Patent Publication Number: US-2023162326-A1

Title: Method for training post-processing device for denoising mri image and computing device for the same

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to Korean Patent Application No. 10-2021-0161789 filed on Nov. 22, 2021, and all the benefits accruing therefrom under 35 U.S.C. §119, the contents of which are incorporated by reference in their entirety. 
     BACKGROUND 
     The present disclosure relates to a signal processing technology for training a post-processing device for denoising an MRI image and a computing device employing the same. 
     Magnetic resonance imaging (MRI), which is used in disease detection, diagnosis, and treatment monitoring, is an imaging technology for generating a three-dimensional anatomical image based on a technology for exciting and detecting a change in a rotation axis direction of protons of water in living tissue. MRI applies radiofrequency (RF) energy to a region of interest of a human body in a magnet having a strong external magnetic field to resonate hydrogen nuclei in the region of interest of the body, measures a signal coming from corresponding tissue, and reconstructs the signal by a computer to transform the signal into cross-section and three-dimensional images. An MRI scanner that enables MRI is a device including a patient table, a scanner, a magnet, a gradient coil, and a radiofrequency coil. 
       FIG.  1    illustrates a main configuration of an MRI scanner  1200  that enables MRI. A space in which an object  70  to be detected may be disposed may be formed in the MRI scanner  1200 . The object  70  may be, for example, a person. The MRI scanner  1200  may include a plurality of coils  211 ,  212 ,  221 , and  222  arranged therein, and may receive a signal generated from the object  70  through the coils. Although  FIG.  1    illustrates four coils for convenience, the number of coils may not be limited thereto. The MRI scanner  1200  may further include therein other coils that output RF pulses. 
       FIG.  2    is a diagram illustrating a process of generating a K-space or MRI image using an MRI signal obtained by the MRI scanner illustrated in  FIG.  1   . 
     An MRI signal  500  may be generated by combining all of signals output from the plurality of coils  211 ,  212 ,  221 , and  222 . The MRI signal  500  may be transformed into an MRI image  600  through a predetermined transformation algorithm. The MRI signal  500  may be K-space data. An example of the MRI image  600  is illustrated in  FIG.  3   . 
     The signals output from each of the coils may be signals constituting a portion of the K-space data. One complete piece of K-space data may be generated using all of the signals output from the plurality of coils. The complete K-space data may be transformed into the MRI image  600  through the predetermined transformation algorithm. 
     In an embodiment, a process of transforming the MRI signal  500  into the MRI image  600  may be performed in a transform part  1230  included in the MRI scanner  1200 . 
     In another embodiment, the process of transforming the MRI signal  500  into the MRI image  600  may be performed in a separate computing device  1100 . 
     The MRI image  600  may be further processed by a post-processing part  1110  implemented in the computing device  1100 . For example, noise in the MRI image  600  may be processed and reduced by the post-processing part  1110 . 
     In an embodiment, the MRI scanner  1200  and the computing device  1100  may be an integrally provided MRI system. 
     In another embodiment, the MRI scanner  1200  may be an MRI system provided independent of the computing device  1100 . Here, the MRI scanner  1200  and the computing device  1100  may be communicatively connected to each other by a local network or metropolitan network. 
     The embodiment illustrated in  FIG.  2   , the signals output from the four coils are input to the transform part  1230  after being combined by a signal combining part  1240 . However, in a modified embodiment, the signals output from the four coils may be directly input to the transform part  1230  without passing through the signal combining part  1240 , and may be combined with each other in the transform part  1230 . 
       FIG.  3    is a diagram illustrating a concept of an MRI image including noise. 
     The MRI image  600  (x+n) obtained by transforming the K-space data may include a true image  601  (x) and noise  602  (n). 
       FIG.  4    illustrates a method of denoising an MRI image using a supervised learning technology according to the related art. 
     The MRI image  600  (x+n) may be input to a network  111  (fθ). An operation objective of the network  111  (f θ ) is to output a post-processed image  603  (f θ (x+n)) that is a denoised image from the MRI image  600  (x+n). To this end, a parameter θ constituting the network  111  (f θ ) is required to be optimized. To this end, the parameter θ is required to be optimized so as to minimize a loss function L between the true image  601  (x) and the post-processed image  603  (f θ (x+n)) for the MRI image  600  (x+n). 
     The loss function L may be referred to as L2 loss. 
     According to the technology illustrated in  FIG.  4   , the true image  601  (x) that is a ground truth image for the MRI image  600  (x+n) is required to be prepared in advance, but it may be very difficult or impossible to simply prepare the true image  601  (x). 
     There may be another technology for obtaining the true image  601  (x). Notwithstanding, the present invention is intended to provide a technology for obtaining an image with quality that is equal to or similar to the quality of the true image more quickly or more efficiently using an MRI scanner in comparison with the other technology. 
       FIG.  5    illustrates a method of denoising an MRI image using another supervised learning technology that may be compared with a best mode of the present invention. 
     Although the MRI image indicated by reference number  600  shown in  FIG.  4    is expressed by x+n, the MRI image indicated by reference number  600  is expressed by x+n 1  in  FIG.  5    for convenience. 
     In the example of  FIG.  4   , the true image  601  (x) is used as a supervised learning label for the MRI image  600  (x+n). On the contrary, in the technology illustrated in  FIG.  5   , another label image  604  (x+n 2 ) that is different from the true image  601  (x) is used as a label for the MRI image  600  (x+n). In a network training method described with reference to  FIG.  5   , the parameter θ is optimized so as to minimize the loss function L between the other label image  604  (x+n 2 ) and the post-processed image  603  (f θ (x+m)). 
     The loss function L may be defined as Equation 1. [0025] 
     
       
         
           
             l 
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             s 
             s 
             = 
             
               
                 
                   
                     
                       f 
                       θ 
                     
                     
                       
                         x+ 
                         
                           n 
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                         x+ 
                         
                           n 
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               2 
             
           
         
       
     
     Here, the true image (x) obtained by eliminating noise n 2  from the other label image  604  (x+n 2 ) is the same as the true image (x) obtained by eliminating noise n 1  from the MRI image  600  (x+n 1 ). 
     Here, when conditions that ① n 1  and n 2  be independent i.i.d, ② E[n 1 ] = E[n 2 ] = 0, ③ n 1  and n 2  be symmetric, and ④ L2 norm loss are satisfied, the technology illustrated in  FIG.  5    exhibits substantially the same effect as the technology illustrated in  FIG.  4   . That is, when the above conditions are satisfied, the same training effect may be achieved even if the network  111  (fe) is trained using the other label image  604  (x+n 2 ) in which other noise (n 2 ) is combined with the true image (x) instead of using the true image  601  (x) as a label image. Notwithstanding, for the technology illustrated in  FIG.  5   , the other label image  604  (x+n 2 ) for the MRI image  600  (x+n 1 ) is required to be prepared, but it may also be very difficult or impossible to prepare the other label image  604  (x+n 2 ). 
       FIG.  6    is a diagram illustrating images measured by using the plurality of coils included in the MRI scanner illustrated in  FIG.  1    and a method of generating an MRI image using the images. 
     The horizontal axis and vertical axis of each of the images having a rectangular boundary shown in  FIG.  6    may represent an x and y coordinates in a space in the MRI scanner. 
     Reference number  601  in  FIG.  6    indicates a true image (ground truth image) of a portion to be obtained using the MRI scanner. 
     Each of the plurality of coils  211 ,  212 ,  221 , and  222  does not have the same sensitivity for all coordinates in the true image  601  (x). That is, each of the coils may have higher sensitivity for a space closer to itself. This difference in sensitivity due to a position of a space may be caused by a characteristic difference between the coils. And/or, this difference in sensitivity due to a position of a space may be caused by a difference in a position of each coil arranged in the MRI scanner. 
     The four sample images  211   s ,  212   s ,  221   s , and  222   s  shown in the second column in  FIG.  6    indicate, by light and shade, a magnitude of sensitivity that a coil corresponding to each sample image has for the x and y coordinates. Referring to the four sample images  211   s ,  212   s ,  221   s , and  222   s  shown in the second column in  FIG.  6   , it may be recognized that space distributions of the sensitivities of the plurality of coils  211 ,  212 ,  221 , and  222  are different from each other. 
     For example, reference numbers  211   s ,  212   s ,  221   s , and  222   s  in  FIG.  6    indicate sensitivity maps according to the x and y coordinates of the coil  211 , coil  212 , coil  221 , and coil  222 , respectively. In each of the maps, a brighter portion indicates higher sensitivity. 
     For example, reference numbers  611 ,  612 ,  621 , and  622  indicate four sub-images generated using signals measured by each of the coil  211 , coil  212 , coil  221 , and coil  222 . Each of the sub-images may include noise, and at least a portion of the noise may be generated by a coil corresponding to each of the sub-images. 
     A reconstructed image  600  may be generated by combining the sub-image  611 , the sub-image  612 , the sub-image  621 , and the sub-image  622 . The MRI image  600  (x+n 1 ) shown in  FIG.  5    may be an image in which the noise n 1  is added to the true image  601  (x). 
       FIG.  7    is a diagram for describing an equation that represents a relationship between a sub-image obtained by a coil [c] having an index c among the above coils and the sensitivity of the coil [c]. 
     For convenience, the coil [c] is assumed to be the above coil  222 . 
     When noise  601   22  is combined with a result of measuring the true image  601  (x) with the sensitivity  222   s  of the coil  222 , the sub-image  622  may be obtained. 
     Here, the true image  601  (x) may be denoted by x,  222   s  may be denoted by  Sc , the sub-image  622  may be denoted by y c , and the noise  601   22  may be denoted by n c . Here, [Equation 2] is established. [0041]  
     
       
         
           
             
               y 
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               s 
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             x 
             + 
             
               
                 
                   n 
                   
                     c 
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                 ∈ 
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                 … 
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             , 
             n= 
             N 
             
               
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               2 
             
           
         
       
     
     Here,  Sc  is a value that may be obtained in advance using a device characteristic of the MRI scanner. 
     Now, s c   H  satisfying [Equation 3} may be determined for all of the coils included in the MRI scanner. [0046]  
     
       
         
           
             
               ∑ 
               c 
             
             
               s 
               c 
             
             
                 
               H 
             
             
               s 
               c 
             
             = 
             1 
           
         
       
     
     Here, each of s c  and s c   H  may be a matrix. 
     Now, [Equation 4] is satisfied by multiplying sub-images obtained for all of the coils included in the MRI scanner by s c   H  and adding up resultant values. Here, the subscript c has a different value for a different coil. [0050] 
     
       
         
           
             
               I 
               
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                 n 
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               c 
             
             
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               c 
             
             
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             x 
             + 
             
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             = 
             x 
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               ∑ 
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     According to [Equation 4], it may be recognized that a result of adding up the sub-images obtained for all of the coils included in the MRI scanner is a combination of the true image (x) and the noise term s c   H n c . Iinput denotes a detection image, output from the MRI scanner, including noise. 
     Now, as illustrated in  FIG.  4   , the network  111  may be trained using the loss function between the true image (x) and the post-processed image f θ  (Input) obtained by inputting I input  of [Equation 4] to the network  111 . However, also in this case, it may be difficult to obtain the true image (x) in advance as described above. 
     SUMMARY 
     The present disclosure provides a specific technology for generating label data and training data for supervised learning of a post-processing part for denoising an MRI image. 
     According to one aspect of the present invention, a magnetic resonance imaging (MRI) system can be provided. The MRI system comprises an MRI scanner including a first group of coils and a second group of coils; and a computing device including a post-processing part for post-processing an MRI image and a training management part. Here, a first image generated based on signals obtained from the first group of coils is used as training input data for supervised learning of the post-processing part, a second image generated based on signals obtained from the second group of coils is used as a label for supervised learning of the post-processing part, and the training management part is configured to perform supervised learning on the post-processing part using the training input data and the label. 
     In an MRI system provided according to an aspect of the present invention, a first group of coils and a second group of coils may be phased-array coils. 
     Here, the first image may be a first MRI image generated based on a first group of MRI signals obtained from the first group of coils. Further, generating of the second image may include generating a second MRI image based on a second group of MRI signals obtained from the second group of coils; generating an intermediate label image based on the second MRI image so as to eliminate a correlation between first noise in the first MRI image and second noise in the second MRI image; and generating a label image based on the intermediate label image so as to compensate for a difference in sensitivity between the first group of coils and the second group of coils, and the second image is the generated label image. 
     Here, the first MRI image may be an image obtained by synthesizing images of a first group generated from the MRI signals of the first group obtained from the first group of coils, the second MRI image may be an image obtained by synthesizing images of a second group generated from the MRI signals of the second group obtained from the second group of coils, and the MRI scanner may include a transform part configured to generate the images of the first group from the MRI signals of the first group and generate the images of the second group from the MRI signals of the second group. 
     Here, the intermediate label image may be generated based on a weighted sum of the first MRI image and the second MRI image. 
     Here, the first image may be a first MRI image generated based on a first group of MRI signals obtained from the first group of coils. Further, generating of the second image may include generating a second MRI image based on a second group of MRI signals obtained from the second group of coils; and generating a label image based on the second MRI image so as to compensate for a difference in sensitivity between the first group of coils and the second group of coils, the second image is the generated label image. 
     Herein, the first image is the first MRI image generated based on the MRI signals of the first group obtained from the first group of coils, and the second image is the second MRI image generated based on the MRI signals of the second group obtained from the second group of coils. 
     Here, while performing the supervised learning, the post-processing part may be configured to receive an input of the first image to generate a post-processed image, the training management part is configured to train the post-training part using a loss function between the post-processed image and the second image. 
     Here, the first image and the second image may be obtained through the same one-time data acquisition process performed by the MRI scanner. 
     Here, the first MRI image and the second MRI image may be obtained through the same one-time data acquisition process performed by the MRI scanner. 
     Here, there may be no correlation between first noise in the first MRI image and second noise in the second MRI image. 
     Here, each coil of the first group of coils and the second group of coils may be configured to output, only one time, an MRI signal corresponding to the each coil in the one-time data acquisition process. 
     Here, each of the first image and the second image may be a cross-sectional image of an object scanned by the MRI scanner. 
     According to another aspect of the present invention, a neural network training method for training a post-processing part configured to receive an input of a magnetic resonance imaging (MRI) image and denoise the MRI image can be provided. The method comprises generating, by an MRI scanner including a first group of coils and a second group of coils, a first image based on signals obtained from the first group of coils; generating, by the MRI scanner, a second image based on signals obtained from the second group of coils; and performing, by a computing device, supervised learning on the post-processing part by using the first image as training input data for supervised learning of the post-processing part and using the second image as a label for supervised learning of the post-processing part. 
     According to still another aspect of the present invention, a magnetic resonance imaging (MRI) system can be provided. The MRI system comprises an MRI scanner including a first group of coils and a second group of coils and configured to output an MRI image; and a computing device including a trainable post-processing part and a training management part configured to train the post-processing part. Here, the post-processing part is configured to, during a training process of the post-processing part, receive an input of a first image generated based on signals obtained from the first group of coils to generate a training post-processed image, the training management part is configured to, during the training process of the post-processing part, train the post-training part using a loss function between the training post-processed image and a second image generated based on signals obtained from the second group of coils, and the post-processing part is configured to receive the MRI image to output an image obtained by denoising the MRI image after the training process of the post-processing part is completed. 
     According to still another aspect of the present invention, a method of denoising a magnetic resonance imaging (MRI) image can be provided. The method comprises outputting, by an MRI scanner, an MRI signal from a plurality of coils included in the MRI scanner; and inputting, by a computing device, an MRI image generated using signals obtained from the plurality of coils to a post-processing part included in the computing device to generate a post-processed image obtained by denoising the MRI image. Here, the post-processing part is trained using a supervised learning method. Here, the supervised learning method includes generating, by a second MRI scanner including a first group of coils and a second group of coils, a first image based on signals obtained from the first group of coils; generating, by the second MRI scanner, a second image based on signals obtained from the second group of coils; and performing, by a second computing device, supervised learning on the post-processing part by using the first image as training input data for supervised learning of the post-processing part and using the second image as a label for supervised learning of the post-processing part. 
     An MRI scanner provided according to an aspect of the present invention may generate K-spaces of a first group from a first group of MRI signals and generate images of a first group from the K-spaces of the first group. Furthermore, the MRI scanner may generate K-spaces of a second group from a second group of MRI signals and generate images of a second group from the K-spaces of the second group. 
     According to an embodiment of the present invention, provided is an MRI system including: an MRI scanner; and a computing device including a post-processing part for post-processing an MRI image and a training management part. The training management part is configured to perform supervised learning on the post-processing part by using, as training input data, a first image generated using a signal obtained from a first group of coils among the plurality of coils included in the MRI scanner and using, as a label, a second image generated using a signal obtained from a second group of coils among the plurality of coils. 
     The supervised learning method includes: generating, by a second MRI scanner, a first image by transforming a first MRI signal obtained by a first group of coils included in the second MRI scanner; generating, by the second MRI scanner, a second image by transforming a second MRI signal obtained by a second group of coils included in the second MRI scanner; and performing, by a second computing device, supervised learning on the post-processing part by using the first image as training input data and using the second image as a label. 
     Here, the second computing device may be the same device as the computing device, the second MRI scanner may be the same device as the MRI scanner, and the plurality of coils included in the MRI scanner may include the first group of coils and the second group of coils. 
     Here, the post-processing part may be configured to receive an input of the first image to generate a post-processed image, and the second computing device may be configured to train the post-processing part using a loss function between the post-processed image and the second image. 
     A training method according to another aspect of the present invention may include: outputting, by an MRI scanner, an MRI signal from a plurality of coils included in the MRI scanner; and performing, by a computing device for post-processing an MRI image, supervised learning on a post-processing part included in the computing device by using, as training input data, a first image generated using a signal obtained from a first group of coils among a plurality of coils included in the MRI scanner and using, as a label, a second image generated using a signal obtained from a second group of coils among the plurality of coils. 
     Here, the performing supervised learning may include: receiving, by the post-processing part, an input of the first image generated by transforming a first MRI signal obtained by the first group of coils to generate a post-processed image; and training, by a training management part included in the computing device, the post-processing part using a loss function between the post-processed image and a second image generated by transforming a second MRI signal obtained by the second group of coils. 
     Here, the first image and the second image may be obtained through the same one data acquisition process performed by the MRI scanner. 
     Here, in the one data acquisition process, each of the plurality of coils included in the MRI scanner may be configured to output an MRI signal one time. 
     Here, the post-processing part may include a neural network. 
     Here, the computing device may be configured to generate a first K-space corresponding to the first MRI signal by transforming the first MRI signal and generate the first image (first MRI image) corresponding to the first MRI signal, and configured to generate a second K-space corresponding to the second MRI signal by transforming the second MRI signal and generate a second MRI image corresponding to the second MRI signal. 
     A computing device according to another aspect of the present invention may include a post-processing part for post-processing an MRI image and a training management part, wherein the training management part may be configured to perform supervised learning on the post-processing part by using, as training input data, a first image generated using a signal obtained from a first group of coils among a plurality of coils included in an MRI scanner and using, as a label, a second image generated using a signal obtained from a second group of coils among the plurality of coils. 
     Here, the post-processing part may be configured to receive an input of the first image generated by transforming a first MRI signal obtained by the first group of coils to generate a post-processed image, and the training management part may be configured to train the post-processing part using a loss function between the post-processed image and a second image generated by transforming a second MRI signal obtained by the second group of coils. 
     Here, the first image and the second image may be obtained through the same one data acquisition process performed by the MRI scanner. 
     An MRI system according to another aspect of the present invention includes: an MRI scanner for outputting an MRI image; and a computing device including a post-processing part for outputting a post-processed image by denoising the MRI image, wherein the post-processing part may be supervised-trained by using, as training input data, a first image generated using a signal obtained from a first group of coils among a plurality of coils included in the MRI scanner and using, as a label, a second image generated using a signal obtained from a second group of coils among the plurality of coils. 
     Here, the computing device may further include a post-processing part, wherein the post-processing part may be configured to receive an input of the first image generated by transforming a first MRI signal obtained by the first group of coils to generate a post-processed image, and the training management part may be configured to train the post-processing part using a loss function between the post-processed image and a second image generated by transforming a second MRI signal obtained by the second group of coils. 
     Here, the first image and the second image may be obtained through the same one data acquisition process performed by the MRI scanner. 
     Here, the MRI scanner and the computing device may be connected to each other by a local network, or may be different devices not connected by a local network. 
     A method of denoising an MRI image according to another aspect of the present invention may include: outputting, by an MRI scanner, an MRI signal from a plurality of coils included in the MRI scanner; and inputting, by a computing device, an MRI image generated using signals obtained from the plurality of coils to a post-processing part included in the computing device to generate a post-processed image obtained by denoising the MRI image. The post-processed part may be one that has been supervised-trained according to a supervised learning method. The supervised learning method may include: outputting, by one MRI scanner among the MRI scanner and another MRI scanner, a second MRI signal from a plurality of coils included in the one MRI scanner; and performing, by one computing device among the computing device and another computing device, supervised learning on the post-processing part by using, as training input data, a first image generated using a signal obtained from a first group of coils among a plurality of coils included in the one MRI scanner and using, as a label, a second image generated using a signal obtained from a second group of coils among the plurality of coils. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments can be understood in more detail from the following description taken in conjunction with the accompanying drawings, in which: 
         FIG.  1    illustrates a main configuration of an MRI scanner; 
         FIG.  2    is a diagram illustrating a process of generating a K-space or MRI image using an MRI signal obtained by the MRI scanner illustrated in  FIG.  1   ; 
         FIG.  3    is a diagram illustrating a concept of an MRI image including noise; 
         FIG.  4    illustrates a method of denoising an MRI image according to a comparative embodiment; 
         FIG.  5    illustrates a method of denoising an MRI image according to another comparative embodiment; 
         FIG.  6    is a diagram illustrating images measured by using a plurality of coils included in an MRI scanner and a method of generating an MRI image using the images; 
         FIG.  7    is a diagram for describing an equation that represents a relationship between a sub-image obtained by a coil [c] having an index c among coils and sensitivity of the coil [c]; 
         FIG.  8    is a diagram illustrating a configuration of an MRI system provided according to an embodiment of the present invention; 
         FIG.  9    is a diagram illustrating a configuration of an MRI system provided according to an embodiment of the present invention modified from  FIG.  8   ; 
         FIG.  10    is a diagram illustrating a function performed by a computing device provided according to an embodiment of the present invention after training of a post-processing part is completed; 
         FIG.  11 A  is a diagram illustrating a process of generating two images through a one-time data acquisition process in an MRI scanner and training a post-processing part by using the two images according to an embodiment of the present invention; 
         FIG.  11 B  illustrates an embodiment modified from the embodiment illustrated in  FIG.  11 A ; 
         FIG.  11 C  illustrates a configuration of a system, which is provided according to a preferred embodiment of the present invention, for performing a training method of a post-processing part for denoising an MRI image; 
         FIG.  12    illustrates a method of denoising an MRI image using a trained post-processing part according to an embodiment of the present invention; and 
         FIG.  13    is a flowchart illustrating a training method provided according to an embodiment of the present invention. 
         FIG.  14    is a flowchart illustrating the supervised learning operation of  FIG.  13    in detail. 
         FIG.  15    is a diagram illustrating the computing device shown in  FIGS.  9 ,  10 , and  12    from a hardware aspect. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present invention will be described with reference to the accompanying drawings. However, the present invention is not limited to the embodiments described herein, and may be implemented in various different forms. The terminology used herein is not for limiting the scope of the present invention but for describing the embodiments. Furthermore, the singular forms used herein include the plural forms as well, unless otherwise indicated. 
       FIG.  8    is a diagram illustrating a configuration of an MRI system provided according to an embodiment of the present invention. 
     An MRI system  1000  may include an MRI scanner  200  and a computing device  100 . 
     In the case where the MRI scanner  200  and the computing device  100  are integrally provided, the MRI system may be simply referred to as an MRI scanner. 
     The MRI scanner  200  may include a plurality of coils  211 ,  212 ,  221 , and  222 . The MRI scanner  200  has a space capable of accommodating an object  70 . 
     The number of the plurality of coils may be, for example, N in total, but only four coils are illustrated in  FIG.  8    for convenience. 
     The plurality of coils are divided into a plurality of groups, for example, two groups. 
     In the example of  FIG.  8   , the plurality of coils  211 ,  212 ,  221 , and  222  are divided into first group coils  211  and  212  [G1] and second group coils  221  and  222  [G2]. The first group is indicated by symbol G1, and the second group is indicated by symbol G2. 
     In an embodiment, a total number of coils included in the first group and a total number of coils included in the second group may be different from each other. Alternatively, in another embodiment, the total number of coils included in the first group and the total number of coils included in the second group may be the same. However, the present invention is not limited by the number of coils included in each coil. 
     In a preferred embodiment, a union of the first group of coils and the second group of coils is the same as a set of all of coils included in the MRI scanner  200 . Here, there may be no overlapping coil between the first group of coils and the second group of coils. 
     The computing device  100  may include a post-processing part  110 , a training management part  120 , and a label image generating part  130 . 
     The post-processing part  110  may be a trainable network. For example, the post-processing part  110  may include an artificial intelligence network, a neural network, or a machine learning network. 
     The training management part  120  may be configured to manage a training process of the post-processing part  110 . 
     In an embodiment of the present invention, a second MRI image  620  may be used as a label for supervised learning as it is. 
     In a preferred embodiment of the present invention, an image generated by correcting the second MRI image  620 , i.e., a label image, may be used as a label for supervised learning. The label image generating part  130  is configured to generate the label image by correcting the second MRI image  620 . 
     A label generation process for generating, by the label image generating part  130 , the label image from the second MRI image  620  may include correcting the second MRI image  620  based on a difference in sensitivity between the first group of coils and the second group of coils. Furthermore, the label generation process may further include correcting the second MRI image  620  by eliminating a correlation between noise included in a first MRI image and noise included in the second MRI image. 
     When training of the post-processing part  110  is completed, the post-processing part  110  may autonomously operate without intervention of the training management part  120 . 
       FIG.  9    is a diagram illustrating a configuration of an MRI system provided according to an embodiment of the present invention modified from  FIG.  8   . 
       FIG.  9    illustrates the same structure as that illustrated in  FIG.  8    except that the computing device  100  is separated from the MRI system  1000 . 
       FIG.  10    is a diagram illustrating a function performed by a computing device provided according to an embodiment of the present invention after training of a post-processing part is completed. 
     The computing device  100  may obtain an MRI image output from the MRI scanner  200  and provide the MRI image to the post-processing part  110 . 
     The MRI image may be an image including noise. The MRI image may be an image generated using all of the coils included in the MRI scanner  200 . For example, the MRI image may be an image including noise and indicated by reference number  600  in  FIGS.  2 ,  3 ,  4 , or  5   . 
     The post-processing part  110  may output a denoised image by processing the MRI image including noise. Performance of the post-processing part  110  may be evaluated to be better as an image output from the post-processing part  110  is closer to the true image (x). 
       FIG.  11 A  is a diagram illustrating a process of generating two images through a one-time data acquisition process in an MRI scanner and training a post-processing part by using the two images according to an embodiment of the present invention. 
     Here, the “one-time data acquisition process” may represent a process of acquiring one output signal from each of substantially available coils among the coils included in the MRI scanner  200 . 
     Here, the coils may have a signal detection function. 
     As described above, the plurality of coils included in the MRI scanner  200  are divided into a plurality of groups, for example, two groups. 
       FIG.  11 A  illustrates an example in which the coils  211  and  212  belong to the first group G1 among the plurality of groups and the coils  221  and  222  belong to the second group G2 among the plurality of groups. 
     The MRI scanner  200  or the MRI system  1000  may be configured to generate a first MRI signal  510  including signals output from the first group G1 of coils and generate a second MRI signal  520  including signals output from the second group of coils G2. 
     In a preferred embodiment, the signals output from the second group G2 of coils may not be included in the first MRI signal  510 , and the signals output from the first group G1 of coils may not be included in the second MRI signal  520 . 
     A transform part  230  included in the MRI scanner  200  or the MRI system  1000  may be configured to transform the first MRI signal  510  into a first image  610  (= first MRI image) (I input ) and transform the second MRI signal  520  into the second MRI image  620  (I label ). 
     In the present disclosure, the first image  610  (I input ) may be referred to as a first MRI image  610  (I input ). 
     In an embodiment of the present invention, the transform part  230  may include a first transform part  231  for transforming the first MRI signal  510  into the first MRI image  610  and a second transform part  232  for transforming the second MRI signal  520  into the second MRI image  620 . 
     The first image  610  (I input ) generated using the signals output from the first group G1 of coils may be provided as training input data of the post-processing part  110 . The post-processing part  110  may output a post-processed image  630  generated by post-processing the first image  610  (I input ). The post-processed image  630  may be provided as a first input to the training management part  120 . 
     In an embodiment, the second MRI image  620  (I label ) generated using the signals output from the second group G2 of coils may be directly provided as a second input to the training management part  120 . In this case, the second MRI image  620  (I label ) is a label image, i.e., a second image  820 . 
     However, as illustrated in  FIG.  11 A , according to a preferred embodiment of the present invention, the image generated by correcting the second MRI image  620 , i.e., the label image  820  (I″ label ), may be used as a label for supervised learning. The label image generating part  130  is configured to generate the label image  820  (I″ label ) by correcting the second MRI image  620 . 
     The label generation process may further include generating a first corrected image (I′ label ) by correcting the second MRI image  620  (I input ) in order to eliminate a correlation between noise included in the first MRI image  610  and noise included in the second MRI image  620 . 
     If there is no correlation between noise included in the first MRI image  610  and noise included in the second MRI image  620 , the second MRI image  620  (I input ) may become the first corrected image (I label ) per se. 
     Furthermore, a label generation process for generating, by the label image generating part  130 , the label image  820  (I″ label ) from the second MRI image  620  (I input ) may include generating the label image  820  (I″ label ) based on a difference in sensitivity between the first group G1 of coils and the second group G2 of coils. 
     By eliminating the difference in sensitivity between the coils, an image obtained by denoising the first MRI image  610  provided to the post-processing part  110  and an image obtained by denoising the label image  820  (I″ label ) provided to the training management part  120  may be rendered identical. 
     The training management part  120  may calculate a loss value according to a loss function between the post-processed image  630  and the label image  820  (I″ label ). Furthermore, update information P 121  for changing a parameter θ of the post-processing part  110  may be generated so as to reduce the loss value according to the loss function. The training management part  120  may train the post-processing part  110  by changing the parameter θ of the post-processing part  110  using the update information P 121 . 
     When the MRI scanner  200  performs the data acquisition process multiple times, a plurality of different sets of the first image and the label image may be obtained. For example, the MRI scanner  200  may perform the data acquisition process N times in order to prepare N number of different sets of the first image and the label image. 
     With regard to two of the different data acquisition processes, a scan target (for example, a person) to be scanned by the MRI scanner  200  may be different. Alternatively, with regard to two of the different data acquisition processes, a scan target (for example, a person) to be scanned by the MRI scanner  200  may have a different posture. 
     The computing device  100  may finish training of the post-processing part  110  by repeating the training using the plurality of different sets of the first image and the label image. 
     Here, the first image  610  (I input ) may satisfy [Equation 5]. [00153] 
     
       
         
           
             
               
                 
                   I 
                   
                     i 
                     n 
                     p 
                     u 
                     t 
                   
                 
                 = 
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 
                   y 
                   i 
                 
                 = 
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 
                   
                     
                       s 
                       i 
                     
                     x+ 
                     
                       n 
                       i 
                     
                   
                 
                 = 
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 
                   s 
                   i 
                 
                 x 
                 + 
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 
                   n 
                   i 
                 
               
             
             
               
                 E 
                 
                   
                     
                       ∑ 
                       i 
                     
                     
                       s 
                       i 
                     
                     
                         
                       H 
                     
                     
                       n 
                       i 
                     
                   
                 
                 = 
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 E 
                 
                   
                     
                       n 
                       i 
                     
                   
                 
                 = 
                 0 
               
             
           
         
       
     
     In [Equation 5], the subscript i denotes an index for identifying the coils belonging to the first group G1, and s i  denotes spatial sensitivity of corresponding coils. 
     Here, the second MRI image  620  (I label ) may satisfy [Equation 6]. [00158] 
     
       
         
           
             
               
                 
                   I 
                   
                     l 
                     a 
                     b 
                     e 
                     l 
                   
                 
                 = 
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   y 
                   j 
                 
                 = 
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   
                     
                       s 
                       j 
                     
                     x+ 
                     
                       n 
                       j 
                     
                   
                 
                 = 
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   s 
                   j 
                 
                 x 
                 + 
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   n 
                   j 
                 
               
             
             
               
                 E 
                 
                   
                     
                       ∑ 
                       j 
                     
                     
                       s 
                       j 
                     
                     
                         
                       H 
                     
                     
                       n 
                       j 
                     
                   
                 
                 = 
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 E 
                 
                   
                     
                       n 
                       j 
                     
                   
                 
                 = 
                 0 
               
             
           
         
       
     
     In [Equation 6], the subscript j denotes an index for identifying the coils belonging to the second group G2, and S j  denotes spatial sensitivity of corresponding coils. 
     In [Equation 5] and [Equation 6], expectation values of the noise terms may be 0 and may be independent of each other. Furthermore, n i  and n j  are symmetric with each other. 
     Meanwhile, when the first image  610  (I input ) and the second MRI image  620  (I label ) are given as expressed in [Equation 5] and [Equation 6], a loss function used by the training management part  120  may be defined as [Equation 7]. [00164] 
     
       
         
           
             l 
             o 
             s 
             
               s 
               ′ 
             
             = 
             
               
                 
                   
                     
                       f 
                       θ 
                     
                     
                       
                         
                           I 
                           
                             i 
                             n 
                             p 
                             u 
                             t 
                           
                         
                       
                     
                     − 
                     
                       I 
                       
                         l 
                         a 
                         b 
                         e 
                         l 
                       
                     
                   
                 
               
               2 
             
             
                 
               2 
             
           
         
       
     
     Here, f θ (I input ) represents the post-processed image  630 . 
     Descriptions have been provided with reference to  FIG.  5    on the assumption that a value (x) of the term obtained by eliminating noise from the MRI image  600  (x+n 1 ) input to the network  111  (fθ) is equal to a value (x) of the term obtained by eliminating noise from the other label image  604  (x+n 2 ) used as a label. 
     However, on the contrary, the left term Σ i S i   H   Si X among the terms constituting I input  is a value obtained by multiplying the true image (x) by Σ i S i   H S i  in [Equation 5], and the left term Σ j S j   H S j X among the terms constituting the second MRI image  620  (I label )) is a value obtained by multiplying the true image x by Σ j S j   H S j  in [Equation 6]. That is, the value of the term obtained by eliminating noise from I input  of [Equation 5] and the value of the term obtained by eliminating noise from I label  of [Equation 6] are different from each other. 
     Therefore, there may occur an issue in which a combination of [Equation 5], [Equation 6], and [Equation 7] do not satisfy the assumption given with regard to  FIG.  5   . This issue may be resolved by correcting the loss function as expressed in [Equation 8]. [00170] 
     
       
         
           
             l 
             o 
             s 
             s 
             = 
             
               
                 
                   
                     
                       
                         
                           ∑ 
                           j 
                         
                         
                           s 
                           j 
                         
                         
                             
                           H 
                         
                         
                           s 
                           j 
                         
                       
                     
                     
                       f 
                       θ 
                     
                     
                       
                         
                           I 
                           
                             i 
                             n 
                             p 
                             u 
                             t 
                           
                         
                       
                     
                     − 
                     
                       
                         
                           ∑ 
                           i 
                         
                         
                           s 
                           i 
                         
                         
                             
                           H 
                         
                         
                           s 
                           i 
                         
                       
                     
                     
                       I 
                       
                         l 
                         a 
                         b 
                         e 
                         l 
                       
                     
                   
                 
               
               2 
             
             
                 
               2 
             
           
         
       
     
     That is, the loss function may be redefined using a value obtained by multiplying f θ (I input ) by Σ j S j   H S j  that is a proportional constant value included in I label  and a value obtained by multiplying I label  by Σ i S i   H S i  that is a proportional constant value included in fθ(I input ). 
     In an embodiment of the present invention, I input  of [Equation 5] is used as the first image provided to the post-processing part  110 , I label  of [Equation 6] is used as the label image provided to the training management part  120 , and the loss of [Equation 8] is used as the loss function. Here, the above first embodiment satisfies the assumption given with regard to  FIG.  5   . That is, even if the post-processing part  110  is trained using the second MRI image  620  (I label ) as a label image, a training effect may be achieved, which is the same as or similar to the effect exhibited when training the post-processing part  110  using the true image (x) for the first image  610  (I input ) as a label image. 
     In another embodiment of the present invention, I input  of [Equation 5] is used as the first image provided to the post-processing part  110 , I label  of [Equation 9] shown below is used as the label image provided to the training management part  120 , and the loss’ of [Equation 7] is used as the loss function. Here, the above second embodiment satisfies the assumption given with regard to  FIG.  5   . Therefore, the same training effect as that of the first embodiment may be achieved. [00175] 
     
       
         
           
             
               I 
               
                 l 
                 a 
                 b 
                 e 
                 l 
               
             
             = 
             
               
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   s 
                   j 
                 
                 x 
                 + 
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   n 
                   j 
                 
               
             
             
               
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 
                   s 
                   i 
                 
               
             
             / 
             
               ∑ 
               j 
             
             
               s 
               j 
             
             
                 
               H 
             
             
               s 
               j 
             
           
         
       
     
     In another embodiment of the present invention, I input  of [Equation 10] is used as the first image provided to the post-processing part  110 , I label  of [Equation 6] is used as the label image provided to the training management part  120 , and the loss’ of [Equation 7] is used as the loss function. Here, the above third embodiment satisfies the assumption given with regard to  FIG.  5   . Therefore, the same training effect as that of the first embodiment may be achieved. [00178] 
     
       
         
           
             
               I 
               
                 i 
                 n 
                 p 
                 u 
                 t 
               
             
             = 
             
               
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 
                   s 
                   i 
                 
                 x 
                 + 
                 
                   ∑ 
                   i 
                 
                 
                   s 
                   i 
                 
                 
                     
                   H 
                 
                 
                   n 
                   i 
                 
               
             
             
               
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   s 
                   j 
                 
               
             
             / 
             
               ∑ 
               i 
             
             
               s 
               i 
             
             
                 
               H 
             
             
               s 
               i 
             
           
         
       
     
       FIG.  11 B  illustrates an embodiment modified from the embodiment illustrated in  FIG.  11 A . 
     Hereinafter, descriptions about  FIG.  11 B  will be provided with focus on differences with  FIG.  11 A . 
     The transform part  230  may transform the first MRI signal  510  into the first MRI image  610 , and thereafter may transform the second MRI signal  520  into the second MRI image  620 . To this end, the transform part  230  may include a buffer for storing the second MRI signal  520  while transforming the first MRI signal  510  into the first MRI image  610 . 
     In  FIGS.  11 A and  11 B , the transform part  230  may be a computing module including a programmed FPGA or dedicated calculation part and a memory. 
     In  FIGS.  11 A and  11 B , the signals output from the first group of coils are input to the transform part  230  after being combined by a first signal combining part  241 , and the signals output from the second group of coils are input to the transform part  230  after being combined by a second signal combining part  242 . However, in the modified embodiment, all of the signals output from the coils belonging to the first and second groups may be directly input to the transform part  230  without passing through the first signal combining part  241  and the second signal combining part  242 . Furthermore, the signals output from the first group of coils may be combined with each other in the transform part  230 , and the signals output from the second group of coils may be combined with each other in the transform part  230 . 
     Preferred Embodiment 
       FIG.  11 C  illustrates a configuration of a system, which is provided according to a preferred embodiment of the present invention, for performing a training method of a post-processing part for denoising an MRI image. 
     Described below with reference to  FIG.  11 C  is a process of generating two images through a one-time data acquisition process in an MRI scanner and training a post-processing part by using the two images according to an embodiment of the present invention. 
     The post-processing part is a denoising network. 
     The MRI scanner  200  may include the plurality of coils  211 ,  212 ,  221 , and  222 , the transform part  230 , and the image combining parts  251  and  252 . 
     The plurality of coils included in the MRI scanner  200  are divided into a plurality of groups, for example, two groups. In the example of  FIG.  11 C , the coils  211  and  212  belong to the first group G1 among the plurality of groups and the coils  221  and  222  belong to the second group G2 among the plurality of groups. 
     When the one-time data acquisition process is performed in the MRI scanner  200 , the 11th coil  211 , the 12th coil  212 , the 21st coil  221 , and the 22nd coil  222  output an 11th MRI signal  511 , a 12th MRI signal  512 , a 21st MRI signal  521 , and a 22nd MRI signal  522 , respectively. 
     The transform part  230  may generate an 11th MRI image  611 , a 12th MRI image  612 , a 21st MRI image  621 , and a 22nd MRI image  622  by transforming the 11th MRI signal  511 , the 12th MRI signal  512 , the 21st MRI signal  521 , and the 22nd MRI signal  522 , respectively. 
     In the present disclosure, an MRI image obtained by combining all of the 11th MRI image  611 , the 12th MRI image  612 , the 21st MRI image  621 , and the 22nd MRI image  622  may be denoted by x. Here, each of the 11th MRI image  611 , the 12th MRI image  612 , the 21st MRI image  621 , and the 22nd MRI image  622  may be referred to as an individual channel image and denoted by yi. 
     Here, [Equation 11] is established. [00195] 
     
       
         
           
             
               
                 
                   y 
                   i 
                 
                 = 
                 
                   s 
                   i 
                 
                 x 
                 + 
                 
                   n 
                   i 
                 
               
             
             
               
                 Where, x 
                 ∈ 
                 
                   C 
                   2 
                 
                 , 
                 
                   y 
                   i 
                 
                 ∈ 
                 
                   C 
                   2 
                 
                 , 
                 
                   s 
                   i 
                 
                 ∈ 
                 
                   C 
                   2 
                 
                 . 
               
             
           
         
       
     
     Here, s i  is the coil sensitivity, and n i  is the noise of i th  channel image, modeled as zero mean Gaussian with the standard deviation of σ i  for both real and imaginary axis. The matrix multiplication (or division) hereafter indicates Hadamard multiplication (or division). 
     In an embodiment, the transform part  230  may include an 11th transform part  2311  for generating the 11th MRI image  611  from the 11th MRI signal  511 , a 12th transform part  2312  for generating the 12th MRI image  612  from the 12th MRI signal  512 , a 21st transform part  2321  for generating the 21st MRI image  621  from the 21st MRI signal  521 , and a 22nd transform part  2322  for generating the 22nd MRI image  622  from the 22nd MRI signal  522 . 
     The first image combining part  251  may generate the first MRI image  610  (I input ) by combining the 11th MRI image  611  and the 12th MRI image  612 . 
     The second image combining part  252  may generate the second MRI image  620  (I label ) by combining the 21st MRI image  621  and the 22nd MRI image  622 . 
     The first MRI image  610  (I input ) and the second MRI image  620  (I label ) satisfy [Equation 12]. [00203] 
     
       
         
           
             
               I 
               
                 i 
                 n 
                 p 
                 u 
                 t 
               
             
             = 
             
               
                 
                   ∑ 
                   j 
                 
                 
                   s 
                   j 
                 
                 
                     
                   H 
                 
                 
                   y 
                   j 
                 
               
             
           
         
       
     
     
       
         
           
             
               I 
               
                 l 
                 a 
                 b 
                 e 
                 l 
               
             
             = 
             
               
                 
                   ∑ 
                   k 
                 
                 
                   s 
                   k 
                 
                 
                     
                   H 
                 
                 
                   y 
                   k 
                 
               
             
           
         
       
     
     Where, j denotes the first group G1, and k denotes the second group G2. And S i   H  is the hermitian of s i . It is assumed that the two images cover all imaging volumes because most of the individual coils have relatively large volume coverage and are mutually coupled. 
     The first MRI image  610  (I input ) and the second MRI image  620  (I label ) may be provided to the computing device  100 . 
     The first MRI image  610  may be provided as training input data of the post-processing part  110 . The post-processing part  110  may output the post-processed image  630  generated by post-processing the first image  610  (I input ). The post-processed image  630  may be provided as a first input to the training management part  120 . 
     The second MRI image  620  (I label ) may be input to the noise decorrelation part  131 . The noise decorrelation part  131  is configured to transform the second MRI image  620  (I label ) so as to eliminate a correlation between first noise in the first MRI image  610  (I input ) and second noise in the second MRI image  620  (Ilabel). 
     The noise decorrelation part  131  is configured to output an intermediate label image  720  (I′ label ) by transforming the second MRI image  620  (I label ). 
     These two images, I input  and I label , have different coil sensitivity weighting and may have noise correlation (e.g., mutual inductance between channels). Therefore, they need to be further processed to satisfy the three conditions, first, the paired images have independent noise, second, they have the same noise-free image, and third, the expectation of the noise is zero. In order to impose the independence of noise between the two images, a generalized least-square solution is applied, resulting in the following modification in the label image as indicated by Equation 13. 
     The intermediate label image  720  (I′ label ), the second MRI image  620  (I label ), and the first MRI image  610  (I input ) have a relationship as expressed in [Equation 13].  
     
       
         
           
             
               
                 I 
                 ′ 
               
               
                 l 
                 a 
                 b 
                 e 
                 l 
               
             
             = 
             α 
             
               I 
               
                 i 
                 n 
                 p 
                 u 
                 t 
               
             
             + 
             β 
             
               I 
               
                 l 
                 a 
                 b 
                 e 
                 l 
               
             
           
         
       
     
      with α = -σ JK   2  / root{σJ 2 σK 2  - (σ JK   2 ) 2 }, and β = -σJ 2  / root {σ J   2 σK 2  -(σ JK   2 ) 2  } 
     Here, σ J   2 , σ K   2 , and σ JK   2  are matrices (∈R 2 ) calculated as var(|Σ j S j   H y j |), var(|Σ k S k   H yk|), and  COV (|ΣjSj H y j|,  |Σ k S k   H y k|),  respectively. In these equations, all operations are voxel-wise operations. As a result, I label  is modified to I′ label , and thereby the noise covariance between I input  and I′ label  becomes zero. 
     In this specification, I′ label  may be called as an intermediate label image  720 . 
     If there is no correlation between first noise in the first MRI image  610  (I inPut ) and second noise in the second MRI image  620  (I label) , the intermediate label image  720  (I′ label ) is the same as the second MRI image  620  (I label ). 
     The intermediate label image  720  (I′ label ) may be input to a coil sensitivity compensation part  132 . 
     The coil sensitivity compensation part  132  is configured to transform the intermediate label image  720  (I′ label ) by compensating for a difference in sensitivity between the coils  211  and  212  of the first group and the coils  221  and  222  of the second group. 
     To impose the requirement of the same noise-free image, the coil sensitivity of I′ label  (i.e., S′K=a|ΣkSk H |+β|ΣjSj H |) is modified to match that of I nput  (i.e., S J = |Σ j S j H|)by multiplying the sensitivity ratio (S J /S′ K ) to I′ label  in each voxel, generating a final image (I″ label =(Sj/S′K)·S′k) • I′ label ). Since multiplying a coefficient is a linear process, the first condition of noise independence still holds after the processing. 
     In this specification, the final image I″ label  may be called as a label image  820 . 
     The coil sensitivity compensation part  132  is configured to output the label image  820  (I″ label ) by transforming the intermediate label image  720  (I′ label ). 
     Here, covariance between first noise included in the first MRI image  610  (I input ) and third noise included in the label image  820  (I″ label ) is zero. Furthermore, an image obtained by eliminating the first noise from the first MRI image  610  (I input ) and an image obtained by eliminating the third noise from the label image  820  (I″ label ) are the same. 
     The above mentioned third condition of zero-mean noise is valid, assuming that the combined images have reasonably high SNR such that the noise characteristics within the image can be considered as Gaussian with zero mean. 
     The label image  820  (I″ label ) may be provided as a second input to the training management part  120 . 
     The training management part  120  may calculate a loss value according to a loss function between the post-processed image  630  and the label image  820  (I″ label ). Furthermore, update information P 121  for changing a parameter θ of the post-processing part  110  may be generated so as to reduce the loss value according to the loss function. The training management part  120  may train the post-processing part  110  by changing the parameter θ of the post-processing part  110  using the update information P 121 . 
     In this embodiment, for the training of a denoising network, the L2 loss is utilized as following Equation 14.  
     
       
         
           
             l 
             o 
             s 
             s 
             = 
             
               
                 
                   
                     
                       
                         S 
                         ′ 
                       
                       K 
                     
                     
                       f 
                       θ 
                     
                     
                       
                         
                           I 
                           
                             i 
                             n 
                             p 
                             u 
                             t 
                           
                         
                       
                     
                     − 
                     
                       S 
                       J 
                     
                     
                       
                         I 
                         ′ 
                       
                       
                         l 
                         a 
                         b 
                         e 
                         l 
                       
                     
                   
                 
               
               2 
             
             
                 
               2 
             
           
         
       
     
      where f θ  is the neural network. It is noted that the scaled version of I′ label  is used instead of I″ label  to avoid division. This loss function is calculated within a brain mask. 
       FIG.  12    illustrates a method of denoising an MRI image using a trained post-processing part according to an embodiment of the present invention. 
     The post-processing part illustrated in  FIG.  12    may be one that has been trained using the method described with reference to  FIGS.  11 A and  11 B . 
     The MRI scanner  200  may output the MRI image  600 . The MRI image  600  may be an image generated using all of the coils included in the MRI scanner  200 . The MRI image  600  may be an image in which noise (n) is added to a true image (x). 
     The output MRI image  600  may be input to the post-processing part  110  of the computing device  100 . The post-processing part  110  may output the post-processed image  603 . When the post-processing part  110  has been sufficiently trained according to an embodiment of the present invention, an error between the post-processed image and the true image  601  (x) may be very small. 
     A method of denoising an MRI image provided according to an embodiment of the present invention may include: outputting, by the MRI scanner  200 , an MRI signal from the plurality of coils  211  included in the MRI scanner  200 ; and inputting, by the computing device  100 , an MRI image generated using signals obtained from the plurality of coils to the post-processing part  110  included in the computing device  100  to generate a post-processed image obtained by denoising the MRI image. 
     Here, the post-processed part  110  may be one that has been supervised-trained according to a supervised learning method. 
       FIG.  13    is a flowchart illustrating a training method provided according to an embodiment of the present invention. 
     In operation S 10 , the MRI scanner  200  may output an MRI signal from the plurality of coils  211  included in the MRI scanner  200 . 
     In operation S 20 , the computing device  100  that post-processes an MRI image may perform supervised learning on the post-processing part  110  included in the computing device  100  by using, as training input data, an image generated using a signal obtained from a first group of coils among the plurality of coils included in the MRI scanner  200  and using, as a label, an image generated using a signal obtained from a second group of coils among the plurality of coils. 
       FIG.  14    is a flowchart illustrating the supervised learning operation of  FIG.  13    in detail. 
     Above supervised learning operation S 20  may include operation S 21  and operation S 22 . 
     In operation S 21 , the post-processing part  110  receives an input of the image  610  generated by transforming the first MRI signal  510  obtained by the first group of coils and generates the post-processed image  630 . 
     In operation S 22 , the training management part  120  included in the computing device  100  trains the post-processing part  110  using a loss function between the post-processed image  630  and an image generated by transforming the second MRI signal  520  obtained by the second group of coils. 
     Here, the image generated by transforming the second MRI signal  520  may be the label image  820  (I″ label ) illustrated in  FIGS.  11 A,  11 B, and  11 C . 
       FIG.  15    is a diagram illustrating the computing device shown in  FIGS.  9 ,  10 , and  12    from a hardware aspect. 
     The computing device  100  may include a device interface unit 3 capable of reading a computer-readable nonvolatile recording medium 2 and a processing unit 4. 
     The nonvolatile recording medium 2 may store a program including a first instruction code for executing a function of the post-processing part  110 . The first instruction code may be referred to as a post-processing instruction code. The processing unit 4 may be configured to execute the function of the post-processing part  110  by reading and executing the first instruction code through the device interface unit 3. 
     Furthermore, the nonvolatile recording medium 2 may store a program including a second instruction code for executing a function of the training management part  120 . The second instruction code may be referred to as a training management instruction code. The processing unit 4 may be configured to execute the function of the training management part  120  by reading and executing the second instruction code through the device interface unit 3. 
     The nonvolatile recording medium 2 may store a program including a third instruction code for executing: controlling, by the computing device  100 , the MRI scanner  200  to operate so as to output an MRI signal from a plurality of coils included in the MRI scanner  200 ; and performing supervised learning on the post-processing part  110  included in the computing device  100  by using, as training input data, the first image  610  generated using a signal obtained from a first group of coils among the plurality of coils included in the MRI scanner  200  and using, as a label, the second image  820  generated using a signal obtained from a second group of coils among the plurality of coils. The processing unit 4 may be configured to perform a method of performing supervised learning on the post-processing part  110  by reading and executing the third instruction code through the device interface unit 3. 
     Here, the performing supervised learning may include: receiving, by the post-processing part  110 , an input of the first image  610  generated by transforming the first MRI signal  510  obtained by the first group of coils to generate the post-processed image  630 ; and training, by the training management part  120 , the post-processing part  110  using a loss function between the post-processed image  630  and the second image  820  generated by transforming the second MRI signal  520  obtained by the second group of coils. 
     The nonvolatile recording medium 2 may store a program including a fourth instruction code for executing: generating, by the computing device  100 , a first K-space corresponding to the first MRI signal by transforming the first MRI signal and generating the first image  610  corresponding to the first MRI signal; and generating, by the computing device  100 , a second K-space corresponding to the second MRI signal by transforming the second MRI signal and generating the second image  820  corresponding to the second MRI signal. The processing unit 4 may be configured to perform a method of generating the first image  610  and the second image  820  by reading and executing the fourth instruction code through the device interface unit 3. 
     According to the present invention, a specific technology for generating label data and training data for supervised learning of a post-processing part for denoising an MRI image can be provided. 
     Those skilled in the art could easily make various alterations or modifications to the above-mentioned embodiments of the present invention without departing the essential characteristics of the present invention. The claims that do not refer to each other may be combined with each other within the scope of understanding of the present disclosure.