Patent Publication Number: US-10761167-B2

Title: System and method for generating a magnetic resonance fingerprinting dictionary using semi-supervised learning

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based on, claims priority to, and incorporates herein by reference in its entirety U.S. Ser. No. 62/673,819 filed May 18, 2018, and entitled “System And Method For Learning Bloch Equations Via Generative Adversarial Network For Use in Magnetic Resonance Fingerprinting.” 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with government support under EB016728 and EB017219 awarded by the National Institutes of Health. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     Characterizing tissue species using nuclear magnetic resonance (“NMR”) can include identifying different properties of a resonant species (e.g., T1 spin-lattice relaxation, T2 spin-spin relaxation, proton density). Other properties like tissue types and super-position of attributes can also be identified using NMR signals. These properties and others may be identified simultaneously using magnetic resonance fingerprinting (“MRF”), which is described, as one example, by D. Ma, et al., in “Magnetic Resonance Fingerprinting,”  Nature,  2013; 495 (7440): 187-192. 
     Conventional magnetic resonance imaging (“MRI”) pulse sequences include repetitive similar preparation phases, waiting phases, and acquisition phases that serially produce signals from which images can be made. The preparation phase determines when a signal can be acquired and determines the properties of the acquired signal. For example, a first pulse sequence may produce a T1-weighted signal at a first echo time (“TE”), while a second pulse sequence may produce a T2-weighted signal at a second TE. These conventional pulse sequences typically provide qualitative results where data are acquired with various weighting or contrasts that highlight a particular parameter (e.g., T1 relaxation, T2 relaxation). 
     When magnetic resonance (“MR”) images are generated, they may be viewed by a radiologist and/or surgeon who interprets the qualitative images for specific disease signatures. The radiologist may examine multiple image types (e.g., T1-weighted, T2 weighted) acquired in multiple imaging planes to make a diagnosis. The radiologist or other individual examining the qualitative images may need particular skill to be able to assess changes from session to session, from machine to machine, and from machine configuration to machine configuration. 
     Unlike conventional MRI, MRF employs a series of varied sequence blocks that simultaneously produce different signal evolutions in different resonant species (e.g., tissues) to which the radio frequency (“RF”) field is applied. The signals from different resonant tissues will, however, be different and can be distinguished using MRF. The different signals can be collected over a period of time to identify a signal evolution for the volume. Resonant species in the volume can then be characterized by comparing the signal evolution to known signal evolutions. Characterizing the resonant species may include identifying a material or tissue type, or may include identifying MR parameters associated with the resonant species. The “known” evolutions may be, for example, simulated evolutions calculated from physical principles and/or previously acquired evolutions. A large set of known evolutions may be stored in a dictionary. 
     The dictionary of signal evolutions is one of the key components of MRF. A dictionary may include signal evolutions that have been generated for different acquisition parameters from magnetic resonance signal models, such as Bloch equation-based physics simulations or that have been collected from previous acquisitions. Depending on the tissue property of interest, a dictionary may be calculated using different MRF sequences, such as the bSSFP sequence, the FISP sequence, the MRF-X sequence, or the like. The time required for generating these dictionaries varies, but can be prohibitively long, especially when many factors are included into the calculation. For example, a slice profile corrected FISP dictionary requires the simulation of multiple spin evolutions which are then summed for each time frame. Dictionary calculations that involve exchange and other complicated physics can take days to weeks to calculate. 
     There is a need for a system and method for generating a dictionary for MRF that is efficient and reduces the time required for generating the dictionary. 
     SUMMARY OF THE DISCLOSURE 
     In accordance with an embodiment, a method for creating a dictionary for a magnetic resonance fingerprinting (MRF) reconstruction includes training a semi-supervised learning system based on at least a set of MRF data and a set of control variables, generating a plurality of signal evolutions using the trained semi-supervised learning system; generating an MRF dictionary using the plurality of signal evolutions generated using the trained semi-supervised learning system and storing the MRF dictionary in a memory. 
     In accordance with another embodiment, a method for performing magnetic resonance fingerprinting includes accessing a MRF dictionary using an MRI system, the MRF dictionary generated using a semi-supervised learning system, acquiring MRF data from a tissue in region of interest in a subject using the MRI system, comparing the MRF data to the MRF dictionary to identify at least one parameter of the MRF data and generating a report indicating a value of at least one parameter of the MRF data. 
     In accordance with another embodiment, a magnetic resonance fingerprinting (MRF) system includes a magnet system configured to generate a polarizing magnetic field about at least a portion of a subject, a magnetic gradient system including a plurality of magnetic gradient coils configured to apply at least one magnetic gradient field to the polarizing magnetic field and a radio frequency (RF) system configured to apply an RF field to the subject and to receive magnetic resonance signals from the subject using a coil array. The system further includes a computer system programmed to access an MRF dictionary, the MRF dictionary generated using a semi-supervised learning system, acquire MRF data from a tissue in a region of interest in a subject, compare the MRF data to the MRF dictionary to identify at least one parameter of the MRF data and generate a report indicating a value of the at least one parameter of the MRF data. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will hereafter be described with reference to the accompanying drawings, wherein like reference numerals denote like elements. 
         FIG. 1  is a schematic diagram of an example MRI system in accordance with an embodiment; 
         FIG. 2  illustrates a method for using an MRF dictionary generated using a semi-supervised learning system in accordance with an embodiment; 
         FIG. 3  illustrates a method for generating an MRF dictionary using a semisupervised learning system in accordance with an embodiment; 
         FIG. 4  is a block diagram of an MRF generative adversarial network (GAN) for generating a MRF dictionary in accordance with an embodiment; and 
         FIGS. 5A, 5B and 5C  show example signal evolutions generated using a MRF generative adversarial network (GAN) in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Magnetic resonance fingerprinting (“MRF”) is a technique that facilitates mapping of tissue or other material properties based on random or pseudorandom measurements of the subject or object being imaged. In particular, MRF can be conceptualized as employing a series of varied “sequence blocks” that simultaneously produce different signal evolutions in different “resonant species” to which the RF field is applied. The term “resonant species,” as used herein, refers to a material, such as water, fat, bone, muscle, soft tissue, and the like, that can be made to resonate using NMR. By way of illustration, when radio frequency (“RF”) energy is applied to a volume that has both bone and muscle tissue, then both the bone and muscle tissue will produce a nuclear magnetic resonance (“NMR”) signal; however, the “bone signal” represents a first resonant species and the “muscle signal” represents a second resonant species, and thus the two signals will be different. These different signals from different species can be collected simultaneously over a period of time to collect an overall “signal evolution” for the volume. 
     The measurements obtained in MRF techniques are achieved by varying the acquisition parameters from one repetition time (“TR”) period to the next, which creates a time series of signals with varying contrast. Examples of acquisition parameters that can be varied include flip angle (“FA”), RF pulse phase, TR, echo time (“TE”), and sampling patterns, such as by modifying one or more readout encoding gradients. The acquisition parameters are varied in a random manner, pseudorandom manner, or other manner that results in signals from different materials or tissues to be spatially incoherent, temporally incoherent, or both. For example, in some instances, the acquisition parameters can be varied according to a non-random or non-pseudorandom pattern that otherwise results in signals from different materials or tissues to be spatially incoherent, temporally incoherent, or both. 
     From these measurements, which as mentioned above may be random or pseudorandom, or may contain signals from different materials or tissues that are spatially incoherent, temporally incoherent, or both, MRF processes can be designed to map any of a wide variety of parameters. Examples of such parameters that can be mapped may include, but are not limited to, longitudinal relaxation time (T 1 ), transverse relaxation time (T 2 ), main or static magnetic field map (B 0 ), and proton density (ρ). MRF is generally described in U.S. Pat. No. 8,723,518 and Published U.S. Patent Application No. 2015/0301141, each of which is incorporated herein by reference in its entirety. 
     The data acquired with MRF techniques are compared with a dictionary of signal models, or templates, that have been generated for different acquisition parameters from magnetic resonance signal models, such as Bloch equation-based physics simulations. This comparison allows estimation of the physical parameters, such as those mentioned above. As an example, the comparison of the acquired signals to a dictionary can be performed using any suitable matching or pattern recognition technique. The parameters for the tissue or other material in a given voxel are estimated to be the values that provide the best signal template matching. For instance, the comparison of the acquired data with the dictionary can result in the selection of a signal vector, which may constitute a weighted combination of signal vectors, from the dictionary that best corresponds to the observed signal evolution. The selected signal vector includes values for multiple different quantitative parameters, which can be extracted from the selected signal vector and used to generate the relevant quantitative parameter maps. 
     The stored signals and information derived from reference signal evolutions may be associated with a potentially very large data space. The data space for signal evolutions can be partially described by: 
                     SE   =       ∑     s   =   1       N   S       ⁢       ∏     i   =   1       N   A       ⁢           ⁢       ∑     j   =   1       N   RF       ⁢         R   i     ⁡     (   α   )       ⁢       R     RF   ij       ⁡     (     α   .   ϕ     )       ⁢     R   ⁡     (   G   )       ⁢       E   i     ⁡     (       T   1     ,     T   2     ,   D     )       ⁢     M   0               ;           (   1   )               
where SE is a signal evolution; N S  is a number of spins; N A  is a number of sequence blocks; N RF  is a number of RF pulses in a sequence block; α is a flip angle; ϕ is a phase angle; R i (α) is a rotation due to off resonance; R RF     ij   (α,ϕ) is a rotation due to RF differences; R(G) is a rotation due to a magnetic field gradient; T 1  is a longitudinal, or spin-lattice, relaxation time; T 2  is a transverse, or spin-spin, relaxation time; D is diffusion relaxation; E i (T 1 ,T 2 ,D) is a signal decay due to relaxation differences; and M 0  is the magnetization in the default or natural alignment to which spins align when placed in the main magnetic field.
 
     While E i (T 1 ,T 2 ,D) is provided as an example, in different situations, the decay term, E i (T 1 ,T 2 ,D), may also include additional terms, E i (T 1 ,T 2 ,D, . . . ) or may include fewer terms, such as by not including the diffusion relaxation, as E i (T 1 ,T 2 ) or E i (T 1 ,T 2 , . . . ). Also, the summation on “j” could be replace by a product on “j”. The dictionary may store signals described by,
 
 S   i   =R   i   E   i ( S   i−1 )   (2);
 
where S 0  is the default, or equilibrium, magnetization; S i  is a vector that represents the different components of magnetization, M x , M y , and M z  during the i th  acquisition block; R i  is a combination of rotational effects that occur during the i th  acquisition block; and E i  is a combination of effects that alter the amount of magnetization in the different states for the i th  acquisition block. In this situation, the signal at the i th  acquisition block is a function of the previous signal at acquisition block (i.e., the (i−1) th  acquisition block). Additionally or alternatively, the dictionary may store signals as a function of the current relaxation and rotation effects and of previous acquisitions. Additionally or alternatively, the dictionary may store signals such that voxels have multiple resonant species or spins, and the effects may be different for every spin within a voxel. Further still, the dictionary may store signals such that voxels may have multiple resonant species or spins, and the effects may be different for spins within a voxel, and thus the signal may be a function of the effects and the previous acquisition blocks.
 
     Thus, in MRF, a unique signal timecourse is generated for each pixel. This timecourse evolves based on both physiological tissue properties such as T1 or T2 as well as acquisition parameters like flip angle (FA) and repetition time (TR). This signal timecourse can, thus, be referred to as a signal evolution and each pixel can be matched to an entry in the dictionary, which is a collection of possible signal evolutions or timecourses calculated using a range of possible tissue property values and knowledge of the quantum physics that govern the signal evolution. Upon matching the measured signal evolution/timecourse to a specific dictionary entry, the tissue properties corresponding to that dictionary entry can be identified. A fundamental criterion in MRF is that spatial incoherence be maintained to help separate signals that are mixed due to undersampling. In other words, signals from various locations should differ from each other, in order to be able to separate them when aliased. 
     To achieve this process, a magnetic resonance imaging (MRI) system or nuclear magnetic resonance (NMR) system may be utilized.  FIG. 1  shows an example of an MRI system  100  that may be used to perform magnetic resonance fingerprinting. In addition, MRI system  100  may be used to implement the methods described herein. MM system  100  includes an operator workstation  102 , which may include a display  104 , one or more input devices  106  (e.g., a keyboard, a mouse), and a processor  108 . The processor  108  may include a commercially available programmable machine running a commercially available operating system. The operator workstation  102  provides an operator interface that facilitates entering scan parameters into the MRI system  100 . The operator workstation  102  may be coupled to different servers, including, for example, a pulse sequence server  110 , a data acquisition server  112 , a data processing server  114 , and a data store server  116 . The operator workstation  102  and the servers  110 ,  112 ,  114 , and  116  may be connected via a communication system  140 , which may include wired or wireless network connections. 
     The pulse sequence server  110  functions in response to instructions provided by the operator workstation  102  to operate a gradient system  118  and a radiofrequency (“RF”) system  120 . Gradient waveforms for performing a prescribed scan are produced and applied to the gradient system  118 , which then excites gradient coils in an assembly  122  to produce the magnetic field gradients G x , G y , and G z  that are used for spatially encoding magnetic resonance signals. The gradient coil assembly  122  forms part of a magnet assembly  124  that includes a polarizing magnet  126  and a whole-body RF coil  128 . 
     RF waveforms are applied by the RF system  120  to the RF coil  128 , or a separate local coil to perform the prescribed magnetic resonance pulse sequence. Responsive magnetic resonance signals detected by the RF coil  128 , or a separate local coil, are received by the RF system  120 . The responsive magnetic resonance signals may be amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server  110 . The RF system  120  includes an RF transmitter for producing a wide variety of RF pulses used in Mill pulse sequences. The RF transmitter is responsive to the prescribed scan and direction from the pulse sequence server  110  to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole-body RF coil  128  or to one or more local coils or coil arrays. 
     The RF system  120  also includes one or more RF receiver channels. An RF receiver channel includes an RF preamplifier that amplifies the magnetic resonance signal received by the coil  128  to which it is connected, and a detector that detects and digitizes the I and Q quadrature components of the received magnetic resonance signal. The magnitude of the received magnetic resonance signal may, therefore, be determined at a sampled point by the square root of the sum of the squares of the I and Q components:
 
 M= √{square root over (I 2   +Q   2 )}  (3);
 
and the phase of the received magnetic resonance signal may also be determined according to the following relationship:
 
     
       
         
           
             
               
                 
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                         ( 
                         
                           Q 
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     The pulse sequence server  110  may receive patient data from a physiological acquisition controller  130 . By way of example, the physiological acquisition controller  130  may receive signals from a number of different sensors connected to the patient, including electrocardiograph (“ECG”) signals from electrodes, or respiratory signals from a respiratory bellows or other respiratory monitoring devices. These signals may be used by the pulse sequence server  110  to synchronize, or “gate,” the performance of the scan with the subject&#39;s heart beat or respiration. 
     The pulse sequence server  110  may also connect to a scan room interface circuit  132  that receives signals from various sensors associated with the condition of the patient and the magnet system. Through the scan room interface circuit  132 , a patient positioning system  134  can receive commands to move the patient to desired positions during the scan. 
     The digitized magnetic resonance signal samples produced by the RF system  120  are received by the data acquisition server  112 . The data acquisition server  112  operates in response to instructions downloaded from the operator workstation  102  to receive the real-time magnetic resonance data and provide buffer storage, so that data is not lost by data overrun. In some scans, the data acquisition server  112  passes the acquired magnetic resonance data to the data processor server  114 . In scans that require information derived from acquired magnetic resonance data to control the further performance of the scan, the data acquisition server  112  may be programmed to produce such information and convey it to the pulse sequence server  110 . For example, during pre-scans, magnetic resonance data may be acquired and used to calibrate the pulse sequence performed by the pulse sequence server  110 . As another example, navigator signals may be acquired and used to adjust the operating parameters of the RF system  120  or the gradient system  118 , or to control the view order in which k-space is sampled. In still another example, the data acquisition server  112  may also process magnetic resonance signals used to detect the arrival of a contrast agent in a magnetic resonance angiography (“MRA”) scan. For example, the data acquisition server  112  may acquire magnetic resonance data and processes it in real-time to produce information that is used to control the scan. 
     The data processing server  114  receives magnetic resonance data from the data acquisition server  112  and processes the magnetic resonance data in accordance with instructions provided by the operator workstation  102 . Such processing may include, for example, reconstructing two-dimensional or three-dimensional images by performing a Fourier transformation of raw k-space data, performing other image reconstruction algorithms (e.g., iterative or backprojection reconstruction algorithms), applying filters to raw k-space data or to reconstructed images, generating functional magnetic resonance images, or calculating motion or flow images. 
     Images reconstructed by the data processing server  114  are conveyed back to the operator workstation  102  for storage. Real-time images may be stored in a data base memory cache, from which they may be output to operator display  102  or a display  136 . Batch mode images or selected real time images may be stored in a host database on disc storage  138 . When such images have been reconstructed and transferred to storage, the data processing server  114  may notify the data store server  116  on the operator workstation  102 . The operator workstation  102  may be used by an operator to archive the images, produce films, or send the images via a network to other facilities. 
     The MM system  100  may also include one or more networked workstations  142 . For example, a networked workstation  142  may include a display  144 , one or more input devices  146  (e.g., a keyboard, a mouse), and a processor  148 . The networked workstation  142  may be located within the same facility as the operator workstation  102 , or in a different facility, such as a different healthcare institution or clinic. 
     The networked workstation  142  may gain remote access to the data processing server  114  or data store server  116  via the communication system  140 . Accordingly, multiple networked workstations  142  may have access to the data processing server  114  and the data store server  116 . In this manner, magnetic resonance data, reconstructed images, or other data may be exchanged between the data processing server  114  or the data store server  116  and the networked workstations  142 , such that the data or images may be remotely processed by a networked workstation  142 . 
     As mentioned above, magnetic resonance fingerprinting utilizes a MRF dictionary that includes known signal evolutions. In one embodiment, the known signal evolutions may be simulated. The present disclosure provides systems and methods to create a MRF dictionary using semi-supervised learning to simulate signal evolutions. In an embodiment, the semi-supervised learning model or system is a MRF generative adversarial network (GAN). The semi-supervised learning system (e.g., MRF-GAN) may be used to generate signal evolutions for given tissue property combinations and sequence parameters. Using a semi-supervised learning system such as MRF-GAN can significantly reduce the time needed to generate a MRF dictionary, which may make it possible to generate dictionaries with tissue properties of interest on-the-fly. Using semi-supervised learning systems such as MRF-GAN may also enable the rapid calculation of dictionaries with more complex physics. 
       FIG. 2  illustrates a method for using a MRF dictionary generated using a semi-supervised learning system in accordance with an embodiment. At block  202 , a MRF dictionary is generated using a semi-supervised learning system to simulate signal evolutions. In an embodiment, the semi-supervised learning system is a MRF generative adversarial network (GAN) as described further below with respect to  FIG. 4 . The MRF dictionary may be stored in memory or data storage of, for example, an MRI system (e.g., the MRI system  100  of FIG. 1 ) or other computer system. At block  204 , the MRF dictionary is accessed. As used herein, the term “accessing” may refer to any number of activities related to retrieving or processing the MRF dictionary using, for example, MRI system  100  (shown in  FIG. 1 ), an external network, information repository, or combinations thereof. The MRI system  100  may then be used to acquire MRF data at block  206  from a tissue in a region of interest in a subject. Acquiring MRF data may include, for example, performing a pulse sequence using a series of varied sequence blocks to elicit a series of signal evolutions from a tissue in the region of interest. 
     The MRF data acquired at block  206  is stored and compared to the MRF dictionary at block  208  to match the acquired signal evolutions with signal evolutions stored in the MRF dictionary. Comparing the MRF data to the MRF dictionary may be performed in a number of ways such as, for example, using a pattern matching, template matching or other matching algorithm. In one embodiment, the inner products between the normalized measured time course of each pixel and all entries of the normalized dictionary are calculated, and the dictionary entry corresponding to the maximum value of the inner product is taken to represent the closest signal evolution to the acquired signal evolution. At block  210 , one or more parameters of the MRF data are determined based on the comparison and matching at block  208 . The parameters may include, for example, longitudinal relaxation time (T1), transverse relaxation time (T2), main or static magnetic field (B 0 ) and proton density (PD). At block  212 , a report may be generated indicating at least one of the identified parameters for the tissue in a region of interest in a subject. For example, the report may include a quantitative indication of the at least one parameter. The report may include, for example, images or maps, text or metric based reports, audio reports and the like. The report may be provided to a display (e.g., display  104 ,  136  or  144  shown in  FIG. 1 ). 
     As mentioned above with respect to block  202 , the MRF dictionary may be generated using a semi-supervised learning system to simulate signal evolutions.  FIG. 3  illustrates a method for generating a MRF dictionary using a semisupervised learning system in accordance with an embodiment. At block  302 , a set of input data is provided to the semi-supervised learning system and, at block  304 , the semi-supervised learning system is trained based on the input data. In an embodiment, the semi-supervised learning system is a MRF generative adversarial network (GAN).  FIG. 4  is a block diagram of a MRF generative adversarial network (GAN) for generating a MRF dictionary in accordance with an embodiment The MRF-GAN  400  includes a generative network (or generator)  412  and a discriminative network (or discriminator)  414 . Generator  412  and discriminator  414  are configured to receive input data  402 . Generator  412  receives input data including noise  408  and control variables  410 . Noise  408  may be random noise generated from, for example, a normal distribution. Control variables  410  may include, for example, sequence parameters and tissue properties of interest. For example, control variables  410  may include T1, T2, flip angle and repetition time. Discriminator  414  receives input data from input  402  including real (or training) data  404  and control variables  406 . The real data  404  includes real signal evolutions (either acquired or simulated), for example, from an existing MRF dictionary. In one embodiment, the real data  404  may be signal evolutions directly generated from the Bloch equations. In one example, the training data simulated from the Bloch equations contains 1000 time frames and 5970 tissue property combinations with T1 values ranging from 10 ms to 2950 ms and T2 values ranging from 2 ms to 500 ms (T1≥T2). Control variables  406  may include, for example, sequence parameters and tissue properties of interest. For example, control variables  410  may include T1, T2, flip angle and repetition time. In an embodiment, the same control variables are input into the generator  412  and discriminator  414 . 
     Generator  412  is configured to generate data that mimics real (or training) data  404  using the noise  408  and the control variables  410 . The generated data  416  is provided as an output from the generator  412 . The generated data  416  is also input to the discriminator  414 . The discriminator  414  is configured to distinguish the generated data  416  from the real data  404 . Namely, the discriminator evaluates the generated data  416  (e.g., a signal evolution generated by generator  412 ) for authenticity, i.e., the discriminator determines whether each signal evolution is receives from the generator  412  belongs to the real data  404  set. During training, (block  304  of  FIG. 3 ). The discriminator  414  takes as input one or more samples from the real data  404 . The control variables  406 , and the generated data  416  and determines whether the generated data  416  is real or fake at block  418 . The determination of whether a particular signal evolution generated by generator  412  is real or fake  418  is provided back to the generator  412  via back propagation  420  and back to the discriminator  414  via back propagation  422 . The MRF-GAN  400  is formulated as a minimax game that eventually reaches the Nash equilibrium. The generative network  412  and the discriminative network  414  play a continuous game where the generator  412  is learning to provide more and more realistic signal evolutions and the discriminator  414  is learning to get better and better at distinguishing generated data  416  from real data  404 . Training continues until the generated data  416  is indistinguishable from the real data  404 . For example, the training of the MRF-GAN  400  should continue until the generator  412  exactly reproduces the real data and the discriminator  414  is guessing at random, unable to find a difference between the generated data  416  and the real data  404 . 
     In one embodiment, the MRF-GAN  400  system is defined by Eqn. 5: 
               min     θ   g       ⁢           ⁢       min     θ   d       ⁢     [         𝔼     x   ∼     p   data         ⁢   log   ⁢           ⁢       D     θ   d       ⁡     (     x   |   y     )         +       𝔼     z   ∼     p   ⁡     (   z   )           ⁢     log   ⁡     (     1   -       D     θ   d       ⁡     (         G     θ   g       ⁡     (     z   |   y     )       |   y     )         )         +     λ   ⁢           ⁢     𝔼       x   ∼     p   data       ,     x   ∼     p   ⁡     (   x   )             ⁢            x   -       G     θ   g       ⁡     (     z   |   y     )              1         ]             
where D is the discriminator, G is the generator, x is drawn from the training fingerprints simulated from Bloch equations, y is the control variable containing the corresponding sequence parameters and tissue property combination, and z is drawn from normal distribution. The minimax optimization problem in EQN 1 may be solved by alternating between:
 
                       max     θ   d       ⁢     [         𝔼     x   ∼     p   data         ⁢   log   ⁢           ⁢       D     θ   d       ⁡     (     x   |   y     )         +       𝔼     x   ∼     p   ⁡     (   z   )           ⁢     log   ⁡     (     1   -       D     θ   d       ⁡     (         G     θ   g       ⁡     (     z   |   y     )       |   y     )         )           ]       ⁢     
     ⁢           ⁢   and           Eqn   .           ⁢   6                 max     θ   g       ⁢     [         𝔼     z   ∼     p   ⁡     (   z   )           ⁢   log   ⁢           ⁢       D     θ   d       ⁡     (         G     θ   z       ⁡     (     z   |   y     )       |   y     )         -     λ   ⁢           ⁢     𝔼       x   ∼     p   data       ,     z   ∼     p   ⁡     (   z   )             ⁢            x   -       G     θ   g       ⁡     (     z   |   y     )              1         ]             Eqn   .           ⁢   7               
In an embodiment, the generative network  412  and the discriminative network  414  are each built using 4 layers, with each hidden layer containing 128 neurons and followed by a rectified linear unit. The hyperbolic tangent function and the sigmoid function may be used as the activation functions for the output layers of the generative network and the discriminative network respectively.
 
     Returning to  FIG. 3 , once the semi-supervised learning system (e.g., MRF-GAN  400  shown in  FIG. 4 ) is trained, the semi-supervised learning system may be used to generate signal evolutions at block  306 . For example, MRF-GAN  400  shown in FIG,  4 , once trained, may be used to simulate signal evolutions that are indistinguishable from the real data.  FIGS. 5 a -5 c    show example signal evolutions generated using a generative adversarial network (MRF-GAN) in accordance with an embodiment.  FIG. 5 a    shows a sample white matter MRF-GAN signal evolution (or fingerprint) with T1=950 ms and T2=40 ms.  FIG. 5 b    shows a sample gray matter signal evolution (or fingerprint) generated by the MRF-GAN system with T1=1500 ms and T2=60 ms.  FIG. 5 c    shows a sample CSF signal evolution (or fingerprint) generated by the MRF-GAN system with T1=2950 ms and T2=500 ms. Returning to  FIG. 3 , at block  308 , a MRF dictionary may be generated using the signal evolutions generated by the semisupervised learning system at block  306 . In an example using the MRF-GAN system, after training of the MRF-GAN, an MRF dictionary of size 1000×5970 was generated in only 7 seconds. This is a significant reduction in time as opposed to a typical 2-hour generation of, for example, an MSF-FISP dictionary. At block  310 , the MRF dictionary may be stored in memory or data storage of, for example, an MRI system (e.g., the MRI system  100  of  FIG. 1 ) or other computer system. 
     In one embodiment, the MRF-GAN approach described herein is robust enough to generate accurate fine MRF dictionaries using the MRF-GAN system trained from a coarse dictionary. In this embodiment, the MRF-GAN is first trained using, a coarse MRF dictionary as the real (or training) data. For example, the coarse MRF dictionary may be a coarse MRF-FISP dictionary that contains 1000 time frames and 297 tissue property combinations with T1 values ranging from 10 ms to 2950 ms and T2 values ranging from 2 ms to 500 ms. A much finer MRF dictionary containing, for example, 106160 tissue property combinations may be generated using the MRF-GAN trained using the coarse MRF dictionary by refining the input T1/T2 combinations. This makes it feasible to generate on-the-fly new MRF fingerprints with the tissue property of interest as needed. It also provides the possibility to significantly reduce the time needed for large scale dictionary generation. 
     Computer-executable instructions for generating a magnetic resonance fingerprinting dictionary using semi-supervised learning according to the above-described methods may be stored on a form of computer readable media. Computer readable media includes volatile and nonvolatile, removable, and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Computer readable media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), electrically erasable programmable ROM (EEPROM), flash memory or other memory technology, compact disk ROM (CD-ROM), digital volatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired instructions and which may be accessed by a system (e.g., a computer), including by internet or other computer network form of access. 
     The present invention has been described in terms of one or more preferred embodiments, and it should be appreciated that many equivalents, alternatives, variations, and modifications, aside from those expressly states, are possible and within the scope of the invention.