Deep learning system and method for removing truncation artifacts in magnetic resonance images

Abstract

The present invention is entitled "Deep Learning System and Method for Removing Truncation Artifacts in Magnetic Resonance Images". The present disclosure provides a computer-implemented method for removing truncation artifacts from magnetic resonance (MR) images. The method includes receiving a coarse image, the coarse image being based on partial k-space data from a portion of k-space that is asymmetrically truncated in at least one k-space dimension. The method also includes analyzing the coarse image using a neural network model trained with a pair of original images and a corrupted image. The corrupted image is based on the partial k-space data of the portion of k-space that is truncated with one or more partial sampling patterns. The original image is based on complete k-space data corresponding to the partial k-space data of the corrupted image, and a target output image of the neural network model is the original image. The method also includes deriving an improved image of the coarse image based on the analysis, wherein the derived improved image includes reduced truncation artifacts and increased high spatial frequency data.

Description

Background Art

[0001] The field of the present disclosure relates generally to systems and methods for removing truncation artifacts, and more particularly to systems and methods for removing truncation artifacts in medical images using a neural network model.

[0002] Magnetic resonance imaging (MRI) has proven useful in the diagnosis of many diseases. MRI provides detailed images of soft tissue, abnormal tissue (such as tumors), and other structures that cannot be easily imaged by other imaging modalities such as computed tomography (CT). In addition, MRI operates without exposing the patient to the ionizing radiation experienced in modalities such as CT and X-rays.

[0003] In MR imaging, partial k-space is often sampled in order to increase acquisition efficiency and / or suppress artifacts. Reconstructing a partially sampled k-space dataset results in images contaminated by truncation artifacts in the form of both blurring and characteristic oscillations that severely reduce the diagnostic value of MR images. Summary of the Invention

[0004] In one aspect, a computer-implemented method for removing truncation artifacts from a magnetic resonance (MR) image is provided. The method includes receiving a crude image based on partial k-space data from a portion of k-space that is asymmetrically truncated in at least one k-space dimension at a k-space location corresponding to a high spatial frequency. The method also includes analyzing the crude image using a neural network model. The neural network model is trained using a pair of an original image and a corrupted image. The corrupted image is based on partial k-space data from a portion of k-space that is truncated with one or more partial sampling patterns at a k-space location corresponding to a high spatial frequency, the one or more partial sampling patterns including asymmetric truncation in at least one k-space dimension. The original image is based on full k-space data corresponding to the partial k-space data of the corrupted image, and a target output image of the neural network model is the original image. The method also includes deriving an improved image of the crude image based on the analysis, wherein the derived improved image includes reduced truncation artifacts and increased high spatial frequency data compared to the crude image; and outputting the improved image.

[0005] In another aspect, a computer-implemented method for removing truncation artifacts in a magnetic resonance (MR) image is provided. The method includes receiving a pair of original images and a corrupted image. The corrupted image is based on partial k-space data from a portion of k-space truncated at a k-space location corresponding to a high spatial frequency with one or more partial sampling patterns, the one or more partial sampling patterns including an asymmetric truncation in at least one k-space dimension. The original image is based on full k-space data corresponding to the partial k-space data of the corrupted image. The method also includes training a neural network model using the pair of original and corrupted images by inputting the corrupted image into the neural network model; setting the original image as a target output for the neural network model; analyzing the corrupted image using the neural network model; comparing the output of the neural network model to the target output; and adjusting the neural network model based on the comparison. The trained neural network model is configured to reduce truncation artifacts in the corrupted image and increase high spatial frequency data in the corrupted image.

[0006] In one aspect, a truncation artifact reduction system is provided. The system includes a truncation artifact reduction computational device comprising at least one processor in communication with at least one memory device. The at least one processor is programmed to receive a coarse image based on partial k-space data from a partial k-space that is asymmetrically truncated in at least one k-space dimension at a k-space location corresponding to a high spatial frequency. The at least one processor is further programmed to analyze the coarse image using a neural network model. The neural network model is trained using a pair of an original image and a corrupted image. The corrupted image is based on partial k-space data from a partial k-space that is truncated in one or more partial sampling patterns at a k-space location corresponding to a high spatial frequency, the one or more partial sampling patterns including asymmetric truncation in at least one k-space dimension. The original image is based on full k-space data corresponding to the partial k-space data of the corrupted image, and a target output image of the neural network model is the original image. The at least one processor is further programmed to derive an improved image of the coarse image based on the analysis, wherein the derived improved image includes reduced truncation artifacts and increased high spatial frequency data compared to the coarse image; and output the improved image. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 is a schematic diagram of an exemplary magnetic resonance imaging (MRI) system.

[0008] Figure 2A is an exemplary truncation artifact reduction system.

[0009] Figure 2B is a flow chart of an exemplary method for reducing truncation artifacts.

[0010] Figure 2CIt is a schematic diagram of partial k-space sampling.

[0011] Figure 3A is used for Figure 2A An exemplary neural network model of the system shown.

[0012] Figure 3B is used for Figure 2A Another exemplary neural network model of the system is shown.

[0013] Figure 3C is used for Figure 2A Yet another exemplary neural network model of the system is shown.

[0014] Figure 3D is used for Figure 2A Yet another exemplary neural network model of the system is shown.

[0015] Figure 4A is the comparison of the complex image and the corresponding conjugate reflection image.

[0016] Figure 4B A schematic diagram of conjugate reflection is shown.

[0017] Figure 4C is the zero-filled reconstructed image and the image from the input with and without conjugate reflection Figure 2A Comparison of images output by the neural network models shown.

[0018] Figure 5 is a schematic diagram of a multi-acquisition pulse sequence.

[0019] Figure 6 is to use known methods and use Figure 2A Comparison of digital phantom images reconstructed by the neural network model shown in .

[0020] Figure 7 is achieved by zero padding and using Figure 2A Comparison of human images reconstructed by the neural network models shown in .

[0021] Figure 8A It is a schematic diagram of the neural network model.

[0022] Figure 8B yes Figure 8A Schematic diagram of neurons in the neural network model shown.

[0023] Figure 9 is a schematic diagram of an exemplary convolutional neural network.

[0024] Figure 10 is a block diagram of an exemplary computing device. DETAILED DESCRIPTION

[0025] The present disclosure includes systems and methods for removing truncation artifacts in magnetic resonance (MR) images of a subject using a deep learning model. As used herein, a subject is a human, an animal, or a pseudo-animal. Unlike signals representing the anatomy or structure of the subject, artifacts are visual abnormalities in a medical image that are not present in the subject, which can be caused by imaging modalities such as partially sampled pulse sequences. Artifact removal is the reduction and / or removal of artifacts from an image. The systems and methods disclosed herein also synthesize missing data and interpolate high spatial frequency data while removing truncation artifacts. Methodological aspects will be apparent in part and discussed explicitly in part in the following description.

[0026] In magnetic resonance imaging (MRI), a subject is placed in a magnet. When the subject is in the magnetic field generated by the magnet, the magnetic moments of nuclei such as protons attempt to align with the magnetic field, but precess in a random order around the magnetic field at the Larmor frequency of the nuclei. The magnetic field of the magnet is called B0 and extends in the longitudinal or z-direction. During the acquisition of MRI images, a magnetic field in the xy plane and close to the Larmor frequency (called the excitation field B1) is generated by a radio frequency (RF) coil and can be used to rotate or "tilt" the net magnetic moment Mz of the nucleus from the z-direction toward the transverse or xy plane. After the excitation signal B1 terminates, the nucleus emits a signal, which is called an MR signal. In order to use the MR signals to generate an image of the subject, magnetic field gradient pulses (Gx, Gy, and Gz) are used. The gradient pulses are used to scan through k-space, the space or distance of spatial frequency. There is a Fourier relationship between the acquired MR signals and the image of the subject, so the image of the subject can be derived by reconstructing the MR signals.

[0027] Figure 1 A schematic diagram of an exemplary MRI system 10 is shown. In the exemplary embodiment, the MRI system 10 includes a workstation 12 having a display 14 and a keyboard 16. The workstation 12 includes a processor 18, such as a commercially available programmable machine running a commercially available operating system. The workstation 12 provides an operator interface that allows scanning plans to be entered into the MRI system 10. The workstation 12 is connected to a pulse sequence server 20, a data acquisition server 22, a data processing server 24, and a data storage server 26. The workstation 12 and each of the servers 20, 22, 24, and 26 communicate with each other.

[0028] In the exemplary embodiment, the pulse sequence server 20 operates the gradient system 28 and the radio frequency ("RF") system 30 in response to instructions downloaded from the workstation 12. The instructions are used to generate gradient waveforms and RF waveforms in an MR pulse sequence. The RF coil 38 and the gradient coil assembly 32 are used to execute the prescribed MR pulse sequence. The RF coil 38 is shown as a whole-body RF coil. The RF coil 38 can also be a local coil that can be placed near the anatomical structure to be imaged, or a coil array including multiple coils.

[0029] In the exemplary embodiment, gradient waveforms for performing a delimiting scan are generated and applied to a gradient system 28, which energizes the gradient coils in a gradient coil assembly 32 to generate magnetic field gradients G for position encoding the MR signals. x , G y and G z The gradient coil assembly 32 forms part of a magnet assembly 34 , which also includes a polarizing magnet 36 and an RF coil 38 .

[0030] In an exemplary embodiment, the RF system 30 includes an RF transmitter for generating RF pulses used in MR pulse sequences. The RF transmitter responds to the scan plan and direction from the pulse sequence server 20 to generate RF pulses with a desired frequency, phase, and pulse amplitude waveform. The generated RF pulses are applied by the RF system 30 to an RF coil 38. The responsive MR signals detected by the RF coil 38 are received by the RF system 30 and amplified, demodulated, filtered, and digitized according to commands generated by the pulse sequence server 20. The RF coil 38 is depicted as both a transmitter and receiver coil, such that the RF coil 38 transmits RF pulses and detects MR signals. In one embodiment, the MRI system 10 may include a transmitter RF coil for transmitting RF pulses and a separate receiver coil for detecting MR signals. The transmit channels of the RF system 30 may be connected to the RF transmit coil, and the receiver channels may be connected to separate RF receiver coils. Typically, the transmit channels are connected to the whole-body RF coil 38, and each receiver segment is connected to a separate local RF coil.

[0031] In the exemplary embodiment, the RF system 30 also includes one or more RF receiver channels. Each RF receiver channel includes an RF amplifier that amplifies the MR signals received by the RF coil 38 to which the channel is connected; and a detector that detects and digitizes the I and Q quadrature components of the received MR signals. The magnitude of the received MR signal can then be determined as the square root of the sum of the squares of the I and Q components, as shown in the following equation (1):

[0032]

[0033] And the phase of the received MR signal can also be determined as shown in the following equation (2):

[0034]

[0035] In an exemplary embodiment, the digitized MR signal samples generated by the RF system 30 are received by the data acquisition server 22. The data acquisition server 22 can operate in response to instructions downloaded from the workstation 12 to receive real-time MR data and provide buffer memory so that no data is lost due to data overflow. In some scans, the data acquisition server 22 only passes the acquired MR data to the data processing server 24. However, in scans where information derived from the acquired MR data is needed to control further execution of the scan, the data acquisition server 22 is programmed to generate the required information and transmit it to the pulse sequence server 20. For example, during a pre-scan, MR data is acquired and used to calibrate the pulse sequence executed by the pulse sequence server 20. In addition, navigator signals can be acquired during the scan and used to adjust operating parameters of the RF system 30 or gradient system 28, or to control the order in which views are sampled in k-space.

[0036] In an exemplary embodiment, the data processing server 24 receives MR data from the data acquisition server 22 and processes the MR data according to instructions downloaded from the workstation 12. Such processing may include, for example, performing Fourier transforms on the raw k-space MR data to produce two-dimensional or three-dimensional images, applying filters to reconstructed images, performing backprojection image reconstruction on the acquired MR data, generating functional MR images, and computing motion or flow images.

[0037] In an exemplary embodiment, the image reconstructed by the data processing server 24 is transmitted back to the workstation 12 and stored there. In some embodiments, the real-time image is stored in a database memory cache ( Figure 1 (not shown), real-time images can be output from the database memory cache to the operator display 14 or a display 46 located near the magnet assembly 34 for use by the attending physician. Batch mode images or selected real-time images can be stored on a disk storage device 48 or in a host database on the cloud. When such images have been reconstructed and transferred to the storage device, the data processing server 24 notifies the data storage server 26. The operator can use the workstation 12 to archive images, generate films, or send images to other facilities via the network.

[0038] MR signals are represented by complex numbers, where each location in k-space is represented by a complex number, with the I and Q quadrature MR signals being real and imaginary components. A composite MR image can be reconstructed from the I and Q quadrature MR signals using a process such as Fourier transform. A complex MR image is an MR image in which each pixel is represented by a complex number, also having real and imaginary components.

[0039] In MRI, asymmetric sampling in the frequency and phase encoding directions or dimensions is referred to as fractional echo and fractional acquisition number (NEX), respectively, and is widely used in both 2D and 3D MR imaging. These undersampling techniques are typically used to shorten the echo time (e.g., to increase SNR or change tissue contrast), shorten the repetition time (e.g., to reduce scan time), and / or suppress unwanted artifacts (such as fine line artifacts in fast spin echo (FSE) imaging, or off-resonance artifacts in gradient echo sequences (GRE) and echo planar imaging (EPI)). Asymmetric sampling of k-space introduces truncation artifacts into the reconstructed image in the form of blurring and oscillations. Therefore, various image reconstruction techniques have been designed for reconstructing partial k-space data, such as conjugate synthesis, homodyne, and projection onto convex sets (POCS). These known techniques rely on some inherent estimate of the underlying image phase, which can then be removed (or "corrected"), allowing the synthesis of missing or unsampled data based on the Hermitian symmetry principle of real-valued signals. This phase estimate is often derived from a centrosymmetric sampled portion of k-space and is limited in several important ways. First, the phase estimate is contaminated by thermal noise, which is particularly problematic in low-signal image regions and / or when this phase estimate is performed on a per-channel (or per-view) basis. Second, this phase estimate is inherently bandwidth-limited and must be further low-pass filtered when applied to prevent the introduction of additional truncation artifacts. Consequently, high-spatial-frequency phase information is not corrected, leaving residual blur in the final reconstructed image. The application of this low-frequency phase estimate also tends to bias the noise in the reconstructed image, which would otherwise tend to be normally distributed. The presence of this biased noise signal in the reconstructed image reduces image contrast, especially in low-signal regions, and the altered distribution of this noise degrades noise averaging performance (such as in multi-NEX EPI diffusion) and / or complicates downstream denoising efforts, which are often based on assumed noise models. Furthermore, known partial k-space reconstruction techniques tend to exhibit various strengths and weaknesses, and the choice of method often leads to various performance tradeoffs. For example, POCS tends to localize reconstruction artifacts, while homodyne tends to introduce contrast errors. Finally, in the case of homodyne and conjugate synthesis, phase information is discarded during reconstruction, making them unsuitable for phase-sensitive applications such as Dixon chemical shift imaging, phase-sensitive inversion restoration imaging, and image-based phase-sensitive atlas generation.

[0040] Using deep learning to directly remove these asymmetric truncation artifacts can provide superior performance to conventional methods. The deep learning method involves no explicit phase correction, no low-pass filtering, and no conventional filtering of any type. Unlike the conventional methods mentioned above, the deep learning method uses all acquired data (vs. low-pass filtered phase estimates), and this results in reconstructed images with sharper edges, more realistic contrast, and less noise deviation. In addition, the underlying phase of the image is well preserved after truncation artifact removal, even at high frequencies, making this technique suitable for phase-sensitive imaging applications. In addition to reducing truncation artifacts, the systems and methods described herein also increase or restore high spatial frequency data that is missing due to asymmetric and / or symmetric truncation.

[0041] Figure 2A is a schematic diagram of an exemplary truncation artifact reduction system 200. In an exemplary embodiment, the system 200 includes a truncation artifact reduction computing device 202 configured to reduce truncation artifacts and increase high spatial frequency data. The computing device 202 also includes a neural network model 204. The system 200 may include a second truncation artifact reduction computing device 203. The second truncation artifact reduction computing device 203 may be used to train the neural network model 204, and the truncation artifact reduction computing device 202 may then use the trained neural network model 204. The second truncation artifact reduction computing device 203 may be the same computing device as the truncation artifact reduction computing device 202, so that the training and use of the neural network model 204 are performed on a single computing device. Alternatively, the second truncation artifact reduction computing device 203 may be a separate computing device from the truncation artifact reduction computing device 202, so that the training and use of the neural network model 204 are performed on a separate computing device. The truncation artifact reduction computational device 202 may be included in the workstation 12 of the MRI system 10 , or may be included on a separate computational device in communication with the workstation 12 .

[0042] Figure 2Bis a flow chart of an exemplary method 250. The method 250 may be implemented on the truncation artifact reduction system 200. In an exemplary embodiment, the method includes executing 252 a neural network model for analyzing MR images. The neural network model is trained with training images. The training images may be pairs of original and corrupted images, and a target output image of the neural network model is the original image. The corrupted image is an image reconstructed based on partial k-space data from a portion of k-space in one or more partial sampling patterns of k-space. As used herein, partial sampling or truncation is the partial sampling of k-space in one or more dimensions by truncating k-space in locations corresponding to high spatial frequencies. High spatial frequencies are located at the periphery of k-space compared to low spatial frequencies located at and around the center of k-space. Truncation of k-space results in truncation artifacts, such as blurring and oscillations in the corrupted image. The original image is an image based on the full k-space corresponding to the partial k-space.

[0043] Figure 2C is a schematic diagram of a partial sampling pattern or truncated pattern 259 of the complete k-space 261. The complete k-space 261 is composed of the maximum kx or ky value k x，max and k y，max The maximum kx or ky value is defined by the maximum frequency encoding gradient or phase encoding gradient. In partial sampling, a portion of the high spatial frequency data 263 is not acquired. The truncation can be in the kx dimension and / or the ky dimension, and in three-dimensional (3D) acquisition, in the kz dimension. The full k-space 261 is truncated into partial k-space 264. Figure 2A The partial k-space 264 shown in is the complete k-space 261 truncated in the ky dimension, wherein negative high spatial frequency data is not acquired during image acquisition of the partial k-space 264. The truncation can be asymmetric, wherein k-space is truncated asymmetrically in a certain dimension. Figure 2A The portion of k-space 264 shown in FIG is asymmetrically truncated in the k dimension. Truncation can be symmetrical, where k-space is symmetrically truncated at k-space locations of positive and negative spatial frequencies. Truncation can be symmetrical and asymmetrical in one dimension, where k-space is truncated at k-space locations of both positive and negative spatial frequencies, but by unequal amounts. Truncation reduces high spatial frequency data and causes truncation artifacts. Figure 2CThe truncation shown along the axis of a 2D Cartesian coordinate system is shown as an example only. The systems and methods described herein can also be used to remove truncation artifacts in images based on k-space data from k-space that is asymmetrically truncated along the axis of a 2D / 3D Cartesian coordinate system, a 2D / 3D non-Cartesian coordinate system (such as a polar, spherical, or cylindrical coordinate system), or a combination thereof. For example, the partial sampling pattern is k-space that is asymmetrically truncated in the radial dimension. In another example, the k-space data is acquired as a stack of radial lines along the kz direction in the kx-ky plane, and the partial sampling pattern is k-space that is asymmetrically truncated in the radial dimension in the kx-ky plane and asymmetrically truncated in the kz dimension.

[0044] In an exemplary embodiment, the corrupted images used for training can be in various partial sampling patterns at various partial sampling factors or partial k-space factors. The partial k-space factor is the ratio between the partial k-space and the full k-space in the truncated dimension. For example, if the partial k-space factor is 0.5 in the ky dimension, only half of k-space is acquired, either the positive ky half or the negative ky half. In some embodiments, the corrupted images and the original images are simulated images. The neural network model 204 can be trained with a partial sampling pattern and configured to remove truncation artifacts and increase high spatial frequency data for corrupted images based on MR k-space data from partial k-space acquired with the partial sampling pattern. For example, the neural network model 204 is trained with paired corrupted and original images for asymmetric truncation in the kx dimension, and the trained neural network model 204 is specifically designed to remove truncation artifacts and increase high spatial frequency data in the kx dimension for images acquired with asymmetric truncation in the kx dimension. Alternatively, the neural network model 204 may be a general neural network model 204 configured to remove truncation artifacts and increase high spatial frequency data for partial k-space data acquired with various partial sampling patterns. The general neural network model 204 may be trained using pairs of corrupted and original images for the various partial sampling patterns. The specialized neural network model 204 may be trained with less time and computational burden than the general neural network model 204.

[0045] In some embodiments, the neural network model 204 includes one or more layers of neurons configured to reconstruct an image based on the partial k-space data. During training, the partial k-space data in various partial sampling patterns is used for training, where the partial k-space data is input to the neural network model 204.

[0046] Return Reference Figure 2B, the method 250 further includes receiving 254 partial k-space data from the partial k-space truncated in at least one dimension. The method 250 also includes reconstructing 256 a coarse image based on the partial k-space data. The coarse image can be reconstructed by zero-padding the partial k-space data to have zeros at positions corresponding to skipped k-space positions, thereby deriving full k-space data; and then reconstructing the coarse image based on the zero-padding k-space data. The full k-space data for the coarse image can be reconstructed by methods other than zero-padding, such as interpolation. Reconstructing 256 the coarse image can be performed external to the neural network model 204 and input to the neural network model. Alternatively, reconstructing 256 the coarse image is performed by the neural network model 204, wherein the partial k-space data is directly input to the neural network model 204, and the neural network model 204 includes one or more layers of neurons configured to reconstruct the coarse image based on the partial k-space data. Furthermore, the method 250 includes analyzing 258 the coarse image. Furthermore, the method 250 includes deriving 260 an improved image of the coarse image based on the analysis. The neural network model 204 outputs an improved image, which is an image corresponding to the coarse image with improved image quality. Compared to the coarse image, the improved image has reduced truncation artifacts and increased high spatial frequency data. In some embodiments, the neural network model 204 includes one or more layers of neurons configured to generate complete k-space data by methods such as Fourier transforming the improved image inferred by the neural network model 204. The method 250 also includes outputting 262 the improved image.

[0047] Figures 3A to 3D is a schematic diagram of an exemplary neural network model 204. The neural network model 204 may include a convolutional neural network 302. The neural network 302 is trained using a corrupted image 304 as input and an original image 306 as output. Compared to the corrupted image 304, artifacts 307 (such as truncation artifacts) are reduced, and missing high spatial frequency data 263 is restored in the original image 306. In an exemplary embodiment, partial k-space data 303 is received that is missing high spatial frequency data 263. Figures 3A to 3D The difference between them is the different partial sampling patterns in acquiring partial k-space data 303-a, 303-b, 303-c, 303-d (collectively referred to as partial k-space data 303). Figure 3A In , for the partial k-space data 303 - a , the k-space 310 is asymmetrically truncated in one dimension (such as the kx dimension), wherein the positive kx portion of the k-space 310 is skipped and the negative kx portion is fully acquired. Figure 3B In FIG, for the partial k-space data 303-b, the k-space 310 is asymmetrically truncated in two dimensions (such as the kx dimension and the ky dimension). Figure 3C In , for the partial k-space data 303 - c , the k-space 310 is truncated asymmetrically in the kx dimension and symmetrically in the ky dimension. Figure 3D In the embodiment of the present invention, for partial k-space data 303-d, k-space 310 is asymmetrically truncated in the kx dimension and symmetrically truncated in both the kx and ky dimensions. That is, the partial k-space data 303 has a varying partial sampling pattern. In various partial sampling patterns, the partial sampling factor in the kx or ky dimensions may vary. The neural network model is configured to reduce truncation artifacts and recover missing k-space data for the partial k-space data in different partial sampling patterns.

[0048] In some embodiments, the neural network 302 is trained with a corrupted image 304 as input and a residual image 305 as a target output. The residual image 305 is a difference image between the corrupted image 304 and a ground truth image 306, which is based on the complete k-space data corresponding to the partial k-space data 303-a, 303-b, 303-c, 303-d. Figure 3B In , the residual image 305 is an image with asymmetric truncation artifacts of the corrupted image 304. Figure 3C and Figure 3D , the residual image 305 is an image having asymmetric truncation artifacts and symmetric truncation artifacts of the corrupted image 304 and having high spatial frequency data at a higher spatial frequency than the partial k-space data 303 - c , 303 - d .

[0049] The output of neural network 302 can be a residual image or an improved image of the input to neural network model 204. When the output of neural network 302 is a residual image, neural network model 204 can include one or more layers of neurons configured to generate an improved image based on the output residual image. For example, the improved image is calculated as the residual image minus the input image. As a result, the output image has reduced truncation artifacts and increased high spatial frequency data compared to the input image to neural network model 204. Alternatively, neural network model 204 outputs a residual image, and generating the improved image based on the residual image is performed outside of the neural network model. In one embodiment, the user is provided with options such as outputting the improved image, the residual image, or both.

[0050] The neural network model 204 can be specialized, such as trained to reduce truncation artifacts and recover missing k-space data from asymmetric truncation in one dimension. The neural network model 204 can be generalized, such as trained to reduce truncation artifacts and recover missing k-space data from asymmetric truncation in one or more dimensions and / or symmetric truncation in one or more dimensions. As the neural network model 204 is more generalized, more training data is obtained for the neural network model 204 to be used to infer improved images for partial k-space data in various truncation patterns and truncation factors. Thus, the computational burden is increased. For example, in order to train Figure 3A The neural network model shown is provided with asymmetric partial k-space data in the same dimension with various partial sampling factors, or a damaged image based on such partial k-space data as input. Figure 3D The neural network model shown in FIG is provided with corrupted images based on partial k-space data in various symmetric partial sampling factors in the kx dimension, in various symmetric partial sampling factors in the kx dimension, and in various asymmetric partial sampling factors in the kx dimension as input. As the number of training image pairs increases significantly and the complexity of the partial sampling pattern increases greatly, the complexity of the truncation artifact increases and is related to Figure 3A Compared with the neural network model 204 in Figure 3D The training of the neural network model 204 in is more computationally intensive and time consuming.

[0051] In one embodiment, the neural network model 204 includes an input layer for the conjugate reflectance of the k-space data, or a conjugate reflectance image ( Figures 4A to 4C As described above, MRI signals / k-space data and MR images are represented by complex numbers. The conjugate reflection of the k-space data at a k-space position k is the complex conjugate of the k-space data at a k-space position -k, as shown in the following equation (3):

[0052] S cj(k) =S * (-k), (3)

[0053] Among them S cj(k) is the conjugate reflection at k-space position k, S(-k) is the original k-space data at k-space position -k, and * denotes complex conjugate.

[0054] In other words, to synthesize the conjugate reflection of the original k-space data, each complex number at each k-space location is conjugated and reflected across the origin. For example, the k-space data in the first quadrant in the conjugate reflection is the complex conjugate of the original k-space data in the third quadrant. The conjugate reflection image is derived by Fourier transforming the conjugate reflection. The conjugate reflection or conjugate reflection image can be input into the neural network model 204 as part of the training corrupted image during training, or input during inference along with the original partial k-space data or a coarse image based on the original partial k-space data. Figure 4A A comparison of real components 402-o, 402-vc, imaginary components 404-o, 404-c and magnitude components 406-o, 406-vc of an original complex image 408-o and a conjugate reflected image 408-vc of the complex image 408-o is shown. The magnitude images 406-o, 406-vc are identical. Figure 4B Exemplary conjugate reflections 410-a, 410-b, 410-c of the raw k-space data 303-a, 303-b, 303-c are shown. The raw k-space data 303-a, 303-b, 303-c are acquired using different k-space portion sampling patterns (see also Figures 3A to 3C ), wherein the k-space is asymmetrically truncated in the kx dimension in the k-space data 303-a, asymmetrically truncated in both the kx dimension and the ky dimension in the k-space data 303-b, and asymmetrically truncated in the kx dimension and symmetrically truncated in the ky dimension in the original k-space data 303-c.

[0055] Figure 4CA comparison of an image 420 reconstructed with zero padding, an image 422 output by the neural network model 204 with a conjugate reflection input layer, and an image 424 output by the neural network model 204 without a conjugate reflection input layer is shown. The partial k-space data is from a partial k-space that is asymmetrically truncated in the left and right (kx) dimensions and symmetrically truncated in both the kx and ky dimensions using a zero padding interpolation (ZIP) factor of 2. The ZIP factor indicates the degree of symmetrical zero padding in the kx or ky dimensions. The image resolution of the reconstructed image with zero padding is increased by a factor indicated by the ZIP factor. For example, if the image resolution before zero padding is 128×128, the image reconstructed by zero padding in both dimensions with a ZIP factor of 2 has an image resolution of 256×256. In the neural network model with a conjugate reflection input layer, the conjugate reflections of the partial k-space data are provided as additional inputs to the neural network model 204. Compared to the image 420 reconstructed by zero padding, the images 422, 424 output by the neural network model 204 with or without the additional input of the conjugate reflection have reduced truncation artifacts 307. The artifacts 307 in the image 422 output by the neural network model 204 with the additional input of the conjugate reflection are further reduced to a level that is not visually noticeable compared to the image 424. The conjugate reflection 410 provides a different representation of the partial k-space data 303 and improves the image quality of the output from the neural network model 204.

[0056] Figure 5An embodiment of acquiring k-space data of various partial sampling patterns in a multi-acquisition pulse sequence is shown. In an exemplary embodiment, four acquisitions are acquired. Multiple acquisitions can be acquired as multiple triggers, multiple phases, or multiple acquisitions (NEX). K-space is truncated asymmetrically in the kx and ky dimensions. In acquisition 1, positive kx positions and negative ky positions are truncated, where k-space data at these positions is not acquired. In acquisition 2, negative kx positions and negative ky positions are truncated. In acquisition 3, positive kx positions and positive ky positions are truncated. In acquisition 4, negative kx positions and positive ky positions are truncated. To adjust the partial sampling pattern in the kx dimension, the echo time can be adjusted to sample different portions of the echo. To adjust the partial sampling pattern in the ky dimension, in a Cartesian acquisition, ky lines at the truncation positions are not acquired, where the truncation positions are positions in k-space where k-space data is acquired. The partial k-space data from the multiple acquisitions are input into the neural network model 204. K-space data from multiple acquisitions are acquired using complementary partial sampling patterns, wherein k-space locations that were not sampled in one acquisition are sampled in at least one of the other acquisitions, and complementary information in the k-space data is provided to each other. The complementary sampling patterns along the axes of the above-mentioned 2D Cartesian coordinate system are shown only as examples. Similar to the truncation mode, the complementary sampling patterns can be along the axes of a 2D / 3D Cartesian coordinate system, a 2D / 3D non-Cartesian coordinate system (such as a polar, spherical or cylindrical coordinate system), or a combination thereof. The k-space data from multiple acquisitions are jointly processed by the neural network model 204, and at the same time, the image quality of the image from each acquisition and the composite image from the combination of multiple acquisitions is improved due to the complementary information.

[0057] Figure 6 is a comparison of digital phantom images reconstructed using the deep learning (DL) method described herein and known methods. Image 601 is a target image. Images 603-zf, 603-dl, 603-pocs, 603-hd are images reconstructed by zero padding, the method described herein, POCS, and homodyning, respectively. Images 605- dl, 605-pocs, 605-hd are the differences between the target image 601 and the reconstructed images 603-zf, 603-dl, 603-pocs, 603-hd. In this example, the neural network model 204 is trained to remove truncation artifacts only in the left and right (kx) dimensions. The partial sampling factor is 0.54. As Figure 6 As shown, the systems and methods described herein outperform iterative POCS and homodyne reconstruction methods in terms of edge sharpness and contrast preservation.

[0058] Figure 7The axial abdominal image 702 (top row) and sagittal knee joint image 704 (bottom row) images reconstructed using the zero padding and DL methods described herein are shown. The abdominal image 702 is acquired using a single fast spin echo sequence. The knee joint image 704 is acquired using a fast spin echo sequence. Images 706-zf and 708-zf are amplitude images reconstructed using zero padding. Images 710-dl and 712-dl are residual images output by the neural network model 204 that include truncation artifacts. Images 706-dl and 708-dl are amplitude images of the images reconstructed using the DL method. Images 714 and 716 are phase images of the images reconstructed using the DL method. Figure 7 As shown, truncation artifacts are greatly reduced in images 706-d1, 708-d1 when reconstructed using the DL method compared to images 706-zf, 708-zf when reconstructed using zero padding. Phase information is substantially preserved, as shown in images 714, 716. In this example, the neural network model 204 is trained for a half-NEX and ZIP factor of 2 in both the phase encoding dimension and the frequency encoding dimension.

[0059] In some embodiments, k-space data is acquired by a multi-channel / multi-coil RF coil, and the input to the neural network model 204 is k-space data or images acquired by individual channels of the RF coil. The k-space data or images acquired by the individual coils are individually input to the neural network model 204, and the outputs from the neural network model 204 are combined into one image. The coil sensitivity map is used in the generation of the combined image.

[0060] Figure 8A An exemplary artificial neural network model 204 is depicted. The exemplary neural network model 204 includes neuron layers 502, 504-1 to 504-n, and 506, including an input layer 502, one or more hidden layers 504-1 to 504-n, and an output layer 506. Each layer may include any number of neurons, i.e., Figure 8A Where q, r and n can be any positive integer. It should be understood that Figure 8A The depicted structures and configurations may be used to implement the methods and systems described herein using neural networks of varying structures and configurations.

[0061] In an exemplary embodiment, the input layer 502 may receive different input data. For example, the input layer 502 may include a first input a1 representing a training image, a second input a2 representing a pattern identified in the training image, a third input a3 representing an edge of the training image, and so on. The input layer 502 may include thousands or more inputs. In some embodiments, the number of elements used by the neural network model 204 is changed during the training process, and if, for example, some neurons are determined to have low relevance during execution of the neural network, these neurons are bypassed or ignored.

[0062] In an exemplary embodiment, each neuron in hidden layers 504-1 to 504-n processes one or more inputs from input layer 502 and / or one or more outputs from neurons in one of the previous hidden layers to generate a decision or output. Output layer 506 includes one or more outputs, each indicating a label, a confidence factor, a weight describing an input, and / or an output image. However, in some embodiments, outputs of neural network model 204 are obtained from hidden layers 504-1 to 504-n in addition to or instead of outputs from output layer 506.

[0063] In some embodiments, each layer has a discrete, identifiable function with respect to the input data. For example, if n is equal to 3, the first layer analyzes the first dimension of the input, the second layer analyzes the second dimension of the input, and the last layer analyzes the third dimension of the input. The dimensions may correspond to aspects that are considered to be highly deterministic, then to those that are considered to be of medium importance, and finally to those that are considered to be less relevant.

[0064] In other embodiments, the layers are not clearly delineated in terms of the functionality they perform. For example, two or more of the hidden layers 504-1 through 504-n may share decisions related to labels, with no single layer making independent decisions regarding labels.

[0065] Figure 8B Depicted is a diagram corresponding to the embodiment of Figure 8A Example neuron 550 labeled "1, 1" in hidden layer 504-1 in FIG. For each input to neuron 550 (e.g., Figure 8A The input layer 502 in the input) is weighted so that the input a1 to a p corresponds to the weights w1 to w2 determined during the training process of the neural network model 204 p .

[0066] In some embodiments, some inputs lack explicit weights, or have weights below a threshold. The weights are applied to a function α (labeled by reference numeral 510), which may be a summation and may produce a value z1 that is input to a function labeled f 1，1 (z1) function 520. Function 520 is any suitable linear or nonlinear function. Figure 8B As depicted, function 520 produces a plurality of outputs that may be provided to neurons of subsequent layers or used as outputs of neural network model 204. For example, an output may correspond to an index value into a list of labels, or may be a calculated value used as input to a subsequent function.

[0067] It should be understood that the structure and function of the depicted neural network model 204 and neurons 550 are for illustrative purposes only and that other suitable configurations exist. For example, the output of any given neuron may depend not only on the values ​​determined by past neurons, but also on future neurons.

[0068] The neural network model 204 may include a convolutional neural network (CNN), a deep learning neural network, a reinforcement or enhanced learning module or program, or a combined learning module or program that learns in two or more areas or aspects of interest. Supervised and unsupervised machine learning techniques can be used. In supervised machine learning, the processing element may be provided with exemplary inputs and their associated outputs, and may attempt to discover general rules that map inputs to outputs so that when subsequent new inputs are provided, the processing element can accurately predict the correct output based on the discovered rules. Unsupervised machine learning programs can be used to train the neural network model 204. In unsupervised machine learning, the processing element may need to find its own structure in unlabeled exemplary inputs. Machine learning can involve identifying and recognizing patterns in existing data to facilitate prediction of subsequent data. Models can be created based on exemplary inputs to make effective and reliable predictions for new inputs.

[0069] In addition or alternatively, a machine learning program can be trained by inputting sample data sets or certain data such as images, object statistics and information into the program. The machine learning program can use a deep learning algorithm that can focus primarily on pattern recognition and can be trained after processing multiple examples. The machine learning program can include Bayesian program learning (BPL), speech recognition and synthesis, image or object recognition, optical character recognition and / or natural language processing, alone or in combination. The machine learning program can also include natural language processing, semantic analysis, automated reasoning and / or machine learning.

[0070] Based on these analyses, the neural network model 204 can learn how to identify features and patterns that can then be applied to analyze image data, model data, and / or other data. For example, the model 204 can learn to identify features in a series of data points.

[0071] Figure 9 6 is a block diagram of an exemplary CNN 600 that may be included in neural network model 204. CNN 600 includes a convolutional layer 608. In a convolutional layer, convolution is used instead of the usual matrix multiplication in the neural network model. In one example, 1×1 convolution is used to reduce the number of channels in neural network 600. Neural network 600 includes one or more convolutional layer blocks 602, a fully connected layer 604 in which neurons in a layer are connected to every neuron in the previous layer, and an output layer 606 that provides an output.

[0072] In an exemplary embodiment, the convolutional layer block 602 includes a convolutional layer 608 and a pooling layer 610. Each convolutional layer 608 is flexible in terms of its depth, such as the number of convolutional filters and the size of the convolutional filters. The pooling layer 610 is used to simplify the underlying calculations and reduce the dimensionality of the data by combining the outputs of the neuron cluster at the previous layer into a single neuron in the pooling layer 610. The convolutional layer block 602 may also include a normalization layer 612 between the convolutional layer 608 and the pooling layer 610. The normalization layer 612 is used to normalize the distribution within the training image batch and update the weights in the layer after normalization. The number of convolutional layer blocks 602 in the neural network 600 may depend on the image quality of the training images and the level of detail in the extracted features.

[0073] In operation, during training, a training image and other data, such as extracted features of the training image, are input into one or more convolutional layer blocks 602. An observed mask corresponding to the training image is provided as an output of an output layer 606. The neural network 600 is adjusted during training. Once the neural network 600 is trained, an input image is provided to one or more convolutional layer blocks 602, and the output layer 606 provides an output including a mask associated with the input image.

[0074] The workstation 12 and truncation artifact reduction computing devices 202 , 203 described herein may be any suitable computing device 800 and software implemented therein. Figure 10 800 is a block diagram of an exemplary computing device 800. In an exemplary embodiment, the computing device 800 includes a user interface 804 that receives at least one input from a user. The user interface 804 may include a keyboard 806 that enables the user to enter relevant information. The user interface 804 may also include, for example, a pointing device, a mouse, a stylus, a touch-sensitive panel (e.g., a touchpad and a touch screen), a gyroscope, an accelerometer, a position detector, and / or an audio input interface (e.g., including a microphone).

[0075] Furthermore, in an exemplary embodiment, the computing device 800 includes a display interface 817 for presenting information (such as input events and / or verification results) to a user. The display interface 817 may also include a display adapter 808 coupled to at least one display device 810. More specifically, in an exemplary embodiment, the display device 810 may be a visual display device such as a cathode ray tube (CRT), a liquid crystal display (LCD), a light emitting diode (LED) display, and / or an "electronic ink" display. Alternatively, the display interface 817 may include an audio output device (e.g., an audio adapter and / or speakers) and / or a printer.

[0076] The computing device 800 also includes a processor 814 and a memory device 818. The processor 814 is coupled to the user interface 804, the display interface 817, and the memory device 818 via a system bus 820. In an exemplary embodiment, the processor 814 communicates with the user, such as by prompting the user via the display interface 817 and / or by receiving user input via the user interface 804. The term "processor" generally refers to any programmable system, including system and microcontrollers, reduced instruction set computers (RISCs), complex instruction set computers (CISCs), application specific integrated circuits (ASICs), programmable logic circuits (PLCs), and any other circuit or processor capable of performing the functions described herein. The above examples are exemplary only and are therefore not intended to limit the definition and / or meaning of the term "processor" in any way.

[0077] In an exemplary embodiment, the memory device 818 includes one or more devices that enable information (such as executable instructions and / or other data) to be stored and retrieved. In addition, the memory device 818 includes one or more computer-readable media, such as, but not limited to, dynamic random access memory (DRAM), static random access memory (SRAM), a solid-state drive, and / or a hard disk. In an exemplary embodiment, the memory device 818 stores, but is not limited to, application source code, application object code, configuration data, additional input events, application state, assertion statements, verification results, and / or any other type of data. In an exemplary embodiment, the computing device 800 may also include a communication interface 830 coupled to the processor 814 via the system bus 820. In addition, the communication interface 830 is communicatively coupled to a data acquisition device.

[0078] In an exemplary embodiment, processor 814 may be programmed by encoding operations using one or more executable instructions and providing the executable instructions in memory device 818. In an exemplary embodiment, processor 814 is programmed to select a plurality of measurements received from a data collection device.

[0079] In operation, a computer executes computer-executable instructions embodied in one or more computer-executable components stored on one or more computer-readable media to implement various aspects of the present invention described and / or illustrated herein. Unless otherwise specified, the order in which the operations in the embodiments of the present invention shown and described herein are performed or implemented is not required. That is, unless otherwise specified, the operations may be performed in any order, and embodiments of the present invention may include more or fewer operations than those disclosed herein. For example, it is contemplated that performing or implementing a particular operation before, simultaneously with, or after another operation is within the scope of various aspects of the present invention.

[0080] At least one technical effect of the systems and methods described herein includes (a) reducing truncation artifacts; (b) increasing high spatial frequency information while reducing truncation artifacts; (c) a neural network model for reducing truncation artifacts caused by various partial sampling patterns; and (d) using conjugate reflection to increase image quality of images output from the neural network model.

[0081] Exemplary embodiments of truncation artifact reduction systems and methods are described in detail above. These systems and methods are not limited to the specific embodiments described herein, but rather, components of the systems and / or operations of the methods can be used independently and separately from other components and / or operations described herein. In addition, the components and / or operations described can also be defined in or used in conjunction with other systems, methods, and / or devices, and are not limited to practice with only the systems described herein.

[0082] Although specific features of various embodiments of the present invention may be shown in some drawings and not in others, this is for convenience only. In accordance with the principles of the invention, any feature of a drawing may be referenced and / or claimed in combination with any feature of any other drawing.

[0083] This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any included methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insignificant differences from the literal language of the claims.

Claims

1. A computer-implemented method for removing truncation artifacts from a magnetic resonance image, the method comprising: receiving a coarse image based on partial k-space data from a partial k-space asymmetrically truncated in at least one k-space dimension at k-space locations corresponding to high spatial frequencies; analyzing the coarse image using a neural network model, wherein the neural network model is trained using pairs of original and corrupted images, wherein the corrupted image is based on partial k-space data from a portion of k-space truncated with one or more partial sampling patterns at the k-space location corresponding to the high spatial frequency, the one or more partial sampling patterns including asymmetric truncation in at least one k-space dimension, the original image is based on full k-space data corresponding to the partial k-space data of the corrupted image, and a target output image of the neural network model is the original image; deriving a modified image of the coarse image based on the analyzing, wherein the derived modified image comprises reduced truncation artifacts and increased high spatial frequency data compared to the coarse image; as well as outputting the improved image, The partial k-space data of the damaged image includes a first set of k-space data and a second set of k-space data, wherein the second set of k-space data is a conjugate reflection of the first set of k-space data.

2. The method according to claim 1, wherein the original image further includes a residual image, the residual image including a difference image between the damaged image and a reference real image of the damaged image, and the reference real image is based on the complete k-space data corresponding to the partial k-space data of the damaged image with the truncation artifact removed.

3. The method of claim 1 , wherein the partial k-space data of the corrupted image comprises k-space data from a portion of k-space that is symmetrically truncated in at least one k-space dimension, and wherein the added high spatial frequency data in the derived improved image comprises high spatial frequency data having a spatial frequency higher than a spatial frequency of the partial k-space data. 4 . The method of claim 1 , wherein the partial k-space data of the corrupted image comprises k-space data from a portion of k-space that is asymmetrically truncated in more than one k-space dimension.

5. The method of claim 1 , wherein analyzing the coarse image further comprises analyzing the coarse image and a conjugate reflected image of the coarse image, wherein the neural network model takes both the coarse image and the conjugate reflected image as input. 6 . The method of claim 1 , wherein the partial k-space data is acquired by a multi-acquisition pulse sequence, and the partial k-space data of each acquisition includes partial k-space data from partial k-space truncated with a complementary partial sampling pattern.

7. The method according to claim 1, wherein the partial k-space data is acquired by a multi-channel radio frequency coil, the method comprising: For each channel, receiving a coarse image based on the portion of k-space data acquired through the channel; Analyzing the coarse image using the neural network model; as well as deriving a refined image of the coarse image based on the analyzing; as well as The modified images of at least two channels are combined into a combined image.

8. A computer-implemented method for removing truncation artifacts from a magnetic resonance image, the method comprising: receiving a pair of an original image and a corrupted image, wherein the corrupted image is based on partial k-space data from a portion of k-space truncated with one or more partial sampling patterns at a k-space location corresponding to a high spatial frequency, the one or more partial sampling patterns including an asymmetric truncation in at least one k-space dimension, and the original image is based on full k-space data corresponding to the partial k-space data of the corrupted image; as well as A neural network model is trained using pairs of the original image and the corrupted image in the following manner: Inputting the damaged image into the neural network model; Setting the original image as the target output of the neural network model; analyzing the damaged image using the neural network model; comparing the output of the neural network model with the target output; as well as adjusting the neural network model based on the comparison, wherein the trained neural network model is configured to reduce truncation artifacts in the corrupted image and increase high spatial frequency data in the corrupted image, The partial k-space data of the damaged image includes a first set of k-space data and a second set of k-space data, wherein the second set of k-space data is a conjugate reflection of the first set of k-space data.

9. The method of claim 8, wherein the original image further comprises a residual image comprising a difference image between the damaged image and a reference true image of the damaged image, and the reference true image is based on the complete k-space data corresponding to the partial k-space data of the damaged image with the truncation artifact removed.

10. The method of claim 8, wherein the partial k-space data of the damaged image comprises k-space data from a portion of k-space that is symmetrically truncated in at least one k-space dimension, and wherein the added high spatial frequency data comprises high spatial frequency data having a spatial frequency higher than a spatial frequency of the partial k-space data.

11. The method of claim 8, wherein the partial k-space data of the corrupted image comprises k-space data from a portion of k-space that is asymmetrically truncated in more than one k-space dimension.

12. A truncation artifact reduction system, the truncation artifact reduction system comprising a truncation artifact reduction computing device, the truncation artifact reduction computing device comprising at least one processor, the at least one processor in communication with at least one memory device, and the at least one processor being programmed to: receiving a coarse image based on partial k-space data from a partial k-space asymmetrically truncated in at least one k-space dimension at k-space locations corresponding to high spatial frequencies; analyzing the coarse image using a neural network model, wherein the neural network model is trained using pairs of original and corrupted images, wherein the corrupted image is based on partial k-space data from a portion of k-space truncated with one or more partial sampling patterns at the k-space location corresponding to the high spatial frequency, the one or more partial sampling patterns including asymmetric truncation in at least one k-space dimension, the original image is based on full k-space data corresponding to the partial k-space data of the corrupted image, and a target output image of the neural network model is the original image; deriving a modified image of the coarse image based on the analyzing, wherein the derived modified image comprises reduced truncation artifacts and increased high spatial frequency data compared to the coarse image; as well as outputting the improved image, The partial k-space data of the damaged image includes a first set of k-space data and a second set of k-space data, wherein the second set of k-space data is a conjugate reflection of the first set of k-space data.

13. The truncation artifact reduction system according to claim 12, wherein the original image further includes a residual image, the residual image including a difference image between the damaged image and a reference real image of the damaged image, and the reference real image is based on the complete k-space data corresponding to the partial k-space data of the damaged image with the truncation artifact removed.

14. The truncation artifact reduction system of claim 12 , wherein the partial k-space data of the corrupted image comprises k-space data from a portion of k-space that is symmetrically truncated in at least one k-space dimension, and wherein the increased high spatial frequency data in the derived improved image comprises high spatial frequency data having a spatial frequency higher than a spatial frequency of the partial k-space data.

15. The truncation artifact reduction system of claim 12, wherein the partial k-space data of the corrupted image comprises k-space data from a portion of k-space that is asymmetrically truncated in more than one k-space dimension.

16. The truncation artifact reduction system of claim 12, wherein the at least one processor is further programmed to analyze the coarse image and a conjugate reflected image of the coarse image, wherein the neural network model takes both the coarse image and the conjugate reflected image as input.

17. The truncation artifact reduction system of claim 12, wherein the partial k-space data is acquired by a multi-acquisition pulse sequence, and the partial k-space data of each acquisition includes partial k-space data from partial k-space truncated with a complementary partial sampling pattern.

Images