Systems and methods for processing magnetic resonance images using a phase-sensitive structural similarity index measure

Abstract

The present invention provides a computer-implemented method for processing composite magnetic resonance (MR) images. The method includes: receiving a pair of corrupted composite data and original composite images. The method further includes: using the pair to train a neural network model by: inputting the corrupted composite data into the neural network model, setting the original composite images as target outputs, and processing the corrupted composite data using the neural network model to derive output composite images of the corrupted composite data. Training the neural network model further includes: comparing the output composite images with the target outputs by calculating a phase-sensitive structural similarity index measure (PS-SSIM) between each output composite image in the output composite images and the corresponding target composite image of each output composite image, wherein the PS-SSIM is real-valued and varies with the phase of the output composite image and the phase of the target composite image; and adjusting the neural network model based on the comparison.

Description

Background Art

[0001] The present disclosure generally relates to systems and methods for image processing, and more particularly, to systems and methods for processing magnetic resonance (MR) images using a phase-sensitive structural similarity index measure.

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

[0003] Compared to other imaging modalities, MRI is not common because MRI signals are represented by complex numbers rather than by scalars or real numbers. Thus, the image value of each image pixel includes a magnitude and a phase. The phase of an MR image is typically discarded, although it carries important information and can be used in many applications, particularly in applications for estimating parameters that cannot be estimated using only the magnitude. Magnitude operations also change the noise distribution and affect image quality and parameter estimation using MR images. Summary of the Invention

[0004] In one aspect, a computer-implemented method for processing a composite magnetic resonance (MR) image is provided. The method includes: receiving a pair of corrupted composite data and an original composite image corresponding to the corrupted composite data. The method further includes: training a neural network model using the pair of corrupted composite data and the original composite image by inputting the corrupted composite data into the neural network model, setting the original composite image as the target output of the neural network model, and processing the corrupted composite data using the neural network model to derive an output composite image of the corrupted composite data. Training the neural network model further includes: comparing the output composite image with the target output by calculating a phase-sensitive structural similarity index measure (PS-SSIM) between each output composite image in the output composite image and the corresponding target composite image of each output composite image, where the PS-SSIM is real-valued and varies with the phase of the output composite image and the phase of the target composite image; and adjusting the neural network model based on the comparison.

[0005] In another aspect, an image processing system is provided. The system includes an image processing computing device that includes at least one processor communicatively coupled to at least one memory device. The at least one processor is programmed to: receive a pair of corrupted composite data and an original composite image corresponding to the corrupted composite data. The at least one processor is also programmed to: use the pair of corrupted composite data and the original composite image to train a neural network model by: inputting the corrupted composite data into the neural network model, setting the original composite image as the target output of the neural network model, and processing the corrupted composite data using the neural network model to derive an output composite image of the corrupted composite data. The at least one processor is further programmed to: train the neural network model by comparing the output composite image with the target output by calculating the PS-SSIM between each output composite image in the output composite image and the corresponding target composite image of each output composite image, where the PS-SSIM is a real value and varies with the phase of the output composite image and the phase of the target composite image. The at least one processor is further programmed to: train the neural network model by adjusting the neural network model based on the comparison.

[0006] In another aspect, an image processing system is provided. The system includes an image processing computing device that includes at least one processor communicatively coupled to at least one memory device. The at least one processor is programmed to: receive coarse composite data. The at least one processor is also programmed to: process the coarse composite data using a neural network model, where the neural network model is trained using a pair of corrupted composite data and an original composite image, where the corrupted composite data is used as an input and the original composite image is used as a target output, and a loss function of the neural network model that compares the output of the neural network model and the target output of the neural network model includes the PS-SSIM between each output composite image in the output composite image and the corresponding target composite image of each output composite image, where the PS-SSIM is a real value and varies with the phase of the output composite image and the phase of the target composite image. The at least one processor is further programmed to: generate a predicted image of the coarse composite data based on the processing; and output the predicted 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 image processing method using the phase-sensitive structural similarity index measure (PS-SSIM).

[0009] Figure 2B is a comparison of the conventional structural similarity index measure (SSIM) and the PS-SSIM.

[0010] Figure 3A is an exemplary image processing system including a neural network model.

[0011] Figure 3B is including training Figure 3A is a flowchart of another exemplary image processing method of the neural network model shown.

[0012] Figure 3C is including using Figure 3A is a flowchart of yet another exemplary image processing method of the neural network model shown.

[0013] Figure 3D is by Figure 3A is a comparison between an image reconstructed by the neural network model shown and an image reconstructed by a conventional neural network model.

[0014] Figure 4A is a schematic diagram of a neural network.

[0015] Figure 4B is Figure 4A is a schematic diagram of a neuron in the neural network shown.

[0016] Figure 5 is a block diagram of an exemplary user computing device.

[0017] Figure 6 is a block diagram of an exemplary server computing device. DETAILED DESCRIPTION

[0018] The present disclosure includes systems and methods for processing magnetic resonance (MR) images using a phase-sensitive structural similarity index measure (PS-SSIM). The structural similarity index measure (SSIM) measures the similarity between two images and is an important metric in image processing. Different from the conventional SSIM, which is based on the assumption that images are real-valued and not affected by image phase, the PS-SSIM disclosed herein varies with the phase of the image. For purposes of detailed description, MR images are used herein only as examples. However, the systems and methods described herein are not limited to use in MR systems and application to MR images, and in general can be applied to images represented by complex numbers. For example, the systems and methods disclosed herein can be applied to phase contrast microscopy, synthetic aperture radar, fringe pattern analysis, lensless imaging and speckle correlation imaging, diffraction imaging, holographic interferometry, electronic speckle pattern interferometry, microwave sparse reconstruction, and computed tomography (CT). As used herein, a complex image is an image represented by a complex number at each pixel, and complex data is data represented by a complex number at each data point. Method aspects will be in part apparent in the following description and in part will be explicitly discussed.

[0019] In magnetic resonance imaging (MRI), a subject is placed within 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 around the magnetic field in a random order at the Larmor frequency of the nuclei. The magnetic field of the magnet is referred to as B0 and extends in the longitudinal or z direction. During the acquisition of an MRI image, a magnetic field (referred to as the excitation field B1) that is in the x-y plane and near the Larmor frequency is generated by a radio frequency (RF) coil and can be used to rotate or "tilt" the net magnetic moment Mz of the nuclei from the z direction toward the transverse or x-y plane. After the termination of the excitation signal B1, the nuclei emit a signal, which is referred to as the MR signal. To use the MR signal 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 of spatial frequencies, or the reciprocal of distance. There is a Fourier relationship between the acquired MR signal and the image of the subject, and thus the image of the subject can be derived by reconstructing the MR signal.

[0020] Figure 1 A schematic diagram of an exemplary MRI system 10 is shown. In an 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 a scan protocol to be input into the MRI system 10. The workstation 12 is coupled 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 one another.

[0021] In an exemplary embodiment, the pulse sequence server 20 operates a gradient system 28 and a 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. An RF coil 38 and a gradient coil assembly 32 are used to perform a 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 that includes a plurality of coils.

[0022] In an exemplary embodiment, gradient waveforms are generated for performing a defining scan and applied to the gradient system 28, which energizes the gradient coils in the gradient coil assembly 32 to generate magnetic field gradients G x 、G y and G z . The gradient coil assembly 32 forms part of a magnet assembly 34, which also includes a polarization magnet 36 and an RF coil 38.

[0023] In an exemplary embodiment, the RF system 30 includes an RF transmitter for generating RF pulses used in an MR pulse sequence. The RF transmitter responds to a scan protocol and orientation from the pulse sequence server 20 to generate RF pulses having a desired frequency, phase, and pulse amplitude waveform. The generated RF pulses can be applied by the RF system 30 to the RF coil 38. The response MR signal detected by the RF coil 38 is received by the RF system 30 and is amplified, demodulated, filtered, and digitized under the direction of commands generated by the pulse sequence server 20. The RF coil 38 is described as 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 can include a transmitter RF coil that transmits RF pulses and a separate receiver coil that detects MR signals. The transmission channel of the RF system 30 can be connected to the RF transmission coil, and the receiver channel can be connected to a separate RF receiver coil. Generally, the transmission channel is connected to the whole body RF coil 38, and each receiver segment is connected to a separate local RF coil.

[0024] In an 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 signal received by the RF coil 38 to which the channel is connected; and a detector that detects and digitizes the I quadrature component and the Q quadrature component of the received MR signal. Then, the magnitude of the received MR signal can be determined as the square root of the sum of the squares of the I component and the Q component, as shown in equation (1) below:

[0025]

[0026] And the phase of the received MR signal can also be determined as shown in equation (2) below:

[0027]

[0028] In an exemplary embodiment, digitized MR signal samples generated by the RF system 30 are received by the data acquisition server 22. The data acquisition server 22 may operate in response to instructions downloaded from the workstation 12 to receive real-time MR data and provide a buffer memory such 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 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 prescan, MR data is acquired and used to calibrate the pulse sequence executed by the pulse sequence server 20. Additionally, navigator signals may be acquired during the scan and used to adjust the operating parameters of the RF system 30 or the gradient system 28, or to control the view order for sampling k-space.

[0029] 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 a Fourier transform on the raw k-space MR data to generate a two-dimensional or three-dimensional image, applying filters to the reconstructed image, performing back-projection image reconstruction on the acquired MR data, generating functional MR images, and calculating motion or flow images.

[0030] In an exemplary embodiment, the images reconstructed by the data processing server 24 are transmitted back to the workstation 12 and stored at the workstation. In some embodiments, real-time images are stored in a database memory cache ( Figure 1 (not shown), from which the real-time images can be output 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 may be stored in a disk storage device 48 or a host database in the cloud. When such images have been reconstructed and transmitted 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 the images to other facilities via a network.

[0031] A composite MR image can be reconstructed using processes such as Fourier transform, based on the I quadrature MR signal and the Q quadrature MR signal. The composite MR image is an MR image in which each pixel has a complex number representation, the complex number having a real component and an imaginary component where (x,y) is the position of the pixel in the image. The magnitude of the composite MR image (referred to as the magnitude image) is generated as A phase image, i.e., the phase of the composite MR image, can also be generated and used, where the phase The real image is an MR image, where the value at each pixel serves as the real component The imaginary image is an MR image, where the value at each pixel serves as the imaginary component

[0032] Compared to the magnitude image, the phase image is generally not used because the composite MR signal is typically contaminated by unwanted static and dynamic background phase variations caused by magnet and gradient imperfections, physiological noise (such as cardiac and respiratory motion), and the object's intrinsic susceptibility, especially exacerbated near the interface between air and tissue. Thus, the phase image is typically discarded and only the magnitude image is used. However, the magnitude operation changes the noise distribution from a central Gaussian distribution with zero expected value to a non-central chi-squared noise distribution with a positive expected value. Therefore, the magnitude operation causes overestimation of the signal and introduces significant bias in the derived quantitative maps, especially in applications with insufficient signal-to-noise ratio (SNR). Additionally, the magnitude operation irreversibly reduces the dynamic range of the image in low SNR applications, thus reducing the efficiency of SNR improvement by averaging multiple magnitude images. Averaging in the complex domain is not always feasible because inconsistent background phases can lead to signal cancellation or destructive interference.

[0033] Furthermore, certain types of information can be encoded in the image phase. As discussed above, the magnetic moment of the nucleus precesses around the magnetic field at the Larmor frequency of the nucleus. The Larmor frequency depends on the nucleus and the local magnetic field experienced by the nucleus. The phase information is derived from the time evolution of the Larmor frequency offset of the nucleus. The local magnetic field offset can be caused by different chemical substances (such as fat and water) or by local / non-local susceptibility. The local magnetic field can be affected by motion at the global or microscopic level (such as diffusion, gradients, and susceptibility). The phase image represents this frequency information of the voxels in the object. Thus, in applications for measuring phase-related parameters (such as phase contrast flow assessment and susceptibility quantification), the phase image is saved and used to fit the signal model and derive the maps. In these applications, the goodness of fit depends on the quality of the phase estimation. Therefore, when evaluating the performance of image processing, the comparison of composite images should include phase differences.

[0034] SSIM is a quantitative measure of the difference between two images. SSIM is known to better reflect the human visual perception of image differences compared to more conventional metrics such as mean squared error. SSIM has been used to evaluate the perceptual quality of images by computing the SSIM between the image to be evaluated and the corresponding distortion-free image. SSIM has also been used as a loss function for training neural networks in deep learning. A loss function is a function that measures the inference error of a neural network model with respect to a data point in a training dataset, where the inference error is the error between the output of the neural network model and the ground truth / target output. When used as a loss function, SSIM is computed between the network output image and the corresponding target image or ground truth image.

[0035] However, conventional SSIM is based on the assumption that images are real-valued and the resulting SSIM values for such images are real numbers between -1 and 1 (inclusive of the end values). If conventional SSIM is computed for a complex image by separately computing the real and imaginary components (or magnitude and phase), the resulting SSIM value will be complex. Complex SSIM is not used for comparison purposes because complex values are not intuitive and complex numbers cannot be ordered.

[0036] When computing SSIM for a complex MR image, the magnitude image is typically used. However, potentially important phase information is lost in the magnitude image. Additionally, when SSIM is used as a loss function in deep learning, if only the magnitude image is used, the opportunity to learn about the phase from the training data is missed, potentially resulting in sub-optimal results.

[0037] Taking into account the phase information of MR images and still outputting a real-valued SSIM, the systems and methods disclosed herein provide PS-SSIM. PS-SSIM includes a complex luminance comparison function, a complex contrast comparison function, and a complex structure comparison function such that at least one of these terms varies with the phase of the input image. The three terms can be multiplied by weights to derive PS-SSIM. The complex luminance comparison function, the complex contrast comparison function, and the complex structure comparison function are based on the complex mean, complex standard deviation, and complex variance of the pair of complex images being compared. PS-SSIM can be used to evaluate the quality of complex MR images in denoising, image restoration, and image alignment, and can also be used as a loss function for training a neural network that reconstructs or enhances the quality of a complex MR image by denoising and / or reducing or removing artifacts. As used herein, denoising includes reducing or removing noise. Denoising can result in reducing or removing artifacts. PS-SSIM also operates on non-standard weights for the luminance comparison function, the contrast comparison function, and the structure comparison function.

[0038] Figure 2Ais a flowchart of an exemplary image processing method 100. The method 100 is used to calculate the PS-SSIM of two composite images. In an exemplary embodiment, the method 100 includes receiving 102 two composite images. Each of the composite images is divided into image patches. For example, the size of each image patch is 11×11, where 11 is the number of pixels in a row or column of the image patch. The size of the image patch can be predetermined or based on user input or selection. During the calculation of the PS-SSIM, an 11×11 window is moved in each of the two images. The image patches can be overlapping or non-overlapping. Calculating the PS-SSIM through the image patches focuses on local similarity. An image patch in one image corresponds to an image patch at the same pixel position in the other image. In other words, a pair of image patches (one image patch in one image and the other image patch in the other image) moves in pairs during the calculation of the PS-SSIM. In some embodiments, the two composite images are not divided into image patches when calculating the PS-SSIM.

[0039] In an exemplary embodiment, the method 100 further includes calculating 104 the PS-SSIM between a pair of image patches for each pair of composite image patches from the two images. The calculated PS-SSIM values for the image patches are averaged 106 to provide a representative PS-SSIM value for the entire image.

[0040] Figure 2B shows a comparison of the conventional SSIM and PS-SSIM when measuring the similarity of two composite images 152-1, 152-2. The two composite images 152-1, 152-2 are Figure 2B shown with corresponding real images 154-1, 154-2, virtual images 156-1, 156-2, magnitude images 158-1, 158-2, and phase images 160-1, 160-2 of the two composite images. The composite images 152-1, 152-2 have the same magnitude images 158-1, 158-2. However, the phase images 160-1, 160-2 of the composite images 152-1, 152-2 are very different from each other. Since the conventional SSIM only considers the real-valued magnitude images 158-1, 158-2, the calculated conventional SSIM of the two composite images 152-1, 152-2 is 1, indicating that the composite images 152-1, 152-2 are the same. In contrast, the PS-SSIM considers the phase of the composite images 152-1, 152-2 and varies with the phase of the images. Therefore, the calculated PS-SSIM is 0.1049, indicating that the two composite images 152-1, 152-2 are very different from each other.

[0041] The PS-SSIM for two composite image patches or images x and y includes a luminance comparison function l, a contrast comparison function c, and a structure comparison function s, and is defined as:

[0042] PS-SSIM(x,y) = l(x,y) α c(x,y) β s(x,y) γ ,(1)

[0043] where α, β, and γ are weights for the luminance comparison function l, the contrast comparison function c, and the structure comparison function s. The choice of weights α, β, and γ depends on user interest or application purpose when emphasizing luminance, contrast, and structure comparison. In some embodiments, the weights α, β, and γ are equal. α, β, and γ can all be equal to 1, which is equivalent to an unweighted product. Alternatively, a particular comparison function can be weighted more heavily than other comparison functions. For example, a combination of α = 0.3, β = 1, and γ = 0.3 emphasizes the contrast comparison function. This combination of α, β, and γ can improve image sharpness when used as a loss function for training a neural network for MR image reconstruction from downsampled k-space data.

[0044] In PS-SSIM, the luminance comparison function, the contrast comparison function, the structure comparison function, and the weights α, β, and γ are all real-valued. Thus, PS-SSIM measures the similarity between two composite images or image patches and provides a real-valued indication. Different from the conventional SSIM that measures the similarity between real-valued images and is not affected by phase, PS-SSIM measures the similarity between two composite images and is affected by the phase of the images. In other words, when the phase of two images changes, the conventional SSIM does not change, while PS-SSIM changes with the phase. For example, for MR composite images, the magnitudes of these MR composite images are usually used, and the conventional SSIM is not affected by the phase in the MR composite images. However, the value of PS-SSIM changes when the phase of the MR composite images changes.

[0045] In an exemplary embodiment, in designing the luminance comparison function, the contrast comparison function, and the structure comparison function, conditions are set for these functions respectively. For example, the conditions are:

[0046] 1. Luminance comparison function:

[0047] a) is real-valued,

[0048] b) reaches its maximum value when the means of the image patches are equal and / or when the means of the real components of the image patches are equal and the means of the imaginary components of the image patches are equal, and

[0049] c) changes with the phase of the image patches.

[0050] 2. Contrast comparison function:

[0051] a) is real-valued,

[0052] b) reaches its maximum value when the standard deviations of the image patches are equal and / or when the standard deviations of the real components of the image patches are equal and the standard deviations of the imaginary components of the image patches are equal, and

[0053] c) varies with the phase of the image patch.

[0054] 3. Structure comparison function:

[0055] a) is real-valued,

[0056] b) reaches its maximum value when the real components of the image patches are linearly correlated and the imaginary components of the image patches are linearly dependent and / or when the real components of the image patches are completely positively correlated and the imaginary components of the image patches are completely positively correlated, and

[0057] c) varies with the phase of the image patch.

[0058] The real components x and y of two image patches are linearly dependent when, for each pixel in the image patch, the real component Re(x) of the first image patch x is a linear function of the real component Re(y) of the second image patch y at the same pixel position. That is, Re(x) = a1 * Re(y) + b1, where a1 and b1 are constants. Similarly, the imaginary components of image patches x and y are linearly dependent when, for each pixel in the image patch, the imaginary component Im(x) of the first image patch x is a linear function of the imaginary component Im(y) of the second image patch y at the same pixel position. That is, Im(x) = a2 * Im(y) + b2, where a2 and b2 are constants. a1 and a2 are not necessarily the same. b1 and b2 are not necessarily the same.

[0059] When the cross-correlation value between the real component Re(x) of the first image patch x and the real component Re(y) of the second image patch y is 1, the real components of the two image patches x and y are completely positively correlated. That is, COV(Re(x), Re(y)) = σ Re(x) σ Re(y) , where COV(Re(x), Re(y)) is the variance between the real components Re(x) and Re(y), and σ Re(x) and σ Re(y) are the variances of the real components Re(x) and Re(y) respectively. When the (normalized) cross-correlation value between the imaginary component Im(x) of the first image patch x and the imaginary component Im(y) of the second image patch is 1, the imaginary components of the two image patches x and y are completely positively correlated. That is, COV(Im(x), Im(y)) = σ Im(x) σIm(y) , where COV(Im(x), Im(y)) is the variance between the imaginary components Im(x) and Im(y), and σ Im(x) and σ Im(y) are the variances of the imaginary components Im(x) and Im(y), respectively.

[0060] For the structure comparison function, more conditions can be added. For example, the following condition 3.d can be added: the structure comparison function reaches its maximum value when the image patches are linearly dependent and / or when the image patches are completely positively correlated. Two image patches x and y are linearly dependent when for each pixel in the image patch, each pixel of the first image patch x is a linear function of the pixel of the second image patch y at the same pixel position. That is, Re(x) + i Im(x) = a3 * (Re(y) + i Im(y)) + b3, where a3 and b3 are constants. a3 may not be the same as a1 or a2. b3 may not be the same as b1 or b2. Two image patches x and y are completely positively correlated when the (normalized) cross-correlation value between the first image patch x and the second image patch y is 1. That is, COV(x,y)) = σ x σ y , where COV(x,y) is the variance between the two image patches x and y, and σ x and σ y are the variances of the image patches x and y, respectively. An exemplary calculation method for the covariance and variance of the composite image is described later in this document.

[0061] In another example, the additional condition is that if the image patch is real-valued, then PS-SSIM is equal to the conventional SSIM. For the luminance comparison function, the contrast comparison function, and the structure comparison function, conditions 1.a, 2.a, and 3.a are used to keep the comparison functions real-valued, even when the image is complex-valued, so that PS-SSIM is a real-valued direct quantitative indication of the similarity between images. Conditions 1.b, 2.b, 3.b, and 3.d indicate that these comparison functions are similarity metrics that measure the degree of similarity between image patches and reach their maximum values when the image patches are most similar under those conditions. Conditions 1.c, 2.c, and 3.c are used to keep these comparison functions sensitive to the phase of the image patches. If these comparison functions are based only on the magnitude of the complex-valued image patches, the comparison functions will be independent of the phase, and conditions 1.c, 2.c, and 3.c will not be satisfied. The value of the luminance comparison function can be scaled or shifted to be within [0,1].

[0062] In some embodiments, because MR phase images tend to be noisy and have low levels of signal and random phase, PS-SSIM may overemphasize the dissimilarity between noise and phase by considering only the phase, thus providing an unreliable indication of the similarity between composite images. Additionally, due to these characteristics of the phase of MR images, training a neural network model using a loss function that considers only the phase, such as PS-SSIM, can become unstable. Therefore, PS-SSIM considers both the real and imaginary components of the image or both the magnitude and phase of the image.

[0063] Exemplary PS-SSIM

[0064] Let μ (·) 、σ (·) and σ (·)(·) represent the mean, standard deviation, and covariance, respectively. That is, and are the means of the image patches x and y, respectively, where N is the number of pixels in the image patch. are the standard deviations of the image patches x and y, respectively, where |·| represents the magnitude or absolute value, and is the covariance of the image patches x and y, where (·) * represents the complex conjugate.

[0065] Luminance comparison function

[0066] A conventional luminance comparison function is given as: for c1 a positive constant, For example, c1 can be set to (k1L) 2 , where k1 = 0.01 and L is the dynamic range. However, if x and y are complex-valued, the conventional luminance comparison function does not satisfy condition 1.a because μ x and μ y can be complex-valued. Even if the conventional luminance comparison function is modified by using the magnitude images |x| and |y| to satisfy condition 1.a, as in the following

[0067]

[0068] where μ |x| and μ |y| are the means of the magnitude images |x| and |y|, respectively, condition 1.c is not satisfied due to loss of phase information, i.e., the luminance comparison function is independent of the phase of the images x and y.

[0069] An exemplary luminance comparison function that satisfies conditions 1.a - 1.c is:

[0070]

[0071] where Re{·} and Im{·} represent the real and imaginary components, respectively. It can be shown that this luminance comparison function satisfies Condition 1.b, as follows. It should be noted that where if μ x = μ y , the equation holds. Thus, where if μ x = μ y , the equation holds. If μ x = μ y , it is sufficient to prove that this luminance comparison function achieves its maximum value of 1.

[0072] Another exemplary luminance comparison function that satisfies Conditions 1.a - 1.c is:

[0073]

[0074] Yet another exemplary luminance comparison function that satisfies Conditions 1.a - 1.c is:

[0075]

[0076] If μ x = μ y or μ x = -μ y , the maximum value of this luminance comparison function is achieved.

[0077] Yet another exemplary luminance comparison function that satisfies Conditions 1.a - 1.c is:

[0078]

[0079] If μ x = μ y , μ x = -μ y , or , the maximum value of this luminance comparison function is achieved.

[0080] More exemplary luminance comparison functions that satisfy Conditions 1.a - 1.c include:

[0081]

[0082] And

[0083]

[0084] Contrast comparison function

[0085] An exemplary contrast comparison function that satisfies Conditions 2.a - 2.c is:

[0086]

[0087] wherein and c2 is a positive constant. For example, c2 can be set to (k2L) 2 and k2 = 0.03. It can be noted that and thus wherein if σ x = σ y , the equation holds. If σ x = σ y , then this contrast comparison function achieves its maximum value of 1.

[0088] Another exemplary comparison function that satisfies Conditions 2.a - 2.c is:[[]]

[0089]

[0090] If σ Re{x} = σ Re{y} and σ Im{x} = σ Im{y} , then the maximum value of this contrast comparison function is achieved.

[0091] If only the magnitudes |x| and |y| of the image patch are adopted and used to calculate a conventional contrast comparison function, as in the following

[0092]

[0093] then Condition 2.c is not satisfied.

[0094] Structure comparison function

[0095] If only the magnitudes |x| and |y| of the image patch are adopted and used to calculate a conventional structure comparison function, as in the following

[0096]

[0097] then Condition 3.c is not satisfied.

[0098] An exemplary structure comparison function that satisfies Conditions 3.a - 3.d is:[[]]

[0099]

[0100] where c3 is usually set to c2 / 2. It can be noted from the Cauchy - Schwarz inequality that |σ xy | ≤ σ x σ y , where for some constant k, the inequality holds if x = ky. This structure comparison function satisfies Conditions 3.b and 3.d.

[0101] Another exemplary structural comparison function that satisfies Conditions 3.a - 3.d is

[0102]

[0103] For some k > 0, if x = ky, then this structural comparison function achieves its maximum value.

[0104] Yet another exemplary structural comparison function that satisfies Conditions 3.a - 3.d is

[0105] Yet another exemplary structural comparison function that satisfies Conditions 3.a - 3.c is

[0106]

[0107] Other exemplary structural comparison functions include:

[0108]

[0109]

[0110]

[0111]

[0112] PS - SSIM(x,y) = l(x,y) α c(x,y) β s(x,y) γ And And are exemplary phase - sensitive SSIMs that satisfy Conditions 1 - 3.

[0113] Figure 3AIt is a schematic diagram of an exemplary image processing system 200. In an exemplary embodiment, the system 200 includes an image processing computing device 202 configured to process composite images or data. The computing device 202 further includes a neural network model 204. The system 200 may include a second image processing computing device 203. The second image processing computing device 203 can be used to train the neural network model 204, and then the image processing computing device 202 can use the trained neural network model 204. The second image processing computing device 203 can be the same computing device as the image processing computing device 202, such that the training and use of the neural network model 204 are performed on one computing device. Alternatively, the second image processing computing device 203 can be a computing device separate from the image processing computing device 202, such that the training and use of the neural network model 204 are performed on separate computing devices. The image processing computing device 202 can be included in the workstation 12 of the MRI system 10 or can be included in a separate computing device that communicates with the workstation 12.

[0114] Figure 3B It is a flowchart of an exemplary method 250 for processing a composite image using PS-SSIM. In an exemplary embodiment, the method 250 includes receiving 252 a training data set. The training data set includes a pair of corrupted composite data and an original composite image. Each original composite image corresponds to one of the corrupted composite data. The corrupted composite data can be a corrupted composite image or composite raw data from which a composite image is reconstructed. The corresponding original composite image is an improved image of the corrupted image or a reconstructed image of the corrupted composite data. For example, compared with the corresponding original composite image, the corrupted composite image or the composite image directly reconstructed from the corrupted composite data has increased noise, artifacts, or distortion and / or reduced resolution, contrast, or structure and any combination thereof.

[0115] In one example, the corrupted composite data is the MR signal of a subject from undersampled k-space. As used herein, a subject is a human, an animal, a phantom, or any subject from which an MR image is acquired. The MR signal is used to reconstruct the MR image of the subject. The corresponding original image is the MR image of the subject based on fully sampled k-space data. The corrupted composite data can be generated by downsampling the fully sampled k-space data. In another example, the corrupted composite data is a noisy composite image, and the original composite image is the corresponding composite image with reduced noise or no noise. The corrupted composite data can be generated by adding noise to the original composite image. In yet another example, the corrupted composite data is an MR image of a subject, such as an MR head image including motion artifacts, and the corresponding original composite image is an MR head image with reduced motion or no motion. The corrupted composite data can be generated by adding inconsistencies generated by simulating motion to the original image.

[0116] In an exemplary implementation, method 250 includes training 253 a neural network model 204. The neural network model 204 includes one or more transformations, such as image reconstruction, image alignment, denoising, or image restoration. For example, the neural network model is configured to reconstruct an MR signal into an MR image, reduce noise in the MR image, or align the MR image. Training 253 includes inputting 254 corrupted composite data into the neural network model. Training 253 also includes setting 256 the original composite image as the target output of the neural network model. Training 253 further includes processing 258 the corrupted composite data using the neural network model to derive an output composite image of the neural network model. For example, the output composite image may reconstruct an MR image based on the corrupted composite data, a denoised MR image of the corrupted composite data, or an aligned MR image. Additionally, training 253 includes comparing 260 the output composite image with the target output by calculating PS-SSIM between each output composite image in the output composite image and the corresponding target output of each output composite image. The PS-SSIM may be any one of the exemplary PS-SSIMs described above. The PS-SSIM serves as a cost function or part of a cost function for the neural network model 204. The cost function measures how well the neural network performs relative to all training inputs in the training dataset compared to the target output. The cost function may be the sum of loss functions over the training dataset. The cost function is a function of the training inputs, target outputs, and parameters (such as the weights of neurons in the neural network model) of the neural network model. Training 253 also includes adjusting 262 the neural network model. For example, the weights of the neural network model may be adjusted to optimize the cost function. The trained neural network model 204 can then be used to process composite images or data.

[0117] Figure 3CFIG. 0 is a flow chart of another exemplary method 270 for processing a composite image using PS-SSIM. Different from method 250, method 270 processes composite data or images using the trained neural network model 204. In an exemplary embodiment, method 270 includes receiving 272 coarse composite data. The coarse composite data can be a corrupted composite image or composite raw data from which a composite image is reconstructed. For example, the coarse composite data can be composite k-space data or a composite MR image. The coarse composite data can be an MR signal of a subject obtained by downsampling the k-space. In another example, the coarse composite data is a noisy composite image. In yet another example, the coarse composite data is an MR image of a subject obtained when the subject is moving, such as an MR head image. Method 270 further includes processing 274 the coarse composite data using the trained neural network model 204. The neural network model is trained using method 250. Method 270 also includes deriving 276 a predicted image based on the processing from the coarse composite data. The predicted image can be an output image of the neural network model 204, with the coarse composite data as the input. Compared with the coarse composite data or a composite image directly reconstructed from the coarse composite data, the predicted composite image has reduced noise, artifacts, or distortion and / or increased resolution, contrast, or structure and any combination thereof. In addition, method 270 includes outputting 278 the predicted image.

[0118] Figure 3D FIG. 4 is a comparison between the neural network model 204 using PS-SSIM as a loss function and a neural network model using an L1 loss function (referred to as the L1 neural network model), where the L1 loss function is the sum of the absolute differences between the ground truth and the predicted values inferred by the neural network model. The inputs of both the neural network model 204 and the L1 neural network model are downsampled k-space data, where the k-space is not sampled at all k-space positions corresponding to the desired image matrix size. In this example, the k-space data is downsampled using variable density Poisson disk sampling at the peripheral region of the k-space, and 1% of the k-space region such as the k-space region around the k-space center is fully sampled. The net downsampling factor is 10. The image matrix size is 256x256. Both the neural network model 204 and the L1 neural network model are densely connected iterative networks configured to reconstruct an image from the downsampled k-space data. The exemplary PS-SSIM for training the neural network model 204 is as follows:

[0119] PS-SSIM(x,y) = l(x,y) α c(x,y) β s(x,y) γ ,

[0120] where α = 0.3, β = 1, γ = 0.3,

[0121]

[0122] And

[0123]

[0124] In Figure 3D Image 292 is an image reconstructed based on a fully sampled image, where the image is based on MR signals or k-space data acquired by fully sampling k-space. Image 292 is the ground truth. Image 294 is the image output by neural network model 204. Image 296 is the image output by the L1 neural network model. Image 294 has recognizably better image quality compared to Image 296, where Image 294 is clearer, has higher contrast, and finer structural details compared to Image 296. Additionally, Image 294 is artifact-free, where Image 294 has reduced artifacts or no recognizable artifacts compared to Image 296, where the cerebellum in Image 296 is recognizably blurred.

[0125] Neural network model 204 is compared with neural network models trained using other loss functions (such as L2, conventional SSIM, perceptual loss function, or generative adversarial network (GAN) loss function). The output image of neural network model 204 is clearer and has higher contrast compared to the output images of other neural network models that perform the same function and have the same input. Neural network model 204 is also more robust compared to such other neural models and does not introduce artifacts.

[0126] Image denoising

[0127] Phase-sensitive SSIM (PS-SSIM) can be used to denoise complex-valued images without using a neural network model. An example of an image denoising algorithm is non-local means (NLM). The NLM algorithm based on phase-sensitive SSIM is described below.

[0128] Assume v is the complex-valued noisy image to be denoised. The denoised image u can be calculated as:

[0129]

[0130] where u i represents pixel i of image u, v j represents pixel j of image v and w ij is the weight. The weight w ij can be calculated as:

[0131] w ij = PS-SSIM(v (i) , v (j) ),

[0132] where PS - SSIM(·,·) is the phase - sensitive SSIM, and v (i) is an image patch around the center of pixel i obtained from the image v, and v (j) is an image patch around the center of pixel j obtained from the image v. If pixels i and j are far apart, the weight w ij can be set to 0. For example, this is equivalent to calculating:

[0133]

[0134] where N i represents the search window, which is a set of pixels in a square around the center of pixel i.

[0135] If the conventional SSIM is used, the weight is calculated as w ij = SSIM(|v (i) |,|v (j) |), where SSIM(·,·) is the conventional SSIM, |v (i) | is the magnitude image of v (i) and |v (j) | is the magnitude image of v (j) . In this case, the phases of the image patches v (i) and v (j) are ignored when calculating the weight w ij . Therefore, the denoising of complex - valued images may not be optimal because the phase information is discarded. In contrast, PS - SSIM takes into account the phase information, resulting in better results.

[0136] The procedure for NLM image denoising of complex - valued images using PS - SSIM is as follows. Given a complex - valued noisy image v to be denoised. For each pixel i, an image patch v (i) from the image v around the center of pixel i is adopted. For each pixel j in the search window N i around the center of pixel i, an image patch v (j) around the center of pixel j is adopted. The weight w (i) is calculated by computing PS - SSIM for the image patches v (j) and v ij . The denoised image pixel i, u ij , is calculated by computing the weighted average of the noisy image v over the search window N i using the weight w i , that is:

[0137]

[0138] including the pixel u iThe denoised image u is displayed.

[0139] Image restoration

[0140] Phase-sensitive SSIM (PS-SSIM) can be used for image restoration. An example of an image restoration algorithm is a dictionary-based sparse representation algorithm. A dictionary-based sparse representation algorithm for restoring complex-valued images using phase-sensitive SSIM is described below.

[0141] Image restoration based on sparse representation can be formulated as the following optimization problem:

[0142]

[0143] where Y is a complex-valued distorted image (e.g., blurred or downsampled), is the complex-valued restored image, Ψ is an n×k matrix containing the dictionary (e.g., based on complex wavelet transform or discrete Fourier transform), and k > n, R ij is the matrix for extracting the (ij)-th block from the image, is the sparse vector of the coefficients of the (ij)-th block, S(·,·) is the phase-sensitive SSIM, λ and μ ij are regularization parameters, W is the image obtained from the combined image blocks and D is the distortion operator (e.g., blur or downsampling).

[0144] Given the complex-valued distorted image Y, the complex-valued restored image can be obtained as follows. Initialize using the distorted image Y. The coefficients are calculated using orthogonal matching pursuit. The restored image is updated using the gradient ascent algorithm. Calculate the coefficients and update the restored image Repeat for a predetermined number of times or until a certain convergence criterion is met. The restored image is displayed.

[0145] Image alignment

[0146] Phase-sensitive SSIM (PS-SSIM) can be used for image alignment of complex-valued images.

[0147] Assume that the complex-valued image X is deformed to match the complex-valued target image T. Assume M θ is the deformation operator, where θ is the deformation parameter. The deformation operator can model rigid body or non-rigid body deformations. Image alignment is equivalent to the following optimization problem:

[0148]

[0149] where S(·, ·) is the phase-sensitive SSIM, and R is a regularization function for deformation. Image alignment can be performed as follows. The complex-valued target image T and the image X to be aligned with T are given. The deformation parameters are calculated using a gradient ascent algorithm The image X is deformed using the deformation parameters as and is displayed.

[0150] Figure 4A An exemplary artificial neural network model 204 used in the system 200 is depicted. The exemplary neural network model 204 includes neuron layers 502, 504-1 to 504-n, and 506, which include an input layer 502, one or more hidden layers 504-1 to 504-n, and an output layer 506. Each layer can include any number of neurons, that is, Figure 4A q, r, and n in Figure 4A can be any positive integers. It should be understood that neural networks with structures and configurations different from those

[0151] depicted can be used to implement the methods and systems described herein.

[0151] In an exemplary embodiment, the input layer 502 can receive different input data. For example, the input layer 502 includes 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 the edges of the training image, and so on. The input layer 502 can include thousands or more inputs. In some embodiments, the number of elements used by the neural network model 204 changes during the training process, and if, for example, it is determined during the execution of the neural network that some neurons have less relevance, those neurons are bypassed or ignored.

[0152] In an exemplary embodiment, each neuron in the hidden layers 504-1 to 504-n processes one or more inputs from the input layer 502 and / or one or more outputs from neurons in one of the previous hidden layers to generate a decision or output. The output layer 506 includes one or more outputs, each of which indicates a label, a confidence factor, a weight describing the input, and / or an output image. However, in some embodiments, in addition to or instead of the output from the output layer 506, the output of the neural network model 204 is obtained from the hidden layers 504-1 to 504-n.

[0153] In some embodiments, each layer has a discrete identifiable function with respect to the input data. For example, if n equals 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 can correspond to aspects considered to be strongly deterministic, then to those considered to be of medium importance, and finally to those considered to be less relevant.

[0154] In other embodiments, these layers are not clearly depicted in terms of the functionality they perform. For example, two or more of the hidden layers 504-1 to 504-n may share decisions related to the markings, where no single layer makes an independent decision about the markings.

[0155] Figure 4B An exemplary neuron 550 corresponding to the neuron labeled "1,1" in the hidden layer 504-1 in Figure 4A is depicted. Each input to the neuron 550 (e.g., Figure 4A the inputs in the input layer 502 in p is weighted such that the inputs a1 to a p .

[0156] In some embodiments, some inputs lack a clear weight or have a weight 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, which is input to a function 520 labeled f 1,1 (z1). The function 520 is any suitable linear or non-linear function. As Figure 4B depicted, the function 520 produces multiple outputs, which can be provided to neurons in subsequent layers or used as the output of the neural network model 204. For example, the output may correspond to an index value of a list of labels or may be a computed value that is used as an input to a subsequent function.

[0157] It should be understood that the structure and functionality of the depicted neural network model 204 and neuron 550 are for illustrative purposes only and that there are other suitable configurations. For example, the output of any given neuron may depend not only on values determined by past neurons but also on future neurons.

[0158] The neural network model 204 may include a convolutional neural network (CNN), a deep learning neural network, a reinforcement or enhancement 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 may be used. In supervised machine learning, the processing element may be provided with exemplary inputs and their associated outputs, and may attempt to discover the general rules that map the inputs to the outputs, such that when subsequent novel inputs are provided, the processing element can accurately predict the correct outputs based on the discovered rules. Unsupervised machine learning programs may be used to train the neural network model 204. In unsupervised machine learning, the processing element may need to find its own structure in the unlabeled exemplary inputs. Machine learning may involve identifying and discerning patterns in existing data in order to facilitate predictions about subsequent data. A model may be created based on the exemplary inputs in order to make effective and reliable predictions about novel inputs.

[0159] In addition or alternatively, the machine learning program may be trained by inputting a sample data set or certain data such as images, object statistics, and information into the program. The machine learning program may use deep learning algorithms, which may focus primarily on pattern recognition and may be trained after processing multiple examples. The machine learning program may include, alone or in combination, Bayesian program learning (BPL), speech recognition and synthesis, image or object recognition, optical character recognition, and / or natural language processing. The machine learning program may also include natural language processing, semantic analysis, automated reasoning, and / or machine learning.

[0160] Based on these analyses, the neural network model 204 can learn how to identify characteristics 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.

[0161] The computing devices 202, 203, and the workstation 12 described herein can be any suitable computing device 800 and the software implemented therein. Figure 5 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 input 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 touchscreen), a gyroscope, an accelerometer, a position detector, and / or an audio input interface (e.g., including a microphone).

[0162] In addition, in this exemplary embodiment, the computing device 800 includes a presentation interface 807 that presents information such as input events and / or verification results to the user. The presentation interface 807 may also include a display adapter 808 coupled to at least one display device 810. More specifically, in the 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 presentation interface 807 may include an audio output device (e.g., an audio adapter and / or speakers) and / or a printer.

[0163] 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 presentation interface 807, and the memory device 818 via a system bus 820. In the exemplary embodiment, the processor 814 communicates with the user, such as by prompting the user via the presentation interface 807 and / or by receiving user input via the user interface 804. The term "processor" generally refers to any programmable system, including systems and microcontrollers, reduced instruction set computers (RISC), complex instruction set computers (CISC), application specific integrated circuits (ASIC), programmable logic circuits (PLC), and any other circuit or processor capable of performing the functions described herein. The above examples are merely exemplary and are not intended to limit the definition and / or meaning of the term "processor" in any way.

[0164] In the 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), solid state disks, and / or hard disks. In the exemplary embodiment, the memory device 818 stores, but is not limited to, application source code, application object code, configuration data, additional input events, application states, assertion statements, verification results, and / or any other type of data. In the 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.

[0165] In the exemplary embodiment, the processor 814 may be programmed by encoding operations using one or more executable instructions and providing the executable instructions in the memory device 818. In the exemplary embodiment, the processor 814 is programmed to select a plurality of measurement results received from the data acquisition device.

[0166] 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 aspects of the present invention described and / or shown herein. Unless otherwise specified, the order of execution or performance of the operations in the embodiments of the present invention shown and described herein is not required. That is, unless otherwise specified, these 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 aspects of the present invention.

[0167] Figure 6 An exemplary configuration of a server computing device 1001 is shown, such as cloud-based image processing computing devices 202, 203. The server computing device 1001 also includes a processor 1005 for executing instructions. For example, the instructions may be stored in the memory region 1030. The processor 1005 may include one or more processing units (e.g., in a multi-core configuration).

[0168] The processor 1005 is operatively coupled to a communication interface 1015 such that the server computing device 1001 can communicate with a remote device or another server computer device 1001 to receive and output data and / or commands.

[0169] The processor 1005 may also be operatively coupled to a storage device 1034. The storage device 1034 is any computer-operated hardware suitable for storing and / or retrieving data such as but not limited to wavelength change, temperature, humidity, carbon dioxide level, and / or proximity. In some embodiments, the storage device 1034 is integrated in the server computing device 1001. For example, the server computing device 1001 may include one or more hard disk drives as the storage device 1034. In other embodiments, the storage device 1034 is external to the server computer device 1001 and may be accessed by multiple server computing devices 1001. For example, the storage device 1034 may include multiple storage units (such as hard disks and / or solid state disks) in a redundant array of inexpensive disks (RAID) configuration. The storage device 1034 may include a storage area network (SAN) and / or a network attached storage (NAS) system.

[0170] In some embodiments, processor 1005 is operatively coupled to storage device 1034 via storage interface 1020. Storage interface 1020 is any component capable of providing processor 1005 access to storage device 1034. Storage interface 1020 may include, for example, an Advanced Technology Attachment (ATA) adapter, a Serial ATA (SATA) adapter, a Small Computer System Interface (SCSI) adapter, a RAID controller, a SAN adapter, a network adapter, and / or any component that provides processor 1005 access to storage device 1034.

[0171] At least one technical effect of the systems and methods described herein includes: (a) providing PS-SSIM that takes into account the phase of an image, (b) training a neural network model using PS-SSIM as a loss function, and (c) improving the image quality of processed composite images.

[0172] Exemplary embodiments of systems and methods for image processing have been described in detail above. These systems and methods are not limited to the specific embodiments described herein, but the components of the systems and / or the operations of the methods can be used independently and separately from other components and / or operations described herein. Additionally, the described components and / or operations can also be defined in other systems, methods, and / or devices, or used in combination with other systems, methods, and / or devices, and are not limited to being practiced only with the systems described herein.

[0173] Although specific features of various embodiments of the present invention may be shown in some figures but not in others, this is for convenience only. In accordance with the principles of the present invention, any feature of a figure can be referenced and / or claimed in combination with any feature of any other figure.

[0174] This written description uses examples to disclose the present invention, including the best mode, and also enables those skilled in the art to practice the present invention, including making and using any device or system and performing any included method. The patent scope of the present invention is defined by the claims, and may include other examples that occur to those skilled in the art. If such other examples have structural elements that are not different from the literal language of the claims, or if they include equivalent structural elements with only minor differences from the literal language of the claims, then such other examples are intended to fall within the scope of the claims.

Claims

1. A computer-implemented method for processing a composite magnetic resonance image, the method comprising: Receive a pair of damaged composite data and an original composite image, where the original composite image corresponds to the damaged composite data; And Use the pair of damaged composite data and the original composite image to train a neural network model by: Input the damaged composite data into the neural network model; Set the original composite image as the target output of the neural network model; Use the neural network model to process the damaged composite data to derive an output composite image of the damaged composite data; Compare the output composite image with the target output by calculating the phase-sensitive structural similarity index measure between each output composite image in the output composite image and the corresponding target composite image of each output composite image, where the phase-sensitive structural similarity index measure is real-valued and varies with the phase of the output composite image and the phase of the target composite image and is obtained by multiplying the composite luminance comparison function, the composite contrast comparison function, and the composite structure comparison function with their respective weights; And Adjust the neural network model based on the comparison.

2. The method according to claim 1, wherein the phase-sensitive structural similarity index measure comprises a luminance comparison function that varies with the phase of the output composite image and the phase of the target composite image.

3. The method according to claim 2, wherein the luminance comparison function reaches a maximum when the mean of an image patch in the output composite image is equal to the mean of the corresponding image patch in the target composite image.

4. The method according to claim 2, wherein the luminance comparison function reaches a maximum when the mean of the real component of an image patch in the output composite image is equal to the mean of the real component of the corresponding image patch in the target composite image, and the mean of the imaginary component of the image patch in the output composite image is equal to the mean of the imaginary component of the corresponding image patch in the target composite image.

5. The method according to claim 1, wherein the phase-sensitive structural similarity index measure comprises a contrast comparison function that varies with the phase of the output composite image and the phase of the target composite image.

6. The method according to claim 5, wherein the contrast comparison function reaches a maximum when the standard deviation of an image patch in the output composite image is equal to the standard deviation of the corresponding image patch in the target composite image.

7. The method according to claim 5, wherein the contrast comparison function reaches a maximum when the standard deviation of the real component of an image patch in the output composite image is equal to the standard deviation of the real component of the corresponding image patch in the target composite image, and the standard deviation of the imaginary component of the image patch in the output composite image is equal to the standard deviation of the imaginary component of the corresponding image patch in the target composite image.

8. The method according to claim 1, wherein the phase-sensitive structural similarity index measure comprises a structure comparison function that varies with the phase of the output composite image and the phase of the target composite image.

9. The method according to claim 8, wherein the structural comparison function reaches a maximum value when the real component of the image patch in the output composite image linearly depends on the real component of the image patch in the target composite image, and the imaginary component of the image patch in the output composite image linearly depends on the imaginary component of the image patch in the target composite image.

10. The method according to claim 8, wherein the structural comparison function reaches a maximum value when the image patch in the output composite image linearly depends on the image patch in the target composite image.

11. The method according to claim 8, wherein the structural comparison function reaches a maximum value when the real component of the image patch in the output composite image is completely positively correlated with the real component of the image patch in the target composite image, and the imaginary component of the image patch in the output composite image is completely positively correlated with the imaginary component of the image patch in the target composite image.

12. The method according to claim 8, wherein the structural comparison function reaches a maximum value when the image patch in the output composite image is completely positively correlated with the image patch in the target composite image.

13. An image processing system, the image processing system includes an image processing computing device, the image processing computing device includes at least one processor, the at least one processor communicates with at least one memory device, and the at least one processor is programmed to: Receive a pair of corrupted composite data and an original composite image, the original composite image corresponding to the corrupted composite data; and Use the pair of corrupted composite data and the original composite image to train a neural network model in the following manner: Input the corrupted composite data into the neural network model; Set the original composite image as the target output of the neural network model; Use the neural network model to process the damaged composite data to derive an output composite image of the damaged composite data; Compare the output composite image with the target output by calculating the phase-sensitive structural similarity index measure between each output composite image in the output composite image and the corresponding target composite image of each output composite image, where the phase-sensitive structural similarity index measure is real-valued and varies with the phase of the output composite image and the phase of the target composite image and is obtained by multiplying the composite luminance comparison function, the composite contrast comparison function, and the composite structure comparison function with their respective weights; And Adjust the neural network model based on the comparison.

14. The system according to claim 13, wherein the phase-sensitive structural similarity index measure includes a luminance comparison function, and the luminance comparison function varies with the phase of the output composite image and the phase of the target composite image.

15. The system according to claim 14, wherein the luminance comparison function reaches a maximum value when the mean value of the image patch in the output composite image is equal to the mean value of the image patch in the target composite image.

16. The system according to claim 13, wherein the phase-sensitive structure similarity index measure includes a contrast comparison function that varies with the phase of the output composite image and the phase of the target composite image.

17. The system according to claim 16, wherein the contrast comparison function reaches a maximum when the standard deviation of an image patch in the output composite image is equal to the standard deviation of the image patch in the target composite image.

18. The system according to claim 13, wherein the phase-sensitive structure similarity index measure includes a structure comparison function that varies with the phase of the output composite image and the phase of the target composite image.

19. The system according to claim 18, wherein the structure comparison function reaches a maximum when the real component of an image patch in the output composite image linearly depends on the real component of the image patch in the target composite image, and the imaginary component of the image patch in the output composite image linearly depends on the imaginary component of the image patch in the target composite image.

20. An image processing system, the image processing system including an image processing computing device, the image processing computing device including at least one processor, the at least one processor communicating with at least one memory device, and the at least one processor being programmed to: Receive coarse composite data, the coarse composite data being composite raw data for a damaged composite image or a reconstructed composite image therefrom; Process the coarse composite data using a neural network model, wherein the neural network model is trained using a pair of damaged composite data and an original composite image, wherein the damaged composite data is used as an input and the original composite image is used as a target output, and a loss function for comparing the output of the neural network model and the target output of the neural network model includes a phase-sensitive structure similarity index measure between each output composite image in the output composite image and the corresponding target composite image of each output composite image, wherein the phase-sensitive structure similarity index measure is real-valued and varies with the phase of the output composite image and the phase of the target composite image and is obtained by multiplying a composite luminance comparison function, a composite contrast comparison function, and a composite structure comparison function after assigning respective weights thereto; Generate a predicted image of the coarse composite data based on the processing; and Output the predicted image.

Images