ( y+D )  Equation 3  
           [0013]    respectively, where D is the phase encoding FOV (see FIG. 3).  
           [0014]    Referring still to Equations 2 and 3, assuming that the sensitivities s 1  and s 2  for each of the first and second coils are known, after intensity data has been acquired for each of the first and second coils, only m(y) and m(y+D) are unknown. Thus, Equations 2 and 3 can be solved for each of the unknowns to determine the spin densities m(y) and m(y+D) at pixels y and y+D, respectively. The spin densities at each pixel can then be converted to intensities to “unwrap” the image.  
           [0015]    By increasing the reduction factor R, the amount of data acquired is reduced and therefore throughput is accelerated. The number of unknowns, however, that can be resolved in any system is equal to the number of separate receiver coils in the system. Thus, in any given system the maximum reduction factor R is equal to the number of receiver coils N. For example, in the exemplary system described above that includes four receiver coils the maximum reduction factor R is 4.  
           [0016]    In general terms, the intensity of a particular wrapped pixel y with a reduction factor R can be expressed by the equation:  
                 i   j          (   y   )       =       ∑     k   =   0       R   -   1                           s   j          (     y   +   kD     )            m        (     y   +   kD     )                   Equation   4                               
 
           [0017]    where j refers to coil number and s j (y) refers to the sensitivity of coil j.  
           [0018]    In a system including N coils, intensity, spin density and sensitivity matrices I, M and S can be defined as having dimensions N×1, R×1 And N×R, respectively, and Equation 4 can be rewritten in matrix form as:  
             I=SM   Equation 5  
           [0019]    Again, assuming S is known, S can be inverted and Equation 5 can be rewritten and solved for an estimated spin density M as:  
             {circumflex over (M)}=S   −1   I   Equation 6  
           [0020]    A solution of Equation 6 that can be relied upon should minimize the spin density estimate error. Thus, a typical solution to Equation 6 minimizes |S{circumflex over (M)}−I| 2  resulting in the following equation:  
             {circumflex over (M)} =[( S   +   S ) −1   S   +   ]I   Equation 7  
           [0021]    where + denotes the Hermitian conjugate.  
           [0022]    Obviously the value of the solution to Equation 7 is only as good as the preciseness with which the sensitivities of the coils can be determined. Unfortunately, while the industry has devised several ways to determine coil sensitivities, there are many factors that affect sensitivities such that noise often occurs upon inversion of the sensitivity matrix S that propagates and is exacerbated in resulting images. Thus, while solving Equation 7 in theory provides a way to unwrap image data, in practice the resulting image has a relatively low signal to noise ratio (SNR).  
         BRIEF SUMMARY OF THE INVENTION  
         [0023]    The present invention is a method for reducing the noise in an unwrapped image by modifying the coil sensitivity matrix and using the modified matrix instead of the original matrix to determine the spin densities of image pixels by solving an equation similar to Equation 7 above.  
           [0024]    More specifically, one way to increase the SNR is to minimize the function A({circumflex over (M)})+λB({circumflex over (M)}) where A({circumflex over (M)})=|S{circumflex over (M)}−I| 2 , λ is an adjustable parameter and B({circumflex over (M)}) is chosen to reduce system sensitivity to noise. For some square matrix H, B({circumflex over (M)}) may have the form B({circumflex over (M)})={circumflex over (M)} + H{circumflex over (M)} where, again the + indicates the Hermitian conjugate. With B({circumflex over (M)}) expressed in the above form, Equation 7 can be rewritten as:  
             {circumflex over (M)} =[( S   +   S+λH ) −1   S   +   ]I   Equation 8  
           [0025]    Because high noise often results in large pixel values a simple solution to Equation 8 is to minimize the magnitude of {circumflex over (M)} so that B({circumflex over (M)})={circumflex over (M)} + {circumflex over (M)} giving H=U where U is the unit matrix. Thus, Equation 8 can be rewritten as:  
             {circumflex over (M)} =[( S   +   S+λU ) −1   S   +   ]I   Equation 9  
           [0026]    Upon solving Equation 9 the resulting spin density estimates {circumflex over (M)} can be used to generate an unwrapped image with relatively high SNR.  
           [0027]    In addition to several methods the invention also includes an apparatus for performing each of the methods.  
           [0028]    These and other aspects of the invention will become apparent from the following description. In the description, reference is made to the accompanying drawings which form a part hereof, and in which there is shown a preferred embodiment of the invention. Such embodiment does not necessarily represent the full scope of the invention and reference is made therefore, to the claims herein for interpreting the scope of the invention. 
       
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0029]    [0029]FIG. 1 is a schematic view of a MR imaging system that performs the method of FIG. 5;  
         [0030]    [0030]FIG. 2 is a schematic view of a k-space raster and a resulting image;  
         [0031]    [0031]FIG. 3 is similar to FIG. 2, albeit illustrating a k-space raster with relatively greater space between k-space data rows and a resulting reduced FOV image;  
         [0032]    [0032]FIG. 4 is a schematic view of a receiver coil configuration, an imaging plane and an enlarged point within the imaging plane;  
         [0033]    [0033]FIG. 5 is a flow chart illustrating an exemplary method according to the present invention;  
         [0034]    [0034]FIG. 6 is a flow chart illustrating a manual method for identifying image sectors having disparate replicates; and  
         [0035]    [0035]FIG. 7 is a flow chart similar to FIG. 6, albeit being an automated method. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0036]    Referring first to FIG. 1, there is shown the major components of an exemplary MRI system that incorporates the present invention. Operation of the system is controlled from an operator console  100  that includes a keyboard or control panel  102  and a display  104 . The console  100  communicates through a link  116  with a separate computer system  107  that enables an operator to control the production and display of images on the display  104 . Computer system  107  includes a number of modules that communicate with each other through a backplane. The communicating modules include an image processor module  106 , a CPU module  108  and a memory module  113 , known in the art as a frame buffer for storing image data arrays. Computer system  107  is linked to a disk storage  111  and a tape drive  112  for storage of image data and programs. System  107  communicates with a separate system control  122  through a high-speed serial link  115 .  
         [0037]    The system control  122  includes a set of modules connected together by a backplane. The connected modules include a CPU module  119  and a pulse generator module  121  that connects to operator console  100  through a serial link  125 . It is through this link  125  that the system control  122  receives commands from the operator that indicate the scan sequence that is to be performed. The pulse generator module  121  operates the system components to carry out the desired scan sequence. Generator module  121  produces data that indicates the timing, strength and shape of the RF pulses that are to be produced and the timing of and length of the data acquisition window. Pulse generator module  121  connects to a set of gradient amplifiers  127  and indicates the timing and shape of gradient pulses to be produced during the scan.  
         [0038]    Pulse generator module  121  also receives patient data from a physiological acquisition controller  129  that receives signals from a number of different sensors connected to the patient, such as ECG signals from electrodes or respiratory signals from a bellows. In addition, pulse generator module  121  connects to a scan room interface circuit  133  that receives signals from various sensors associated with the condition of the patient and the magnet system. A patient positioning system  134  also receives commands to move the patient to the desired position for scanning through the scan room interface circuit  133 .  
         [0039]    The gradient waveforms produced by pulse generator module  121  are applied to a gradient amplifier system  127  comprised of G x , G y  and G z  amplifiers. Each gradient amplifier excites a corresponding gradient coil in an assembly generally designated  139  to produce the magnetic field gradients used for position encoding acquired signals. The gradient coil assembly  139  forms part of a magnet assembly  141  which includes a polarizing magnet  140  and a whole-body RF coil  152 . A transceiver module  150  in the system control  122  produces pulses that are amplified by an RF amplifier  151  and coupled to the RF coil  152  via a transmit/receive (T/R) switch  154 . The T/R switch  154  is controlled by a signal from the pulse generator module  121  to electrically connect the RF amplifier  151  to coil  152  during the transmit mode and to connect the preamplifier  153  to separate receiver coils (see FIG. 4) in assembly  141  during a receive mode.  
         [0040]    Referring also to FIG. 4, the exemplary magnet assembly  141  of FIG. 1 includes four separate receiver coils  60 ,  62 ,  64  and  66 . Coils  60 ,  62 ,  64  and  66  are shown in a simple configuration to simplify this explanation but other configurations are contemplated. Thus, point  72  generates a signal in each of coils  60 ,  62 ,  64  and  66 . An exemplary imaging plane  70  is also illustrated and an enlarged space corresponding to an exemplary point within plane  70  is identified by numeral  72 . NMR signals radiated by excited nuclei in a patient generate signals that cumulatively cause magnetic fields B 1  through B 4  that are detected by the coils  60 ,  62 ,  64  and  66 , respectively. Thus, point  72  generates a signal that affects each of fields B 1  through B 4  and hence information about point  72  is present in coil signals. Similarly every other point within plane  70  generates a signal that affects each of fields B 1  through B 4 . Each of the fields sensed by coils  60 ,  62 ,  64  and  66  is converted into data that cumulatively is used to generate an MR image.  
         [0041]    To this end, each of coils  60 ,  62 ,  64  and  66  is coupled to a preamplifier  153 . After amplification, the NMR signals picked up by coils  60 ,  62 ,  64  and  66  are demodulated, filtered, and digitized by the receiver section of the transceiver module  150  and transferred to a memory module  160  in system control  122 . The data collected is stored in k-space rasters, a separate raster corresponding to each coil  60 ,  62 ,  64  and  66 . When the scan is completed and an entire array of data has been acquired in memory module  160 , an array processor  161  performs a Fourier transform on each of the four k-space rasters to generate four separate images corresponding to the received NMR data. The image data is stored as four separate arrays of pixel intensities. Thereafter the data from the four separate images can be combined to generate a single NMR image of relatively high quality.  
         [0042]    Referring to FIG. 2, where a large number of k-space rows of data  112  are accumulated, the resulting image  14  has a relatively large dimension along the phase encoding axis Y and therefore relatively large objects can be imaged. Unfortunately, the time required to complete a data acquisition is proportional to the amount of data collected. One way to increase acquisition speed is to reduce the amount of data collected by increasing the space between k-space rows of data collected as illustrated in FIG. 3. The resulting image  15  has a reduced dimension D along the phase encoding axis Y and may, depending upon the dimension of the object being imaged along axis Y, cause the resulting image to wrap such that various pixels within the resulting image include intensity data corresponding to two or more locations within the object being imaged. The invention includes a method performed by the processors of the FIG. 1 system to effectively unwrap the wrapped sections of a reduced FOV image while maintaining a high SNR.  
         [0043]    Referring now to FIG. 5, an exemplary inventive method  190  is illustrated. Referring also to FIG. 1, at process block  201 , using interface  100  in FIG. 1, a system user can determine the speed with which MR data is collected by setting a FOV reduction factor R. Reduction factor R has a range between 1 and N where N is the number of receiver coils within assembly  141 . In the present example, the number of receiver coils N is 4 and therefore the maximum value for reduction factor R is 4. Thus, in the present example, reduction factor R may have the values 1, 2, 3 or 4. Where the reduction factor R is set to 1, the space between k-space rows is minimized such that the largest amount of data possible is collected and the data acquisition period is relatively long. Where the reduction factor R is set to 4, the space between k-space rows of data is maximized such that the minimum amount of data is collected during an acquisition and the acquisition period is minimized.  
         [0044]    Continuing at block  200 , the components of the system illustrated in FIG. 1 are used to identify coil sensitivities for each of coils  60 ,  62 ,  64 , and  66  (see also FIG. 4). To this end, the coil sensitivities are measured during a commissioning procedure whereby an object having known MRI qualities is positioned within an imaging volume inside magnetic assembly  141 . With the object inside the imaging volume  141 , gradients are applied via assembly  127  and the object generates NMR signals that are picked up by the coils  60 ,  62 ,  64  and  66 . The coils provide the signals to the receiver portion of transceiver  150  which demodulates, filters and digitizes the signals providing separate k-space rasters for each one of coils  60 ,  62 ,  64  and  66 . Next, a Fourier transform is applied to each of the k-space rasters to generate pixel intensities corresponding to a resulting image.  
         [0045]    Because the magnetic resonance characteristics of the test object are known, the spin densities of the materials that form the object are known. Therefore, referring to equation 1 above, after the test images corresponding to each coil are completed and pixel intensities have been determined, Equation 1 can be solved for sensitivity s (i.e., each of intensities i and spin density m are known) and therefore the sensitivities corresponding to each coil for each point within the imaging space inside the imaging volume can be determined. At block  200  the coil sensitivities are arranged to form a sensitivities matrix S for each of the pixels that will exist in a wrapped image to be subsequently generated.  
         [0046]    Referring still to FIGS. 1 and 5, after commissioning has been completed and the sensitivities matrices S have been formed, a data acquisition procedure can commence. At process block  202  NMR signals are collected during a data acquisition period. The NMR signals are stored in k-space rasters, a separate raster corresponding to each of coils  60 ,  62 ,  64  and  66 . Next, at block  202 , image processor  106  (see FIG. 1) performs a two-dimensional Fourier transform on each of the k-space rasters to generate a separate image for each of coils  60 ,  62 ,  64  and  66 . The resulting images comprise pixel intensities for pixels within a wrapped image like the image  15  illustrated in FIG. 3.  
         [0047]    At process block  204 , processor  106  arranges the intensities corresponding to the wrapped image pixels from all of the images into intensity matrices i, one matrix for each pixel in the wrapped image. At block  206 , processor  106  provides an interface via display  104  for the system user to provide a scalar or adjustable parameter λ. The interface may include instructions on how λ is used or the effect of λ on a resulting image. The value for λ will be restricted to between 0 and 1 in the present example. Where λ is relatively large, the amount of noise reduction is increased. However, where is λ is large (i.e., relatively close to 1), while noise reduction is appreciable, some uncorrected aliasing can occur. Therefore, the optimal value for λ will depend upon a system user&#39;s judgment regarding acceptable noise and acceptable uncorrected aliasing. At block  206  the adjustable scalar λ is received by processor  106  via interface  100 .  
         [0048]    At process block  208  processor  106  multiplies the scalar value λ by an R×R unit matrix to generate a correction matrix λH. At block  210 , processor  106  determines the Hermitian conjugates S +  of the sensitivity matrices S (i.e., one for each pixel) and multiplies the Hermitian conjugates S +  sensitivities matrices S to generate intermediate matrices S + S, one for each pixel.  
         [0049]    At block  212 , processor  106  adds the correction matrices λH to corresponding intermediate matrices S + S to generate minimizing matrices, (S + S+λH). At block  214  process  106  inverts each minimizing matrix (S + S+λH) to generate an inverted minimizing matrix.  
         [0050]    At block  216  processor  106  multiplies the each inverted minimizing matrix by the corresponding Hermitian conjugate S +  of the original sensitivities matrix S to generate the modified sensitivities matrix [(S + S+λH) 1 S + ]. At block  218  processor  106  multiplies the modified sensitivities matrices by corresponding intensity matrices I to determine the unwrapped spin densities for the pixels y and y+D in an unwrapped image for the separate images corresponding to coils  60 ,  62 ,  64  and  66 . Continuing, at block  220 , processor  106  uses the unwrapped spin densities to generate an unwrapped image using data corresponding to all four coils  60 ,  62 ,  64  and  66 . Thus, the system of FIG. 1 solves Equation 9 above to determine the spin densities of unwrapped pixels and then uses the spin densities to generate an image with a high SNR.  
         [0051]    The exemplary method described above improves SNR substantially, especially at the maximum acceleration factor where reduction factor R is equal to the number of receiver coils N in an imaging system. During testing of a system using the method described above where the reduction factor R was set to 4, it was determined that a reasonable trade-off between SNR and uncorrected aliasing was achieved with a scalar value λ set equal to 10 −3  independent of pulse sequence parameter, scan plane and coil properties. For this value of scalar λ, noise near the center of the image decreased by 20%.  
         [0052]    Referring again to FIG. 3, it should be appreciated that in a wrapped image certain parts of the image will include more noise than other image parts. For example, wrapped image section  26  that includes information corresponding to two points in an object being imaged instead of one will generally have more noise content than other image sections (e.g.  25 ) that only include information corresponding to a single point in the object being imaged. Hereinafter the number of points for which a single pixel includes information is referred to as the number of replicates. For instance, where two points contribute information to a pixel, the number of replicates is two, where three points contribute information to a pixel the number of replicates is three and so on.  
         [0053]    Because noise in pixels including greater numbers of replicates is relatively higher than in pixels including lesser numbers of replicates, an optimal system should attenuate the noise to a greater degree when unwrapping higher replicate pixels than when unwrapping lower replicate pixels.  
         [0054]    To this end, according to one embodiment of the invention boundaries of objects within a wrapped image are determined so that image areas including higher numbers of replicates and hence higher noise can be distinguished from areas of lower relative noise (i.e., lower number of replicates). Thereafter different scalar λ values can be set or automatically selected for the areas of low and high relative noise so that, upon unwrapping the SNR throughout the resulting image is similar.  
         [0055]    Referring to FIG. 6, a method  250  for setting different λ values for different image sections is illustrated. Referring also to FIG. 5, the method of FIG. 6 is a sub-method of FIG. 5 and begins at block  252  after intensities have been arranged into intensity matrices at block  204 . Next, referring also to FIG. 1, at block  254 , a system user instructs processor  106  to display one of the wrapped images (e.g., the wrapped image corresponding to coil  60 ) via display  104 .  
         [0056]    At block  256  a selection tool is also provided for the user to select sections of the displayed wrapped image for λ specification. For instance, a mouse controlled cursor or the like may be provided that allows the user to select a general area on the displayed image. When the general area is selected, processor  106  may be programmed to identify a most likely boundary for the specific area and then to highlight the area within the boundary and provide an accept icon or the like for the user to accept the area highlighted. For example, referring again to FIG. 3, if a user were to indicate any point within space  26 , processor  106  would highlight entire space  26  and provide the acceptance icon. In addition, at block  256  processor  106  allows the user to indicate a scalar value λ for the image section selected.  
         [0057]    At block  258  processor  106  receives the section selection and scalar value λ setting and stores that information. Next, at block  260  processor  106  asks the user if scalar λ values have to be set for additional image sections. If additional λ values have to be set, control passes back to block  256  where the process is repeated. If all λ values have been specified, control passes to block  262   
         [0058]    At block  262  processor  106  uses the scalar values λ specified above to generate two different correction matrices, one for pixels in spaces  26  and  28  and another for pixels in space  25 . control passes back to block  210  in FIG. 5 where further processing continues to unwrap the wrapped images (see block  264 ).  
         [0059]    While the manual process above for identifying image sections can be used, other more automated processes can be used. For example, given the reduction factor R, processor  106  can determine the likely or potential overlapping that could occur in a wrapped image and then could search for telltale signs of image sections having different replicate numbers. Where R is 2 generally there would only be pixels having one or two replicates and at most there should be three separate image sections (one section including single replicate pixels and two sections each including two replicate pixels).  
         [0060]    One automated method  278  is illustrated in FIG. 7, where starting at block  204  in FIG. 5 (see block  280 ), control passes to block  282  where processor  106  accesses one of the wrapped images. At block  284  processor  106  searches to identify image boundaries along edges perpendicular to the phase encoding axis for image sections that appear to be cut off. For instance, in FIG. 3 processor  106  would search for disparate pixel intensities along edge  51  and locate points  53  and  55 . Having located points  53  and  55  processor  106  can determine the general trends of the boundaries that terminate at those points. At block  286  processor  106  identifies points  57  and  59  at the same locations along the axis perpendicular to the Y-axis along the opposite edge  61  of the image. Thereafter, at block  288  processor  106  continues the boundary trends identified at the other edge (e.g., at points  53  and  55 ) to identify space  28  as one of the image sections including two replicate pixels and earmarks that space as such.  
         [0061]    A similar process is performed to identify space  26  as the second image section including two replicate pixels. The remaining section  25  by default includes single replicates.  
         [0062]    In the present example, after identifying the separate sections  25 ,  26  and  28 , at block  290  processor  106  requests two different scalar values, one for the single replicate section  25  and the other for each of two replicate sections  26  and  28 . Thereafter, at block  300  processor  106  generates two separate correction matrices using the scalar values and then, at block  302  control passes back to block  210  of FIG. 5.  
         [0063]    It should be understood that the methods and apparatuses described above are only exemplary and do not limit the scope of the invention, and that various modifications could be made by those skilled in the art that would fall under the scope of the invention.  
         [0064]    To apprise the public of the scope of this invention, the following claims are made: