Method and system for image reconstruction for magnetic resonance imaging

Abstract

A method and system for reconstructing a magnetic resonance (MR) image, the method comprising the steps of: receiving an undersampled MR image transformed from undersampled k-space data; classifying the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​by using a neural network; and generating a reconstructed MR image based on the classified intensity quantization value for each pixel in the undersampled MR image.

Description

Technical Field

[0001] The present invention generally relates to a method and system for image reconstruction in medical imaging, in particular magnetic resonance imaging (MRI). Background Art

[0002] Magnetic resonance imaging (MRI) is the preferred imaging modality for soft tissue imaging due to its excellent soft tissue contrast. However, compared to other medical imaging modalities such as CT or ultrasound, MRI scan times are often longer.

[0003] One way to achieve faster MRI scans is to reduce k-space data by undersampling k-space. The undersampled k-space MR data needs to be reconstructed into MR images.

[0004] One method of reconstructing an MR image from undersampled MR data is parallel imaging, which uses multiple signal receiver coils located at different spatial locations around the patient. Each receiver coil receives the same signal, but with a different sensitivity modulation. The spatial sensitivity information of the receiver coils provides slightly different measurements of the same signal. Given a priori known sensitivity information for the receiver coils, an MR image can be reconstructed from undersampled data collected from a set of receiver coils.

[0005] Another approach to reconstructing MR images from undersampled MR data involves compressed sensing. This technique exploits the fact that MR images can be sparsely represented in some domains (such as wavelets or total signal variance). Compressed sensing uses nonlinear iterative reconstruction to recover a sparse representation of the image from the undersampled data. However, the iterative algorithms used in compressed sensing can be time consuming and may require significant computing power. Further, the speedup achieved by compressed sensing techniques depends on the inherent sparsity of the image.

[0006] It is hoped that this will solve the above or at least provide a useful alternative. Summary of the invention

[0007] According to one aspect, the present invention provides a method for reconstructing a magnetic resonance (MR) image, the method comprising the following steps:

[0008] receiving an undersampled MR image transformed from undersampled k-space data;

[0009] classifying the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​by using a neural network; and

[0010] A reconstructed MR image is generated based on the quantized value of the classified intensity for each pixel in the undersampled MR image.

[0011] According to a second aspect, the present invention provides a system for reconstructing a magnetic resonance (MR) image, the system comprising at least one processor, the at least one processor being configured to:

[0012] receiving an undersampled MR image transformed from undersampled k-space data;

[0013] classifying the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​by using a neural network; and

[0014] A reconstructed MR image is generated based on the quantized value of the classified intensity for each pixel in the undersampled MR image.

[0015] According to a third aspect, the present invention provides a method for reconstructing a medical image, the method comprising the following steps:

[0016] receiving an undersampled medical image;

[0017] classifying the intensity of each pixel in the undersampled medical image into one of a plurality of predetermined intensity quantization values ​​by using a neural network; and

[0018] A reconstructed medical image is generated based on the quantized value of the classified intensity for each pixel in the undersampled medical image.

[0019] According to a fourth aspect, the present invention provides a system for reconstructing a medical image, the system comprising at least one processor, the at least one processor being configured to:

[0020] receiving an undersampled medical image;

[0021] classifying the intensity of each pixel in the undersampled medical image into one of a plurality of predetermined intensity quantization values ​​by using a neural network; and

[0022] A reconstructed medical image is generated based on the quantized value of the classified intensity for each pixel in the undersampled medical image. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Embodiments of the invention are described hereinafter, by way of example only, with reference to the accompanying drawings, in which:

[0024] Figure 1 An example of a system for MR image reconstruction is shown;

[0025] Figure 2 An exemplary architecture of a convolutional neural network for MR image reconstruction is shown;

[0026] Figure 3is a schematic diagram showing the training of a deep learning model for MR image reconstruction;

[0027] Figure 4 shows the steps performed by a processor during MR image reconstruction;

[0028] Figure 5 The results of applying image reconstruction to undersampled MR data are shown;

[0029] Figure 6 quantization showing the inherent error due to quantization in a classification network; and

[0030] Figure 7 Another exemplary architecture of a convolutional neural network for MR image reconstruction is shown. DETAILED DESCRIPTION

[0031] Embodiments provide a method and system for reconstructing an MR image from undersampled MR data. The method and system use a machine learning-based method to reconstruct an MR image from undersampled MR data, and use simulated undersampled MR data to train a convolutional neural network for image reconstruction.

[0032] The convolutional neural network is trained to classify each pixel in an undersampled MR image (ie, an MR image transformed from undersampled k-space data) as a quantized value of intensity that is one of a plurality of predetermined quantized values.

[0033] In this way, the image reconstruction task is converted into a pixel classification task. This conversion is conducive to accurate image reconstruction.

[0034] Compared to the intensity of each pixel in the undersampled MR image, the quantized values ​​in the reconstructed image have a smaller bit depth. This reduces the use of memory space and computational complexity.

[0035] For example, the intensity of each pixel in the undersampled image can be represented by a floating point number (e.g., a single precision floating point number typically occupying 32 bits, or a double precision floating point number typically occupying 64 bits), and the quantized value can be an 8-bit number, so that the intensity of each pixel is classified into one of 256 different categories. Alternatively, the reconstructed image can be represented using more bits per pixel at the expense of memory usage and computational complexity.

[0036] The method and system can significantly reduce MR scan time without compromising image quality. The method and system do not use an iterative reconstruction algorithm, thereby saving computational costs. Further, the image quality achieved using the described method and system has a significant SNR improvement compared to compressed sensing.

[0037] The described methods and systems may be used to supplement parallel imaging image reconstruction techniques and thereby improve the performance of MR parallel imaging applications.

[0038] General structure

[0039] Figure 1 An example of a system 100 for reconstructing undersampled MR images is shown in FIG.

[0040] In this example, the system 100 also includes components of an MRI machine for performing the functions of an MRI scanner (eg, performing MR scans and acquiring MRI images).

[0041] like Figure 1 As shown, system 100 includes superconducting or resistive main magnet coils 102 for generating a substantially uniform, temporally constant main magnetic field B0 along a z-axis through an examination volume.

[0042] The system 100 also includes a set of shim coils 120. The current flowing through each shim coil 120 is controllable to minimize B0 deviation within the examination volume.

[0043] A gradient pulse amplifier 103 applies current pulses along the x-axis, y-axis, and z-axis of the examination volume to a selected one of whole-body gradient coils 104, 105, and 106. A digital RF frequency transmitter 107 transmits RF pulses or pulse packets to a subject RF coil 109 via a transmit / receive switch 108 to transmit RF pulses into the examination volume. The RF pulses are used to saturate, excite resonance, reverse magnetization, refocus resonance, or manipulate resonance, and select a portion of a patient's body 200 positioned in the examination volume.

[0044] In order to generate an MR image of the patient's body 200 by means of parallel imaging, a set of local array RF coils 111, 112, 113 for receiving MR signals are placed adjacent to a region selected for imaging.

[0045] MR signals induced by the subject coil RF transmissions are picked up by the array RF coils 111 , 112 , 113 and / or by the subject RF coil 109 and subsequently demodulated via the transmit / receive switch 108 by a receiver 114 , which preferably includes a preamplifier.

[0046] A controller 115 (eg, in the form of a mainframe) controls the shim coils 120, the gradient pulse amplifiers 103, and the transmitter 107 to generate an MR imaging sequence, such as a fast field echo (FFE) sequence.

[0047] For the selected sequence, the receiver 114 receives a single or multiple MR data lines following each RF excitation pulse.

[0048] The received analog signal for each MR data line is then converted to a digital format by the data acquisition module 116. In some alternative embodiments, the data acquisition module 116 may be formed as a separate device rather than as part of the system 100.

[0049] The digital raw image data is then sent to a processor 117, which transforms the digital raw image data in k-space into an MR image representation by applying a suitable transformation algorithm (e.g., Fourier transform). For example, the transformed MR image may represent a planar slice through the patient, an array of parallel planar slices, a three-dimensional volume, etc.

[0050] In order to reduce the MRI scan time, k-space undersampling is performed. The reduced number of k-space points is collected and compared with the full number of k-space points required by the Nyquist criterion. This results in undersampling artifacts in the transformed MR image (also referred to as an "undersampled MR image") output by the processor 117.

[0051] To remove or reduce under-sampling artifacts, the under-sampled MR image generated by the processor 117 is subsequently processed by the image reconstruction module 130 , which generates a reconstructed MR image based on the under-sampled MR image.

[0052] The reconstructed MR image output by the image reconstruction module 130 is then stored in a data storage area of ​​the module 130, where the reconstructed MR image can be accessed for converting a slice, projection or other portion of the image representation into an appropriate format for visualization, for example, via a video monitor 118 (which provides a readable display of the reconstructed MR image).

[0053] The image reconstruction module 130 includes a trained deep learning model for image reconstruction. Preferably, the image reconstruction module 130 is implemented by machine executable computer program instructions embedded in and executed by the processor 117. In addition to being implemented by embedded firmware, the image reconstruction module 130 can also be implemented by dedicated hardware (such as ASIC or FPGA). Preferably, the processor 117 and the module 130 are implemented by a GPU cluster.

[0054] Deep Learning Models

[0055] In this embodiment, the deep learning model of the image reconstruction module 130 is a convolutional neural network (CNN). Figure 2 An exemplary architecture of a CNN is shown.

[0056] The CNN architecture is designed and trained for image reconstruction. The input to the network is a 256×256 undersampled MR image, the intensity of each pixel in the 256×256 undersampled MR image is a floating point value (e.g., a single-precision floating point number typically occupying 32 bits, or a double-precision floating point number typically occupying 64 bits), and the output is an 8-bit quantized reconstructed image (each pixel is represented by an 8-bit number). In this way, CNN transforms the image reconstruction task into a pixel classification task.

[0057] Preferably, the pixel intensity is the grayscale intensity of the pixel. However, in some alternative embodiments, the pixel intensity may be the intensity of the pixel in one or more appropriate color channels.

[0058] like Figure 2 As shown, the CNN in this embodiment is an encoder-decoder CNN, which has an encoder network (left side) and a decoder network (right side), followed by a pixel intensity classification layer.

[0059] The encoder network consists of a contracting path with a series of convolutional and pooling layers. More specifically, the contracting path consists of repeatedly applying three 3×3 convolutions (stride 2, padding 1). In each level, the 3×3 convolution is followed by a batch normalization (BN) operation and a rectified linear unit (ReLU), as well as a 3×3 max pooling operation for downsampling. This downsampling halves the height and width dimensions at each consecutive level. Figure 2 The number at the top of each block in shows the resolution of the data, and the number at the bottom of each block shows the number of filtered outputs (the filtered outputs may also be referred to as “feature maps”).

[0060] The decoder network consists of an expansion path with a series of 2×2 upsampling operations (stride 2) of the feature maps, each followed by a 3×3 convolution with stride 1, a batch normalization operation, and a rectified linear unit (ReLU). Each upsampling operation increases the resolution of the corresponding feature map.

[0061] In addition to the dilation paths, the decoder network also includes multiple connection paths that connect the upsampled feature maps with the corresponding feature maps passed directly from the encoder network.

[0062] The last layer of the CNN is a classification layer that uses a 1×1 convolution with a stride of 1. The classification layer treats the output as a quantized 8-bit image and predicts the probability of each pixel being in one of 256 different classes. In this way, the classification layer predicts the quantized image intensity level of the reconstructed image. During the training phase, a multinomial logistic loss function (also known as "cross entropy loss") is used to evaluate the classification performance of the CNN. Alternatively, any other suitable classification loss function can be used as the loss function in training the CNN, such as the Kullback-Leibler (KL) divergence loss.

[0063] The choice of loss function is a major difference between classification and other types of machine learning tasks, such as regression. The loss function chosen for a classification task reflects a measure of the correctness of the classification result, while a regression loss function usually measures the residual of the result. This is because the goal of a classification task is to minimize the risk of misclassification, while the goal of a regression task is usually to minimize the residual of the regression model.

[0064] In conclusion, Figure 2 The encoder-decoder CNN shown in consists of 5 levels (each level consists of Figure 2 ). Alternatively, in some other embodiments, the encoder-decoder CNN may include any suitable number of levels, depending on the input image size. At the last level, the size of the feature map should be larger than the size of the convolution kernel. For example, for an input image of 256×256 in the above example, the CNN may include up to 7 levels to allow the use of a 3×3 convolution kernel. In the example where the CNN has 7 levels, at level 7, the spatial size of the feature map is 4×4.

[0065] Further, in some other embodiments, the encoder-decoder CNN may have Figure 2 Any suitable alternative architecture different from the architecture shown in . For example, one or more characteristics of the CNN architecture (such as the number of CNN layers, convolution kernel size and / or stride) can be modified. In addition, the CNN can have one or more regularization layers (such as, dropout layers).

[0066] Further, in some other embodiments, the CNN used in the image reconstruction module 130 may not be an encoder-decoder CNN, but any other suitable type of image-to-image mapping CNN.

[0067] Training of deep learning models

[0068] Figure 3 is a schematic diagram illustrating the training of a deep learning model used in the image reconstruction module 130 .

[0069] To train the deep learning model (304), an undersampled MR image (i.e., an image with undersampling artifacts as shown by box (302)) is generated and fed to the deep learning model (304).

[0070] Using the image with undersampling artifacts (302), the deep learning model generates corresponding reconstructed MR images (306). For each reconstructed image, the error is calculated using a loss function (308) based on the corresponding reference MR image (310) that does not contain the undersampling artifacts. As described above, for Figure 2 The error of the CNN is calculated using a multinomial logistic loss function or any other suitable classification loss function. The error is used to adjust the parameters of the deep learning model. The image reconstruction and adjustment process is repeated until the desired reconstruction performance is achieved. The adjustment of parameters can be performed by executing an existing CNN training algorithm such as stochastic gradient descent (SGD), AdaGrad, AdaDelta, RMSProp or other suitable gradient descent optimizer.

[0071] like Figure 3 As shown by the dashed line in , an image (302) with undersampling artifacts can be generated by undersampling the reference k-space data (314) to generate undersampled k-space data (312), and then transforming the undersampled k-space data (312) into an MR image. Similarly, the reference k-space data (314) is also used to generate a reference image (310) without undersampling artifacts.

[0072] like Figure 3 The training of the deep learning model shown in can be performed on external hardware (e.g., a separate graphics processing unit (GPU)) separate from the system 100. After training, the deep learning model is embedded as the image reconstruction module 130 in the system 100.

[0073] Figure 4 An image reconstruction process 400 implemented by the image reconstruction module 130 of the system 100 is shown.

[0074] At step 410 , the image reconstruction module 130 receives an undersampled MR image transformed from undersampled k-space data.

[0075] At step 420 , the image reconstruction module 130 classifies the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​by using a neural network (ie, a trained CNN).

[0076] At step 430 , the image reconstruction module 130 generates a reconstructed MR image based on the quantized value of the intensity classified for each pixel in the undersampled MR image.

[0077] Example

[0078] MPRAGE images from 43 subjects were used for training, and MPRAGE images from 10 subjects were used for testing. Reference images (also called "label images") for the classification network were represented as 8-bit unsigned integers.

[0079] The k-space data were pseudo-randomly undersampled by a factor of 3.2 in the phase encoding direction, and the MR images transformed from the undersampled data were used as input to the network.

[0080] The CNN is trained on 2D slices using the stochastic gradient descent algorithm from the CAFFE deep learning library.

[0081] Figure 5 The results of applying image reconstruction to the undersampled data are shown for two test cases.

[0082] Figure 5 Column (b) shows the results of using the above classification CNN, where the loss function used is a multinomial logistic loss. The network predicts the probability of each pixel being in one of 256 different categories. The output is an image represented by an 8-bit unsigned integer, which is converted into an image represented by a floating point by simply scaling between 0 and 1. As shown, the undersampling artifacts in the output image are effectively reduced compared to the input image.

[0083] In contrast, Figure 5 Column (c) shows the results of applying image reconstruction to the same test case data using a regression network, where the loss function used is the mean squared loss. The network predicts a floating point representation of the reconstructed image.

[0084] As shown, the reconstructed image in column (b) generated by using the classification network contains fewer undersampling artifacts than the reconstructed image in column (c) generated by using the regression network.

[0085] For comparison purposes, the mean square error of the images reconstructed from the classification network was calculated and the result was six times lower than that of the images reconstructed from the regression network, which shows the effectiveness of the described classification CNN model in image reconstruction for MRI.

[0086] For regression networks, the source of error is prediction error caused by inaccurate learning of the input-output mapping. In contrast, errors in classification networks arise from two sources, including: (i) prediction error due to the network, and (ii) a second error due to the fixed-point representation as quantization error. Figure 6 Quantization of the inherent error due to quantization in the classification network is shown.

[0087] Figure 6 (a) shows a double precision image scaled between [0, 1]. Figure 6 (b) shows the unsigned 8-bit image representation generated from (a). This step introduces quantization errors due to the fixed-point conversion. Figure 6 (c) shows the same image in (b) converted to double precision by scaling. Figure 6 (d) shows the quantization error image generated by subtracting the original image of (a) and the quantized version of (c) (scaled 300× for viewing). Figure 6 (d) Obviously, the quantization error (MSE: 1.28e-6) is significantly lower than the overall error (MSE: 6.7e-5), showing that quantization has minimal impact on the overall error. In some embodiments, the quantization error can be further reduced by using more bits to represent the target image at the expense of memory usage and computational complexity.

[0088] Higher bit-precision pixel classification

[0089] exist Figure 2 In the example shown, the classification layer treats the output as a quantized 8-bit image (in other words, the quantized value of the intensity of each pixel is an 8-bit number) and predicts the probability of each pixel being in one of the 256 different classes.

[0090] Alternatively, the reconstructed image can be represented using more bits per pixel. However, the memory requirements of the neural network increase exponentially with the bit depth of the quantized values. n_bit The dynamic range is [0, 2 n -1]. To predict the probability of each possible pixel intensity, using the pixel classification method described above requires 2 n The number of channels may be undesirably large, such as 65536 channels for an image with 16-bit depth. A large number of channels may be difficult to implement due to physical memory limitations of computer systems, and it may be difficult to generalize the model due to overfitting from the increased number of parameters.

[0091] In order to reduce the computational complexity and memory usage required for classification networks with higher bit precision, a divide-and-conquer approach is used. Specifically, for higher bit depth prediction, the n-bit integer N representing the pixel intensity n_bit The linear combination of two n / 2-digit numbers a0 and a1 is:

[0092]

[0093] For example, a 16-bit integer can be represented as:

[0094]

[0095] As described in (1), both a0 and a1 are n / 2-digit numbers, so, Figure 2 The convolutional neural network in can be modified to predict both a0 and a1, and then (1) can be used to calculate the n-bit value N n_bit This approach allows convolutional neural networks to be used to reconstruct higher-bit images without significantly increasing the number of parameters or computational complexity. For example, the number of channels required to predict a 16-bit image in the output layer is reduced from 65536 to only 256 using this approach.

[0096] Figure 7 An exemplary network architecture for reconstructing an image with 16-bit precision pixel intensity values ​​using a pixel classification approach is shown. Figure 7 As shown, the convolutional neural network has two outputs a0 and a1. Both a0 and a1 are 256 channel outputs that predict the probability distribution of two 8-bit numbers. Both probability distributions are used to calculate the pixel intensity value using (2). Figure 7 The convolutional neural network in can have Figure 2 The same architecture as the example shown in , but without the final classification layer. In other words, Figure 2 The last classification layer in (which uses a 1×1 convolution with stride 1) is Figure 7 The two classification paths in are used to output a0 and a1 respectively.

[0097] Similarly, this divide-and-conquer approach can be used to divide the predicted intensity value of each pixel into multiple groups of integers α0, a1, ... a n , to reconstruct an image with further higher bit precision (e.g., 32 bits, 64 bits, or more).

[0098] thus, Figure 4 In the image reconstruction process 400 shown in FIG. 4 , the classification step 420 may include:

[0099] converting the quantized values ​​of a plurality of predetermined intensities into a plurality of sets of values ​​having a smaller bit depth than the quantized values ​​of the predetermined intensities;

[0100] For each group, classifying the intensity of each pixel in the undersampled MR image as one of the values ​​in the group by using a neural network; and

[0101] A quantized value of the classified intensity of each pixel is generated based on the classified values ​​in each group.

[0102] Each of the predetermined quantized values ​​may include a first group of bits and a second group of bits. Accordingly, the plurality of groups of values ​​may include at least:

[0103] a first set of values ​​representing the value of the first set of bits of the predetermined quantized value; and

[0104] The second group of values ​​represents the value of the second group of bits of the predetermined quantized value.

[0105] As shown in the above examples, the first group of bits (eg, a0) may be bits of a higher order predetermined quantized value than the second group of bits (eg, a1).

[0106] By developing and utilizing deep learning models for image reconstruction, the described methods and systems significantly reduce MR scan time without compromising image quality.

[0107] Since the method and system do not use an iterative reconstruction algorithm, the computational cost can be reduced and a higher SNR can be achieved compared to compressed sensing techniques.

[0108] The method and system may be used to supplement existing MR image reconstruction techniques, such as parallel imaging, and the method and system may improve the performance of MR parallel imaging applications.

[0109] Further, the use of the method is not limited to MR images, but may also include image reconstruction for other medical imaging modalities.

[0110] For example, the method can be used to reconstruct images from data collected in an undersampled computed tomography (CT) scan. Although scan time reduction is not a major issue in CT, minimizing radiation exposure to the patient is very important. Using this method, a smaller number of angular projections will be required to reconstruct a CT image. This will significantly reduce the radiation dose to the patient, for example, by a factor of three.

[0111] Further, as described above, the deep learning model is not limited to the encoder-decoder CNN or specific architecture in the described embodiments, but may include any other suitable type of CNN with any suitable architecture.

[0112] Reference in this specification to any previous publication (or information derived therefrom) or any known matter is not and should not be taken as an acknowledgment or admission or any form of suggestion that the previous publication (or information derived therefrom) or known matter forms part of the common general knowledge in the field of endeavor to which this specification relates.

[0113] Many modifications will be apparent to those skilled in the art without departing from the scope of the invention as hereinbefore described with reference to the accompanying drawings.

Claims

1. A method for reconstructing a magnetic resonance (MR) image, the method comprising the following steps: receiving an undersampled MR image transformed from undersampled k-space data; classifying the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​by using a neural network to reduce undersampling artifacts; as well as generating a reconstructed MR image based on the quantized value of the intensity classified for each pixel in the undersampled MR image; Wherein, classifying the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​comprises: converting the plurality of predetermined intensity quantized values ​​into a plurality of sets of values ​​having a smaller bit depth than the predetermined intensity quantized values; For each group, classifying the intensity of each pixel in the undersampled MR image into one of the values ​​in the group by using the neural network; and A quantized value of the classified intensity of each pixel is generated based on the classified values ​​in each group.

2. The method according to claim 1, wherein: The neural network is a convolutional neural network (CNN).

3. The method according to claim 2, wherein: The CNN is an encoder-decoder CNN, and the encoder-decoder CNN includes an encoder network and a decoder network.

4. The method according to claim 3, wherein: The encoder network includes a series of convolutional layers and pooling layers, each pooling layer is after the corresponding convolutional layer.

5. The method according to claim 3, wherein: The decoder network includes a series of upsampling layers and convolutional layers, with each convolutional layer following a corresponding upsampling layer.

6. The method according to claim 5, wherein: The decoder network concatenates the output of each upsampling layer with the corresponding feature map generated by the encoder network.

7. The method according to claim 3, wherein: The CNN also includes a pixel intensity classification layer, which follows the decoder network.

8. The method according to claim 1, wherein: The neural network is trained by using a multinomial logistic loss function.

9. The method according to claim 1, wherein: Each of the predetermined intensity quantized values ​​has a smaller bit depth than the intensity of each pixel in the undersampled MR image.

10. The method according to claim 1, further comprising: The undersampled k-space data is transformed into the undersampled MR image.

11. The method according to claim 10, further comprising: receiving raw MR signals generated during a magnetic resonance imaging (MRI) scan; as well as The undersampled k-space data is generated based on the raw MR signals.

12. The method of claim 1, wherein: Each of the predetermined quantized values ​​of strength includes a first set of bits and a second set of bits; as well as The multiple sets of values ​​include at least: a first set of values ​​representing values ​​of the first set of bits of the quantized value of the predetermined strength; as well as A second set of values, said second set of values ​​representing values ​​of said second set of bits of said predetermined strength quantized value.

13. The method according to claim 12, wherein: The first group of bits are bits of the quantized value of the predetermined strength of a higher order than the second group of bits.

14. A system for reconstructing a magnetic resonance (MR) image, the system comprising at least one processor, the at least one processor being configured to: receiving an undersampled MR image transformed from undersampled k-space data; classifying the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​by using a neural network to reduce undersampling artifacts; as well as generating a reconstructed MR image based on the quantized value of the intensity classified for each pixel in the undersampled MR image; in, Classifying the intensity of each pixel in the undersampled MR image into one of a plurality of predetermined intensity quantization values ​​comprises: converting the plurality of predetermined intensity quantized values ​​into a plurality of sets of values ​​having a smaller bit depth than the predetermined intensity quantized values; For each group, classifying the intensity of each pixel in the undersampled MR image into one of the values ​​in the group by using the neural network; and A quantized value of the classified intensity of each pixel is generated based on the classified values ​​in each group.

15. The system of claim 14, wherein: The system is an MR scanner.

16. A method for reconstructing a medical image, the method comprising the following steps: receiving an undersampled medical image; classifying the intensity of each pixel in the undersampled medical image into one of a plurality of predetermined intensity quantization values ​​by using a neural network to reduce undersampling artifacts; as well as generating a reconstructed medical image based on the quantized value of the intensity classified for each pixel in the undersampled medical image; Wherein, classifying the intensity of each pixel in the undersampled medical image into one of a plurality of predetermined intensity quantization values ​​comprises: converting the plurality of predetermined intensity quantized values ​​into a plurality of sets of values ​​having a smaller bit depth than the predetermined intensity quantized values; For each group, classifying the intensity of each pixel in the undersampled medical image into one of the values ​​in the group by using the neural network; and A quantized value of the classified intensity of each pixel is generated based on the classified values ​​in each group.

17. A system for reconstructing a medical image, the system comprising at least one processor, the at least one processor being configured to: receiving an undersampled medical image; classifying the intensity of each pixel in the undersampled medical image into one of a plurality of predetermined intensity quantization values ​​by using a neural network to reduce undersampling artifacts; as well as generating a reconstructed medical image based on the quantized value of the intensity classified for each pixel in the undersampled medical image; in, Classifying the intensity of each pixel in the undersampled medical image into one of a plurality of predetermined intensity quantization values ​​comprises: converting the plurality of predetermined intensity quantized values ​​into a plurality of sets of values ​​having a smaller bit depth than the predetermined intensity quantized values; For each group, classifying the intensity of each pixel in the undersampled medical image into one of the values ​​in the group by using the neural network; and A quantized value of the classified intensity of each pixel is generated based on the classified values ​​in each group.

Images