CN117890844B - Magnetic resonance image reconstruction method based on optimized mask model - Google Patents
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Abstract
The invention belongs to the technical field of magnetic resonance signal image reconstruction, and discloses a magnetic resonance image reconstruction method based on an optimized mask model, which comprises the following steps: acquiring K space data of a magnetic resonance signal to be reconstructed; sampling the K space data through an optimization mask to obtain a sampling measured value and a non-sampling measured value; taking the sampled measured value, the non-sampled measured value, the optimization mask and the complement of the optimization mask as the input of a diffusion model to obtain a non-sampled data predicted value corresponding to the non-sampled measured value; and obtaining a reconstructed image of the magnetic resonance signal to be reconstructed according to the inverse matrix of the coding matrix, the sampling measured value and the non-sampling data predicted value. In the embodiment, the diffusion and sampling processes of the probability diffusion model are defined in a K space domain instead of an image domain, and meanwhile, the diffusion process is conditioned on an undersampling mask, so that data consistency is naturally and internally contained in the model, extra data consistency operation is not required to be executed during sampling, the sampling process is simplified, and the reconstruction efficiency is improved.
Description
Technical Field
The invention relates to the technical field of magnetic resonance image processing, in particular to a magnetic resonance image reconstruction method based on an optimized mask model.
Background
Magnetic resonance imaging (Magnetic Resonance Imaging, MRI) is a medical imaging technique for acquiring high resolution three-dimensional images of internal structures of a human or object, commonly used for diagnosing and assessing diseases, internal injuries, and the like. MRI has been widely used due to its non-invasive, high resolution, non-radiative, safe properties, etc. Magnetic resonance fast reconstruction is an image processing technique for improving the acquisition speed and image quality of MRI images. Traditional magnetic resonance rapid reconstruction methods include partial fourier reconstruction, parallel imaging reconstruction, compressed sensing reconstruction, and the like. In recent years, a magnetic resonance reconstruction method combined with a deep learning model has received a great deal of attention as an emerging reconstruction method. The magnetic resonance reconstruction method combined with the deep learning model mainly comprises two methods of reconstruction based on an optimization mask and undersampled data.
Mask/Mask refers to an undersampled pattern used to select portions of k-space data during image acquisition. The undersampling mode has great influence on accelerating the sampling time of the magnetic resonance imaging, and the good sampling mode can reduce the time required by sampling and improve the comfort level of a patient while keeping effective information as much as possible. In MRI reconstruction, fixed masking, random masking, and optimized masking are three common undersampling patterns. Conventional magnetic resonance fast reconstruction methods generally employ a fixed mask and a random mask approach. Most methods of optimizing masks are combined with deep learning methods, and the optimized mask is determined by a specific learning network. For example, learning-based undersampling pattern optimization models (Learning-based Optimization of the Under-SAMPLING PATTERN, LOUPE), iterative Gradient Sampling (IGs), and the like. The fixed mask is defined in advance, so that estimation errors are easy to cause blurring or distortion artifacts. The random mask requires more samples to ensure reconstruction quality due to its randomness, increasing sampling time. The optimization mask based on the deep learning determines the undersampling mode through a specific learning network, is limited by a deep learning method, has higher requirements on data quality, has certain limitation, has higher requirements on data based on a variation self-encoder and image reconstruction of a generated countermeasure network, has unstable training effect and has low quality of the generated image.
Therefore, how to improve the MRI image reconstruction method based on the deep learning optimized mask model, which can achieve a better image reconstruction effect on the premise of reducing the sampling time, becomes a current urgent problem to be solved.
Disclosure of Invention
In view of the above, the embodiment of the invention provides a magnetic resonance image reconstruction method based on an optimized mask model, so as to solve the problems in the prior art that the optimized mask model based on deep learning has long sampling time and high data quality requirements in MRI reconstruction, and the reconstruction efficiency of the MRI image is not high enough.
The embodiment of the invention provides a magnetic resonance image reconstruction method based on an optimized mask model, which comprises the following steps:
acquiring K space data of a magnetic resonance signal to be reconstructed;
sampling the K space data through an optimization mask to obtain a sampling measured value and a non-sampling measured value;
taking the sampled measured value, the non-sampled measured value, the optimization mask and the complement of the optimization mask as the input of a diffusion model to obtain a non-sampled data predicted value corresponding to the non-sampled measured value;
Obtaining a reconstructed image of the magnetic resonance signal to be reconstructed according to the inverse matrix of the coding matrix, the sampling measured value and the non-sampling data predicted value;
the process for obtaining the optimization mask comprises the following steps:
Inputting a sample K space image, acceleration speed, sample number, bayesian prior image mask and iteration times;
Generating a plurality of mask samples, and obtaining a soft mask through logarithmic probability ratio;
limiting the soft mask to obtain a binary mask;
Expanding the sample K-space image to match a binary mask;
calculating the sample K space image according to the binary mask to obtain an amplitude image of which the full sampling and undersampling are calculated by the inverse Fourier transform;
calculating a loss function according to the sample K space image and the amplitude image;
updating parameters of the logarithmic probability ratio by a gradient descent method;
constraining the updated weights to be within a qualified range by a projection operation;
and until the iteration times are reached, the output mask is the optimized mask.
Optionally, the diffusion model employs a denoising diffusion probability model.
Optionally, the constructing of the diffusion model includes:
setting an undersampled reconstruction model based on a complement of the optimization mask:
；
wherein, A non-sampling data predicted value output by the diffusion model; /(I)Is the complement of the optimization mask M; a is a coding matrix; x is the K-space data of the magnetic resonance signals to be reconstructed; /(I)Is a noise disturbance.
Optionally, the constructing of the diffusion model further includes:
Defining a diffusion process: gaussian noise is gradually added to the non-sampled measurements.
Optionally, the diffusion process comprises:
；
；
Wherein T represents a first number of diffusion steps; t is [1, T ]; And/> Is a super parameter.
Optionally, a superparameterAnd/>The relation of (2) is as follows: /(I)。
Optionally, the training process of the diffusion model includes:
Sampling is carried out from a training set of probability distribution, and sampling values are obtained;
Inputting an optimization mask and a complement of the optimization mask;
From normal distribution Sampling to obtain random noise;
From uniform distribution Obtaining a second diffusion step number t s by middle sampling;
Calculating a predicted value after probability diffusion in the step t s;
Gradient descent is performed until convergence conditions are reached.
Optionally, the testing process of the diffusion model includes:
Inputting a training set, an optimization mask and a predicted value;
From a multi-element normal distribution Sampling to obtain arbitrary predicted value/>；
In the back diffusion process from the step S, the back diffusion process is carried out from the normal distribution of multiple elementsSampling to obtain a noise variable z s;
Calculating the predicted value of the previous step and carrying out iterative updating;
When the number of back-diffusion steps is 1, the noise variable z s is set to 0, and the current prediction result is mapped back to the input space.
Optionally, performing the gradient descent formula includes:
；
wherein, Representing sampling noise.
Alternatively, the soft mask is obtained by gummel Softmax sampling.
The invention has the beneficial effects that:
1. The embodiment of the invention provides a magnetic resonance image reconstruction method based on an optimized mask model, which is characterized in that the mask model after data optimization is applied to a diffusion model defined on a K space, so that MRI reconstruction is completed. The diffusion and sampling processes of the probability diffusion model are defined in a K space domain instead of an image domain, and the diffusion process is conditioned on undersampling masks, so that data consistency is naturally and internally contained in the model, extra data consistency operation is not required to be executed during sampling, the sampling process is simplified, and the MRI reconstruction efficiency is improved.
2. Since DDPM is more flexible in controlling the noise distribution, there is better adaptability to different undersampling modes. Compared with random sampling, the sampling method adopted by the embodiment of the invention can reconstruct better image quality under the condition of the same undersampling rate. Compared with the traditional U-NET reconstruction method, the reconstruction method based on DDPM adopted by the embodiment of the invention has better imaging effect and evaluation index.
Drawings
The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and should not be construed as limiting the invention in any way, in which:
FIG. 1 is a flow chart of a magnetic resonance image reconstruction method based on an optimized mask model in an embodiment of the invention;
FIG. 2 shows a flowchart of an optimization masking method based on probability constraints in an embodiment of the invention;
FIG. 3 shows a diffusion model training flowchart of a magnetic resonance image reconstruction method based on an optimized mask model in an embodiment of the present invention;
FIG. 4 shows a diffusion model test flow chart of a magnetic resonance image reconstruction method based on an optimized mask model in an embodiment of the invention;
FIG. 5 shows an MRI fully sampled image;
FIG. 6 shows a 4 times undersampled random mask;
FIG. 7 shows a zero-padded Fourier reconstructed image based on a 4-fold undersampled random mask;
FIG. 8 shows a Unet reconstructed image based on a 4-fold undersampled random mask;
FIG. 9 shows a DDPM reconstructed image based on a 4-fold undersampled random mask;
FIG. 10 illustrates an optimized mask of 4 times undersampling in an embodiment of the invention;
FIG. 11 illustrates a zero-filled Fourier reconstructed image based on an optimized mask of 4 times undersampling in accordance with an embodiment of the present invention;
FIG. 12 illustrates a Unet reconstructed image based on a 4 times undersampled optimization mask in an embodiment of the present invention;
Fig. 13 shows a DDPM reconstructed image based on a 4 times undersampled optimization mask in an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
The embodiment of the invention provides a magnetic resonance image reconstruction method based on an optimized mask model, which is shown in fig. 1 and comprises the following steps:
step S10, K space data of the magnetic resonance signals to be reconstructed are acquired.
In this embodiment, the MRI magnetic resonance signals are converted into K-space data.
And step S20, sampling the K space data through an optimized mask to obtain a sampling measured value and a non-sampling measured value.
In this embodiment, the K-space data of the magnetic resonance signal to be reconstructed is undersampled by the optimization mask, the optimization mask is sampled to obtain a partial sampling measurement value, and the K-space data corresponding to the complement of the optimization mask is a non-sampling measurement value.
And step S30, taking the sampled measured value, the non-sampled measured value, the optimization mask and the complement of the optimization mask as inputs of a diffusion model to obtain a non-sampled data predicted value corresponding to the non-sampled measured value.
In this embodiment, K-space data of the magnetic resonance signals to be reconstructed, an optimization mask and a complement of the optimization mask are taken as inputs to the diffusion model, wherein the optimization mask and the complement of the optimization mask divide the K-space data into sampled and non-sampled measured values. The sampled measured value is a known value, the non-sampled measured value is an unknown value, and the predicted result is obtained through diffusion model prediction.
And step S40, obtaining a reconstructed image of the magnetic resonance signal to be reconstructed according to the inverse matrix of the coding matrix, the sampling measured value and the non-sampling data predicted value.
In this embodiment, the encoding matrix is a parameter of the diffusion model, and a set of sampled measured values and non-sampled data predictors corresponds to each value of the K-space data, thereby obtaining a reconstructed image of the magnetic resonance signal.
The process for obtaining the optimization mask comprises the following steps:
Inputting a sample K space image, acceleration speed, sample number, bayesian prior image mask and iteration times;
Generating a plurality of mask samples, and obtaining a soft mask through logarithmic probability ratio;
limiting the soft mask to obtain a binary mask;
Expanding the sample K-space image to match a binary mask;
calculating the sample K space image according to the binary mask to obtain an amplitude image of which the full sampling and undersampling are calculated by the inverse Fourier transform;
calculating a loss function according to the sample K space image and the amplitude image;
updating parameters of the logarithmic probability ratio by a gradient descent method;
constraining the updated weights to be within a qualified range by a projection operation;
and until the iteration times are reached, the output mask is the optimized mask.
In this embodiment, as shown in fig. 2, the input K-space data x k is selected, the acceleration multiple a, the number of samples L, and the bayesian prior image mask pM are determined, and the required iteration number i is determined. N in fig. 2 represents the current iteration number.
Z mask samples m= { m 1,m2,…,mZ }, the generated mask samples being the final binary mask, are generated.
The soft mask m soft is obtained by the logarithmic probability ratio of θ m. In order to realize the random mask, gumbel-Softmax technique is applied, and a technology specially designed for processing Bernoulli distribution is adopted, and the specific process for obtaining the binary mask is as follows:
；
；
wherein, For/>M soft is a soft mask, allowing for scalability, which can be obtained by sampling, in fact is an intermediate process, g 1 and g 0 are independent co-distributed samples of the gummel (0, 1) distribution.
Limiting the soft mask:
；
wherein II is an indicating function, which means that the value is 1 when the condition in brackets is satisfied, otherwise, it is 0. Samples of the final binary mask are applied and returned on an element-by-element basis, sg representing the cessation of gradient operations, preventing the gradient from propagating backward.
UsingInitial updating of unconstrained parameter vectorsThe updated weights are constrained to be within the appropriate range by the projection operation:
；
；
wherein, Representing constraint conditions; /(I)And expressing the acceleration factor, and updating the weight at each iteration until the iteration is ended.
As an alternative embodiment, the diffusion model employs a denoising diffusion probability model (Denoising Diffusion Probabilistic Models, DDPM).
In this embodiment, since the K-space data is in discrete form, DDPM model, which is also a discrete calculation, is employed.
As an alternative embodiment, the construction of the diffusion model includes:
setting an undersampled reconstruction model based on a complement of the optimization mask:
；
wherein, Non-sampled data pre-/>, output for diffusion modelMeasuring a value; /(I)Is the complement of the optimization mask M; a is a coding matrix; x is the K-space data of the magnetic resonance signals to be reconstructed; /(I)Is a noise disturbance.
In the present embodiment of the present invention, in the present embodiment,Is a diagonal matrix, and the diagonal element is 1 or 0 according to the sampling mode. /(I)。/>And/>Are n-dimensional vectors whose components at non-sampling locations are 0. Wherein,Representing a complement of known undersamples, and therefore the estimate/>Can use the estimated valueInstead of.
；
In the above formula:
；
wherein, Is a covariance matrix, meaning that noise is only added at non-sampling locations, since for all t,Is always 0 at the undersampled position.
As an alternative embodiment, the construction of the diffusion model further includes:
Defining a diffusion process: gaussian noise is gradually added to the non-sampled measurements. In a specific embodiment, the diffusion process includes:
；
；
Wherein T represents a first number of diffusion steps; t is [1, T ]; And/> Is a super parameter.
As an alternative embodiment, a superparameterAnd/>The relation of (2) is as follows: /(I). In particular embodiments, the superparameter/>And/>Not limited to meeting/>。
As an alternative embodiment, as shown in fig. 3, the training process of the diffusion model includes:
Sampling is carried out from a training set of probability distribution, and sampling values are obtained;
Inputting an optimization mask and a complement of the optimization mask;
From normal distribution Mid-sampling to obtain random noise/>；
From uniform distributionObtaining a second diffusion step number t s by middle sampling;
Calculating a predicted value after probability diffusion in the step t s;
Gradient descent is performed until convergence conditions are reached.
In the present embodiment, provided that the non-sampling matrix M c and the sampled measurement value y M are conditioned, DDPM is defined in the measurement domain as follows:
；
；
wherein, Fixed as a constant, the value of which is specially set,/>，/>For/>From i to t.
The gradient descent formula includes:
。
As an alternative embodiment, as shown in fig. 4, the test procedure of the diffusion model includes:
Inputting a training set, an optimization mask and a predicted value;
From a multi-element normal distribution Sampling to obtain arbitrary predicted value/>；
In the back diffusion process from the step S, the back diffusion process is carried out from the normal distribution of multiple elementsSampling to obtain a noise variable z s;
Calculating the predicted value of the previous step and carrying out iterative updating;
When the number of back-diffusion steps is 1, the noise variable z s is set to 0, and the current prediction result is mapped back to the input space.
In this embodiment, the formula for calculating the predicted value of the previous step is as follows:
；
wherein, Represent the mean value/>Representing variance,/>Depending on the predicted value/>, of the current time stepTime step s, covariance matrix M c, and input data y M. The final output is: I.e. the new K-space data is obtained by mapping the sampled measured values and the non-sampled data predictors back to the input space, thereby reconstructing the image.
The embodiment of the invention provides a magnetic resonance image reconstruction method based on an optimized mask model, which is characterized in that the mask model after data optimization is applied to a diffusion model defined on a K space, so that MRI reconstruction is completed. The diffusion and sampling processes of the probability diffusion model are defined in a K space domain instead of an image domain, and the diffusion process is conditioned on undersampling masks, so that data consistency is naturally and internally contained in the model, extra data consistency operation is not required to be executed during sampling, the sampling process is simplified, and the MRI reconstruction efficiency is improved.
Since DDPM is more flexible in controlling the noise distribution, there is better adaptability to different undersampling modes. Compared with random sampling, the sampling method adopted by the embodiment of the invention can reconstruct better image quality under the condition of the same undersampling rate. Compared with the traditional U-NET reconstruction method, the reconstruction method based on DDPM adopted by the embodiment of the invention has better imaging effect and evaluation index.
The present embodiment provides a constraint-based probability optimization mask for the fastmri dataset single coil knee dataset and applies it to the DDPM for accelerated MRI reconstruction that is diffuse and sampled in the measurement domain. The dataset image size was 320 x 320, trained with a AdamW optimizer at a learning rate of 0.0001, following the previous set of diffusion models, multiplying β t by 0.5, letting β T ≡0.5 to control noise levels. The imaging results of the random mask and the optimized mask in this embodiment are shown in fig. 5 to 13, and the quantitative measurement of the imaging results is shown in table 1.
Table 1 quantitative measurement of imaging results
；
Aiming at the problems that the image quality is reduced, artifacts such as internal folding, blurring or twisting are caused by the application of undersampled acquired data in a deep learning model and the like due to long magnetic resonance imaging time, the embodiment of the invention combines an optimized mask of a dataset with a denoising diffusion probability model based on a K space domain based on a completely micro probability frame for mask optimization based on learning, ensures better adaptability in different undersampling modes due to flexible control of noise distribution, and can obtain better imaging quality than a random mask and Unet reference model.
Although embodiments of the present invention have been described in connection with the accompanying drawings, various modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the invention, and such modifications and variations are within the scope of the invention as defined by the appended claims.
Claims (3)
1. A magnetic resonance image reconstruction method based on an optimized mask model is characterized by comprising the following steps:
acquiring K space data of a magnetic resonance signal to be reconstructed;
Sampling the K space data through an optimization mask to obtain a sampling measured value and a non-sampling measured value;
taking the sampled measured value, the non-sampled measured value, the optimization mask and the complement of the optimization mask as inputs of a diffusion model to obtain a non-sampled data predicted value corresponding to the non-sampled measured value;
Obtaining a reconstructed image of the magnetic resonance signal to be reconstructed according to the inverse matrix of the coding matrix, the sampling measured value and the non-sampling data predicted value;
the process for obtaining the optimization mask comprises the following steps:
Inputting a sample K space image, acceleration speed, sample number, bayesian prior image mask and iteration times;
Generating a plurality of mask samples, and obtaining a soft mask through logarithmic probability ratio;
limiting the soft mask to obtain a binary mask;
expanding the sample K-space image to match the binary mask;
Calculating the sample K space image according to the binary mask to obtain an amplitude image of which the full sampling and undersampling are calculated by inverse Fourier transform;
calculating a loss function according to the sample K space image and the amplitude image;
updating parameters of the logarithmic probability ratio by a gradient descent method;
constraining the updated weights to be within a qualified range by a projection operation;
Until the iteration times are reached, the output mask is the optimized mask;
The diffusion model adopts a denoising diffusion probability model;
the construction of the diffusion model comprises the following steps:
Setting an undersampled reconstruction model based on the complement of the optimization mask:
；
wherein, A non-sampling data predictive value output for the diffusion model; /(I)Is the complement of the optimization mask M; a is the coding matrix; x is K space data of the magnetic resonance signals to be reconstructed; /(I)Is a noise disturbance;
The construction of the diffusion model further comprises the following steps:
Defining a diffusion process: gradually adding gaussian noise to the non-sampled measured values;
the diffusion process includes:
；
；
Wherein T represents a first number of diffusion steps; t is [1, T ]; And/> Is a super parameter;
super parameter And/>The relation of (2) is as follows: /(I)；
The training process of the diffusion model comprises the following steps:
Sampling is carried out from a training set of probability distribution, and sampling values are obtained;
inputting the optimization mask and a complement of the optimization mask;
From normal distribution Sampling to obtain random noise;
From uniform distribution Obtaining a second diffusion step number t s by middle sampling;
Calculating a predicted value after probability diffusion in the step t s;
executing gradient descent until reaching convergence condition;
the test process of the diffusion model comprises the following steps:
Inputting the training set, the optimization mask and the predicted value;
From a multi-element normal distribution Sampling to obtain arbitrary predicted value/>；
In the back diffusion process from the step S, the back diffusion process is carried out from the normal distribution of multiple elementsSampling to obtain a noise variable z s;
Calculating the predicted value of the previous step and carrying out iterative updating;
when the number of back-diffusion steps is 1, the noise variable z s is set to 0, and the current prediction result is mapped back to the input space.
2. The method of claim 1, wherein performing a gradient descent formula comprises:
；
wherein, Representing sampling noise.
3. The method for reconstructing a magnetic resonance image based on an optimized mask model according to claim 1, wherein the soft mask is obtained by gummel Softmax sampling.
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