CN117611453A - Nuclear magnetic resonance image super-resolution recovery method and model construction method - Google Patents
Nuclear magnetic resonance image super-resolution recovery method and model construction method Download PDFInfo
- Publication number
- CN117611453A CN117611453A CN202311603891.5A CN202311603891A CN117611453A CN 117611453 A CN117611453 A CN 117611453A CN 202311603891 A CN202311603891 A CN 202311603891A CN 117611453 A CN117611453 A CN 117611453A
- Authority
- CN
- China
- Prior art keywords
- magnetic resonance
- nuclear magnetic
- resolution
- image
- model
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000005481 NMR spectroscopy Methods 0.000 title claims abstract description 80
- 238000000034 method Methods 0.000 title claims abstract description 79
- 238000011084 recovery Methods 0.000 title claims abstract description 12
- 238000010276 construction Methods 0.000 title abstract description 6
- 238000009792 diffusion process Methods 0.000 claims abstract description 86
- 230000000750 progressive effect Effects 0.000 claims abstract description 49
- 238000005070 sampling Methods 0.000 claims abstract description 34
- 238000006731 degradation reaction Methods 0.000 claims abstract description 28
- 230000015556 catabolic process Effects 0.000 claims abstract description 23
- 238000012549 training Methods 0.000 claims abstract description 20
- 230000008569 process Effects 0.000 claims description 29
- 230000006870 function Effects 0.000 claims description 22
- 239000011159 matrix material Substances 0.000 claims description 22
- 230000000873 masking effect Effects 0.000 claims description 11
- 230000006872 improvement Effects 0.000 claims description 10
- 230000005653 Brownian motion process Effects 0.000 claims description 6
- 238000013461 design Methods 0.000 claims description 5
- 238000009826 distribution Methods 0.000 claims description 5
- ORILYTVJVMAKLC-UHFFFAOYSA-N Adamantane Natural products C1C(C2)CC3CC1CC2C3 ORILYTVJVMAKLC-UHFFFAOYSA-N 0.000 claims description 4
- 238000004364 calculation method Methods 0.000 claims description 2
- 238000005457 optimization Methods 0.000 claims description 2
- 238000013421 nuclear magnetic resonance imaging Methods 0.000 abstract description 9
- 238000002595 magnetic resonance imaging Methods 0.000 description 5
- 238000013135 deep learning Methods 0.000 description 4
- 210000004556 brain Anatomy 0.000 description 2
- 238000003745 diagnosis Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000003759 clinical diagnosis Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 230000007850 degeneration Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 230000005865 ionizing radiation Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012805 post-processing Methods 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 210000004872 soft tissue Anatomy 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformations in the plane of the image
- G06T3/40—Scaling of whole images or parts thereof, e.g. expanding or contracting
- G06T3/4053—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10072—Tomographic images
- G06T2207/10088—Magnetic resonance imaging [MRI]
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Magnetic Resonance Imaging Apparatus (AREA)
Abstract
The invention discloses a nuclear magnetic resonance image super-resolution recovery method and a model construction method, which can recover high-quality high-resolution nuclear magnetic resonance images from low-resolution nuclear magnetic resonance images acquired in nuclear magnetic resonance imaging equipment. The model construction method comprises a forward diffusion process structure of a progressive reconstruction and denoising diffusion model, a loss function structure of the progressive reconstruction and denoising diffusion model and model training, a low-resolution nuclear magnetic resonance image is obtained, and the initial step number of reverse sampling and a noise degradation image corresponding to the initial step number are determined according to the collected low-resolution image; and then starting from the noise degradation image corresponding to the starting point, alternately executing the iterative change step and the progressive diffusion sampling step based on the model until the noiseless high-resolution nuclear magnetic resonance image is recovered, and training network parameters by adopting a plurality of groups of high-resolution nuclear magnetic resonance image data so that the image output of the network and the noiseless high-resolution image are approximated as much as possible.
Description
Technical field:
the invention belongs to the field of medical nuclear magnetic resonance imaging, and particularly relates to a nuclear magnetic resonance image-based super-resolution recovery method and a model construction method, which are used for recovering a high-quality high-resolution nuclear magnetic resonance image from a low-resolution nuclear magnetic resonance image obtained by nuclear magnetic resonance imaging equipment.
The background technology is as follows:
magnetic Resonance Imaging (MRI) is a non-invasive, ionizing radiation free imaging technique that is widely used and provides high soft tissue contrast and rich anatomical and functional information for clinical diagnosis. K-space data in MRI captures only limited spatial frequency samples due to various constraints such as hardware limitations and acquisition time, resulting in loss of high frequency detail. Therefore, the low-resolution MR image thus produced has difficulty in clearly displaying minute structures and boundaries. Therefore, improving the quality and resolution of MR images is of great clinical importance.
As a post-processing tool, super Resolution (SR) technology has been widely used to improve quality of a nuclear magnetic resonance image without changing hardware equipment of a nuclear magnetic resonance imaging apparatus. Conventional super-resolution methods include interpolation-based methods (e.g., bicubic interpolation and B-spline interpolation), as well as regularization-based methods. In recent years, deep learning-based methods directly learn the mapping from Low Resolution (LR) images to High Resolution (HR) images by designing various deep networks (e.g., res Net, U-Net, and transducer). In addition, some studies use generation of countermeasure networks (GANs) to generate realistic and clear high resolution nuclear magnetic resonance images. Although significant image restoration results are achieved, these deep learning-based methods typically focus on fixed integer upsampling factors with limited flexibility, limiting the application of these methods in clinical settings.
The invention comprises the following steps:
the invention provides a diffusion model-based nuclear magnetic resonance image super-resolution recovery method, which can recover high-quality high-resolution nuclear magnetic resonance images from low-resolution nuclear magnetic resonance images collected by nuclear magnetic resonance imaging equipment.
The technical scheme adopted by the invention comprises the following steps: a nuclear magnetic resonance image super-resolution recovery model construction method comprises the following steps:
forward diffusion process of constructing progressive reconstruction and denoising diffusion model: by simulating a nuclear magnetic resonance image downsampling process, a forward diffusion process gradually degenerates a noise-free high-resolution nuclear magnetic resonance image by gradually masking high-frequency data in k-space and adding random noise;
and constructing a back diffusion process of a progressive reconstruction and denoising diffusion model: determining a corresponding forward random differential equation through a forward diffusion process, then reversing the forward random differential equation according to the Andersen theorem to obtain a reverse random differential equation, and obtaining a reverse diffusion process through a discrete reverse random differential equation;
constructing a loss function of the progressive reconstruction and denoising diffusion model and training the progressive reconstruction and denoising diffusion model: the method comprises the steps of deducing a progressive reconstruction and denoising diffusion model loss function through a denoising score matching method and parameterization of a score network, and learning optimal parameters of the score network by using an Adam optimization algorithm and the loss function based on a training data set so as to obtain a trained model.
Further, by simulating a down-sampling process of the nmr image, the forward diffusion process gradually degenerates the noiseless high resolution nmr image by gradually masking high frequency data in k-space and adding random noise, comprising:
design of undersampled matrix M t ＝diag(W t ) Is to mask out high frequency data of different scales, whereinFor masking the matrix, the operation diag (·) represents pulling the matrix Cheng Xiangliang first, constructing the elements of the vector into a diagonal matrix, W t The definition is as follows:
wherein (i, j) represents W t The spatial location of the element(s),is the k-space center window of step t, where h t =h-t×d and w t =w-t×d, d is the truncation step, M when t=0 0 ＝diag(W 0 ) =i, i.e. the full sampling matrix, M when the number of steps t increases t Masking off more high frequency data, M t Gradually build x 0 More severe degradation.
At step t, the forward progressive diffusion process is as follows:
wherein alpha is t And x t The t-th step is to control the noise level coefficients and the degraded nmr image,representing Gaussian noise, wherein->Is an identity matrix>Is a degradation operator for controlling the degree of degradation, wherein +.>And->Representing the fourier transform and the inverse fourier transform, respectively, +.>Is an undersampled matrix;
further, when constructing the back diffusion process of the progressive reconstruction and denoising diffusion model, the forward diffusion process is considered as a solution to the following random differential equation:
where w is the standard wiener process,is->To reverse the forward random differential equation according to the anderson theorem to obtain a reverse random differential equation:
wherein,is the edge distribution q t (x t ) Score function of->The method is a standard wiener process from T to 0 in time steps, and a Euler-Walsh numerical solution and a finite difference instead of differential method are used for dispersing an inverse random differential equation to obtain an inverse diffusion process:
wherein alpha is t And alpha t-Δt The coefficients of the noise level are controlled by the t-th time step and the t-deltat time step, respectively. Estimating unknown itemsAnd->Restoring a noiseless high resolution image according to the above, wherein +.>Representing Gaussian noise->Is the edge distribution q t (x t ) Score function, x 0 Is a noiseless high resolution image.
Further, constructing a loss function of the progressive reconstruction and denoising diffusion model and training the progressive reconstruction and denoising diffusion model comprises:
estimating a score functionAnd when the method is used, training a score model by using a denoising score matching method:
wherein, t-U (0, T), x 0 ～q 0 (x 0 ) And x t ～q t (x t |x 0 ) λ (t) is a positive weighting function;
estimationWhen designing the score model s by the following network parameterization θ
Will beThe rewriting is as follows:
by minimizing the above, network f θ At the degeneracy operatorLearning under guidance to predict noiseless high resolution nuclear magnetic resonance images, f θ After training is completed, by->And->Separate estimationAnd->An item.
The loss function of the diffusion model is obtained by adopting a denoising score matching method and a designed score network parameterization, and the loss function is specifically as follows:
wherein x is 0 For training a high resolution nuclear magnetic resonance image, x t Anda degradation image and a degradation operator corresponding to the t-th diffusion step; calculation of the loss function with respect to the network f using a back propagation algorithm θ Gradient of parameters, and optimizing the network f by Adam algorithm based on the training data set θ Parameters, obtaining the optimal network f θ Parameters.
The invention provides a nuclear magnetic resonance image super-resolution recovery method, which comprises the steps of acquiring a low-resolution nuclear magnetic resonance image, and determining the initial step number of reverse sampling and a noise degradation image corresponding to the initial step number according to the acquired low-resolution image; starting from the noise degradation image corresponding to the starting point, alternately executing iterative improvement and progressive diffusion sampling steps based on the model until the noiseless high-resolution nuclear magnetic resonance image is restored; the model is obtained by constructing the nuclear magnetic resonance image super-resolution recovery model.
Further, the nuclear magnetic resonance images with different scales are regarded as noise-free nuclear magnetic resonance images corresponding to the step of the down-sampling process of the simulated nuclear magnetic resonance images according to the progressive diffusion process, and the initial step of the sampling process is determined according to whether the k-space data size of the low-resolution nuclear magnetic resonance image is matched with the central k-space data size reserved in the forward process.
Further, a low resolution MRI image is givenRegarding the image as a noise-free nuclear magnetic resonance image of a certain intermediate step in the forward process, wherein the k-space data size is hw, and the low-resolution nuclear magnetic resonance image x is based on the scheduling of undersampling masks in the forward diffusion process lr The corresponding initial steps are:
wherein, H and H are heights of high resolution and low resolution images, and a starting point of the acquisition process corresponding to the initial step l is:
wherein g zf Is a zero-padding operator in the frequency domain that transforms k-space dataFrom HW to HW from noisy degraded image x l Starting, alternating from t=l to t=0Model-based iterative improvement and progressive diffusion sampling steps to recover noiseless high-resolution image x 0 。
Further, the iterative improvement step based on the model comprises the following steps: initial prediction from networkThe improved nuclear magnetic resonance image at step t is:
wherein,the first term is a data consistency term which constrains consistency between the restored high-resolution image and the corresponding degraded image of the restored high-resolution image under the guidance of a degradation model, the second term is total variation regularization which is used for constraining a solution space to reconstruct a high-quality nuclear magnetic resonance image and is obtained by solving by using a gradient descent algorithm>
Further, the progressive diffusion sampling step includes: improved network initial predictionThereafter, a progressive diffusion sampling step is performed according to the following equation:
wherein,representing a progressive reconstruction for reconstructing k-space data between two adjacent steps,/>Representing the progressive noise for removing the noise of step t.
Compared with the prior art, the invention has at least the following beneficial technical effects:
the invention provides a diffusion model-based nuclear magnetic resonance image super-resolution recovery method, which can recover high-quality high-resolution nuclear magnetic resonance images from low-resolution nuclear magnetic resonance images collected by nuclear magnetic resonance imaging equipment. Compared with the existing super-resolution method based on deep learning, the method is different from the prior super-resolution method based on the diffusion probability model, the method gradually masks high-frequency data and adds Gaussian noise in the forward diffusion process, and then gradually reconstructs the high-frequency data and removes the noise to generate a clear high-resolution nuclear magnetic resonance image. Compared with the existing super-resolution method based on the diffusion probability model, the method is specially designed for the super-resolution of the nuclear magnetic resonance image, the forward process is inspired by the degradation process of the nuclear magnetic resonance image downsampling, high-frequency data are gradually masked, gaussian noise is added, so that the degradation process of the nuclear magnetic resonance image downsampling is simulated, and the high-resolution nuclear magnetic resonance image can be recovered from the low-resolution nuclear magnetic resonance image with different scales in the backward sampling process; in conclusion, the invention can be mainly used for realizing the super-resolution function in nuclear magnetic resonance imaging, has important application value for research and development and production of nuclear magnetic resonance imaging equipment, provides high-quality image data for later auxiliary diagnosis of doctors, and improves diagnosis precision.
Description of the drawings:
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a block diagram of a progressive reconstruction and denoising diffusion model.
Fig. 3 is a block diagram of a sampling process of a progressive reconstruction and denoising diffusion model.
Fig. 4 is a graph of an example of restored noise-free high resolution nuclear magnetic resonance (8-fold upsampling).
The specific embodiment is as follows:
the present invention will be further described in detail with reference to the accompanying drawings and examples in order to further clarify the objects, technical solutions and advantages of the present invention. These examples are illustrative only and are not limiting of the invention.
As shown in fig. 1, the method for recovering super-resolution of nuclear magnetic resonance image based on diffusion model provided by the invention comprises the following steps:
first, a forward diffusion process is constructed
Inspired by the degradation process of downsampling in nuclear magnetic resonance imaging, the invention proposes a forward process for super-resolution of an arbitrary scale nuclear magnetic resonance image, which gradually masks high-frequency data and adds gaussian noise to simulate the degradation process of downsampling of the nuclear magnetic resonance image. Specifically, at step t, the forward progressive diffusion process is as follows:
wherein alpha is t And x t The t-th step is to control the noise level coefficients and the degraded nmr image,representing Gaussian noise, wherein->Is an identity matrix>Is a degradation operator for controlling the degree of degradation, wherein +.>And->Representing the fourier transform and the inverse fourier transform, respectively. />Is an undersampled matrix of the sample,the position corresponding to the high-frequency k-space data that needs to be preserved in the t-th step is set to 1, and the position corresponding to the high-frequency k-space data truncated in the degradation process of the downsampling in the t-th step is set to 0. It should be noted that the undersampled matrix M t The difference from the truncation operation of the downsampling degeneration process is that M t The position corresponding to the truncated k-space data is set to 0 to ensure that the size of the nmr image remains unchanged.
As shown in fig. 2, the degradation strategy proposed by the present invention is to generate low resolution nmr images of multiple scales by gradually masking off high frequency data of different scales. Specifically, the present invention designs an undersampled matrix M t ＝diag(W t ) To mask out high frequency data of different scales, whereinFor masking the matrix, the operation diag (·) represents pulling the matrix into a vector first, and then constructing the elements of the vector into a diagonal matrix. W (W) t Is defined as:
wherein (i, j) represents W t Spatial location of the element.Is the k-space center window of step t, where h t =h-t×d and w t =w-t×d, d is a truncation step, and is set to 2 in the present invention. When t=0, M 0 ＝diag(W 0 ) I is the full sampling matrix. When the step number t increases, M t Masking off more high frequency data, which would result in x 0 More degradation.
Second, back diffusion process structure
The forward diffusion process in equation (1) can be regarded as a solution to the following random differential equation (SDE)
Where w is the standard wiener process,is->Is a derivative of (a). To restore noiseless high resolution image x 0 The present invention reverses the forward SDE according to Anderson's theshem to obtain a reverse SDE:
wherein,is the edge distribution q t (x t ) Score function of->Is a standard wiener process with time steps from T to 0. Then, the invention applies Euler-Walsh numerical method and finite difference instead of differential method to carry out discrete to the formula (4) to obtain a back diffusion process:
wherein,representing gaussian noise. Alpha t And alpha t-Δt The coefficients of the noise level are controlled by the t-th time step and the t-deltat time step, respectively. However, when the present invention restores a noiseless high-resolution image according to the formula (5), the image in the formula (5) And->Both are unknown. Therefore, the present invention requires first estimating these two terms.
Thirdly, training target of diffusion model
To estimate the score functionThe invention applies a denoising score matching method to train a score model:
wherein, t-U (0, T), x 0 ～q 0 (x 0 ) And x t ～q t (x t |x 0 ) λ (t) is a positive weighting function.
In addition, the present invention also requires estimation of the formula (5)To achieve this objective, the present invention designs a score model s by parameterizing the network as follows θ ：
Wherein f θ For parameterizing the score model s θ In a degraded image x of step t t And time step t is an input. Next, by the fractional model design in equation (7), equation (6) can be rewritten as:
wherein lambda (t) is a positive functionA number. By minimizing equation (8), the network f of the present invention θ At the degeneracy operatorLearning under guidance to predict noiseless high resolution nuclear magnetic resonance images, f θ After training is completed, the invention can be used for And->Respectively estimate +.>And
fourth, the trained network is applied to carry out nuclear magnetic resonance image super-resolution of any scale
Through the training process of the fourth step, the invention can determine the network f in the diffusion model θ Based on the trained network, the invention provides a new sampling process for recovering a noiseless high-resolution nuclear magnetic resonance image from a low-resolution nuclear magnetic resonance image of any scale.
As shown in fig. 3, the sampling process of the diffusion model includes the following three core steps: an initial point matching step, an iterative improvement step based on a model and a progressive diffusion sampling step. Wherein the initial point matching step determines the initial point of sampling by a given low resolution nuclear magnetic resonance image, which accelerates the acquisition process compared to a general diffusion model. The invention executes progressive diffusion sampling steps to progressively reconstruct high-frequency data and remove Gaussian noise after the improved initial network prediction is obtained by combining a weak mechanism and a total variation regularization priori through the iterative improvement based on a model. Next, the sampling process of the present invention will be described in detail.
Initial point matching step: since the different scale nmr images can be regarded as noise-free nmr images corresponding to the intermediate steps of the progressive diffusion process according to equation (1), the inverse process of the super-resolution of the different scale nmr images can start from the different intermediate steps of the progressive diffusion process. The invention determines the initial step of the sampling process depending on whether the k-space data size of the low resolution nmr image matches the central k-space data size remaining in the forward process. Specifically, given a low resolution MRIIt is considered as a noise-free nuclear magnetic resonance image of some intermediate step in the forward process, with k-space data size hw. Low resolution nmr image x according to the scheduling of undersampled masks during forward diffusion lr The corresponding initial steps are:
where H and H are the heights of the high resolution and low resolution images.
Obtaining a starting step l, wherein the starting point of the corresponding acquisition process is as follows:
wherein g zf Is a zero-padding operator in the frequency domain that transforms k-space dataThe size of (3) changes from HW to HW. Next, from the noisy degraded image x l Initially, the present invention alternates between performing model-based iterative improvement and progressive diffusion sampling steps from t=l to t=0 to recover a noise-free high-resolution image x 0 。
Model-based iterative improvement: by lifting the slave network f θ Nuclear magnetic resonance image of initial prediction in (a)Is used to guide the back sampling process. Specifically, the initial prediction +_ in a given network>After that, the improved nmr image at step t is:
wherein,the first term is a data consistency term that constrains consistency between the restored high resolution image and its corresponding degraded image under the direction of the degradation model. The second term is total variation regularization, which is used to constrain the solution space to reconstruct high quality nuclear magnetic resonance images, and in addition, equation (11) can be solved efficiently with gradient descent algorithms.
Progressive diffusion sampling: improved network initial prediction from equation (11)The invention then performs a progressive diffusion sampling step according to equation (5):
wherein the second itemRepresenting a progressive reconstruction that reconstructs k-space data between two adjacent steps, the third term representing progressive noise, which removes noise from step t.
In a numerical experiment, the present invention uses brain nuclear magnetic resonance image data of 1035 subjects, wherein 940 subjects 'data are used as training data and 95 subjects' data are used for testing.
As shown in table 1, the progressive diffusion and reconstructed diffusion model (PRDDiff) of the present invention was compared with two conventional methods (Bicubic and LRTV), five deep learning-based methods (EDSR, swinIR, FPGAN, metaSR and IREM) and three diffusion model-based methods (Score-MRI, r2d2+ and SR 3) on 4-fold and 8-fold super-resolution problems. The progressive diffusion and reconstruction diffusion model designed by the invention achieves the best reconstruction precision on different upsampling multiples. Fig. 3 is a visual result of the reconstructed image, and it can be seen that the restored high resolution nmr image of the present invention has clear structural details and no significant artifacts.
Table 1: comparison results of different methods in brain data test set at different upsampling scales
The above is only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by this, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (10)
1. The method for constructing the super-resolution recovery model of the nuclear magnetic resonance image is characterized by comprising the following steps of:
forward diffusion process of constructing progressive reconstruction and denoising diffusion model: by simulating a nuclear magnetic resonance image downsampling process, a forward diffusion process gradually degenerates a noise-free high-resolution nuclear magnetic resonance image by gradually masking high-frequency data in k-space and adding random noise;
and constructing a back diffusion process of a progressive reconstruction and denoising diffusion model: determining a corresponding forward random differential equation through a forward diffusion process, then reversing the forward random differential equation according to the Andersen theorem to obtain a reverse random differential equation, and obtaining a reverse diffusion process through a discrete reverse random differential equation;
constructing a loss function of the progressive reconstruction and denoising diffusion model and training the progressive reconstruction and denoising diffusion model: the method comprises the steps of deducing a progressive reconstruction and denoising diffusion model loss function through a denoising score matching method and parameterization of a score network, and learning optimal parameters of the score network by using an Adam optimization algorithm and the loss function based on a training data set so as to obtain a trained model.
2. The method of constructing a super-resolution restoration model for a nuclear magnetic resonance image according to claim 1, wherein the forward diffusion process gradually degrades the noise-free high-resolution nuclear magnetic resonance image by gradually masking off high-frequency data in k-space and adding random noise by simulating a down-sampling process of the nuclear magnetic resonance image comprises:
design of undersampled matrix M t ＝diag(W t ) Is to mask out high frequency data of different scales, whereinFor masking the matrix, the operation diag (·) represents pulling the matrix Cheng Xiangliang first, constructing the elements of the vector into a diagonal matrix, W t The definition is as follows:
wherein (i, j) represents W t The spatial location of the element(s),is the k-space center window of step t, h t =h-t×d and w t =w-t×d, d is the truncation stepLong, when t=0, M 0 ＝diag(W 0 ) =i, i.e. the full sampling matrix, M when the number of steps t increases t Masking off more high frequency data, M t Gradually build x 0 More severe degradation;
at step t, the forward progressive diffusion process is as follows:
wherein alpha is t And x t The t-th step is to control the noise level coefficients and the degraded nmr image,representing Gaussian noise, wherein->Is an identity matrix>Is a degradation operator for controlling the degree of degradation, wherein +.>And->Representing the fourier transform and the inverse fourier transform, respectively, +.>Is an undersampled matrix.
3. The method for constructing a super-resolution restoration model for a nuclear magnetic resonance image according to claim 1, wherein when constructing a back diffusion process of a progressive reconstruction and denoising diffusion model, a forward diffusion process is regarded as a solution of the following random differential equation:
where w is the standard wiener process,is->To reverse the forward random differential equation according to the anderson theorem to obtain a reverse random differential equation:
wherein,is the edge distribution q t (x t ) Score function of->The method is a standard wiener process from T to 0 in time steps, and a Euler-Walsh numerical solution and a finite difference instead of differential method are used for dispersing an inverse random differential equation to obtain an inverse diffusion process:
wherein alpha is t And alpha t-Δt The coefficients of the noise level control at the t-th time step and the t-delta t time step are respectively estimated as unknown itemsAnd->Restoring a noiseless high resolution image according to the above, wherein +.>Representing Gaussian noise->Is the edge distribution q t (x t ) Score function, x 0 Is a noiseless high resolution image.
4. The method of constructing a super-resolution restoration model for a nuclear magnetic resonance image according to claim 1, wherein constructing a loss function of a progressive reconstruction and denoising diffusion model and training the progressive reconstruction and denoising diffusion model comprises:
estimating a score functionAnd when the method is used, training a score model by using a denoising score matching method:
wherein, t-U (0, T), x 0 ～q 0 (x 0 ) And x t ～q t (x t |x 0 ) λ (t) is a positive weighting function;
estimationWhen designing the score model s by the following network parameterization θ
Will beThe rewriting is as follows:
by minimizing the above, network f θ At the degeneracy operatorLearning under guidance to predict noiseless high resolution nuclear magnetic resonance images, f θ After training is completed, by->Separate estimationAnd->An item.
5. The method for constructing a super-resolution restoration model of a nuclear magnetic resonance image according to claim 4, wherein the loss function of the diffusion model is obtained by adopting a denoising score matching method and a designed score network parameterization, and is specifically as follows:
wherein x is 0 For training a high resolution nuclear magnetic resonance image, x t Anda degradation image and a degradation operator corresponding to the t-th diffusion step; calculation of loss function using back propagation algorithmWith respect to network f θ Gradient of parameters, and optimizing the network f by Adam algorithm based on the training data set θ Parameters, obtaining the optimal network f θ Parameters.
6. The nuclear magnetic resonance image super-resolution recovery method is characterized by acquiring a low-resolution nuclear magnetic resonance image, and determining the starting step number of reverse sampling and a noise degradation image corresponding to the starting step number according to the acquired low-resolution image; starting from the noise degradation image corresponding to the starting point, alternately executing iterative improvement and progressive diffusion sampling steps based on the model until the noiseless high-resolution nuclear magnetic resonance image is restored; the model is constructed by the nuclear magnetic resonance image super-resolution recovery model according to any one of claims 1 to 5.
7. The method according to claim 6, wherein the nuclear magnetic resonance image of different scales is regarded as a noise-free nuclear magnetic resonance image corresponding to the step of down-sampling the simulated nuclear magnetic resonance image according to the progressive diffusion process, and the initial step of the sampling process is determined according to whether the k-space data size of the low-resolution nuclear magnetic resonance image matches the central k-space data size remaining in the forward process.
8. The method of claim 7, wherein a low resolution nmr image is givenRegarding the image as a noise-free nuclear magnetic resonance image of a certain intermediate step in the forward process, wherein the k-space data size is hw, and the low-resolution nuclear magnetic resonance image x is based on the scheduling of undersampling masks in the forward diffusion process lr The corresponding initial steps are:
wherein, H and H are heights of high resolution and low resolution images, and a starting point of the acquisition process corresponding to the initial step l is:
wherein g zf Is a zero-padding operator in the frequency domain that transforms k-space dataFrom HW to HW from noisy degraded image x l Initially, a model-based iterative improvement and progressive diffusion sampling step are alternately performed from t=l to t=0 to recover a noise-free high-resolution image x 0 。
9. The method of recovering super resolution of a nuclear magnetic resonance image according to claim 6, wherein the iterative improvement step based on the model comprises: initial prediction from networkThe improved nuclear magnetic resonance image at step t is:
wherein,the first term is a data consistency term which constrains consistency between the restored high-resolution image and the corresponding degraded image of the restored high-resolution image under the guidance of a degradation model, the second term is total variation regularization which is used for constraining a solution space to reconstruct a high-quality nuclear magnetic resonance image and is obtained by solving by using a gradient descent algorithm>
10. The method of recovering super resolution of a nuclear magnetic resonance image according to claim 9, wherein the progressive diffusion sampling step includes: improved network initial predictionThereafter, a progressive diffusion sampling step is performed according to the following equation:
wherein,representing a progressive reconstruction for reconstructing k-space data between two adjacent steps,/>Representing the progressive noise for removing the noise of step t.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311603891.5A CN117611453A (en) | 2023-11-28 | 2023-11-28 | Nuclear magnetic resonance image super-resolution recovery method and model construction method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311603891.5A CN117611453A (en) | 2023-11-28 | 2023-11-28 | Nuclear magnetic resonance image super-resolution recovery method and model construction method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN117611453A true CN117611453A (en) | 2024-02-27 |
Family
ID=89949398
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311603891.5A Pending CN117611453A (en) | 2023-11-28 | 2023-11-28 | Nuclear magnetic resonance image super-resolution recovery method and model construction method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117611453A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117890844A (en) * | 2024-03-15 | 2024-04-16 | 山东大学 | Magnetic resonance image reconstruction method based on optimized mask model |
-
2023
- 2023-11-28 CN CN202311603891.5A patent/CN117611453A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117890844A (en) * | 2024-03-15 | 2024-04-16 | 山东大学 | Magnetic resonance image reconstruction method based on optimized mask model |
| CN117890844B (en) * | 2024-03-15 | 2024-05-24 | 山东大学 | Magnetic resonance image reconstruction method based on optimized mask model |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111028306B (en) | AR2U-Net neural network-based rapid magnetic resonance imaging method | |
| CN109410289B (en) | Deep learning high undersampling hyperpolarized gas lung MRI reconstruction method | |
| Trinh et al. | Novel example-based method for super-resolution and denoising of medical images | |
| Chen et al. | Deep learning for image enhancement and correction in magnetic resonance imaging—state-of-the-art and challenges | |
| CN109214989B (en) | Single image super resolution ratio reconstruction method based on Orientation Features prediction priori | |
| Zeng et al. | A comparative study of CNN-based super-resolution methods in MRI reconstruction and its beyond | |
| Bao et al. | Undersampled MR image reconstruction using an enhanced recursive residual network | |
| CN117611453A (en) | Nuclear magnetic resonance image super-resolution recovery method and model construction method | |
| Jia et al. | Single anisotropic 3-D MR image upsampling via overcomplete dictionary trained from in-plane high resolution slices | |
| Aghabiglou et al. | Projection-Based cascaded U-Net model for MR image reconstruction | |
| Aetesam et al. | Noise dependent training for deep parallel ensemble denoising in magnetic resonance images | |
| Li et al. | An adaptive directional Haar framelet-based reconstruction algorithm for parallel magnetic resonance imaging | |
| CN111091517B (en) | Residual weighted imaging method and device | |
| CN104504657B (en) | Method and device for de-noising magnetic resonance diffusion tensor | |
| US20230380714A1 (en) | Method and system for low-field mri denoising with a deep complex-valued convolutional neural network | |
| Rousseau et al. | A supervised patch-based image reconstruction technique: Application to brain MRI super-resolution | |
| Rashid et al. | Single MR image super-resolution using generative adversarial network | |
| Joshi et al. | MRI resolution enhancement using total variation regularization | |
| Ryu et al. | K-space refinement in deep learning mr reconstruction via regularizing scan specific spirit-based self consistency | |
| CN115294229A (en) | Method and apparatus for reconstructing Magnetic Resonance Imaging (MRI) images | |
| JP2023069890A (en) | Magnetic resonance imaging device, image processing device, and image processing method | |
| Liu et al. | Coil-agnostic attention-based network for parallel MRI reconstruction | |
| Qin et al. | A2OURSR: Adaptive adjustment based real MRI super-resolution via opinion-unaware measurements | |
| CN116740217B (en) | Arterial spin marking method, device and storage medium based on artificial intelligence technology | |
| CN112213674B (en) | Magnetic resonance compressed sensing reconstruction method and device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |