CN109671129B - Dynamic magnetic resonance image reconstruction method and device for adaptive parameter learning - Google Patents
Dynamic magnetic resonance image reconstruction method and device for adaptive parameter learning Download PDFInfo
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Abstract
The application provides a dynamic magnetic resonance image reconstruction method and a device for adaptive parameter learning, wherein the method is used for improving regularization terms in a CS-MRI model, and comprises the steps of carrying out redundancy removal on a dynamic magnetic resonance image by using DCT in a spatial domain and TV in a time domain, carrying out adaptive learning on a large number of parameters in the CS-MRI by using a convolutional neural network, and establishing a magnetic resonance image reconstruction model; reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image; calculating the difference value of the fully sampled image and the reconstructed image; and updating parameters in the model, including DCT, TV filter operator, regularization parameter and the like by using a back propagation algorithm in the network according to the difference value. The magnetic resonance image reconstruction model established in the mode can efficiently reconstruct the highly undersampled image to obtain an image with high reconstruction precision and reconstruction speed, so that the time of magnetic resonance scanning can be effectively shortened under the condition of not losing the spatial resolution.
Description
Technical Field
The application belongs to the technical field of image processing, and particularly relates to a dynamic magnetic resonance image reconstruction method and device for adaptive parameter learning.
Background
Magnetic Resonance Imaging (MRI) can accurately acquire physiological functions, anatomical structures, lesions, and functional information of organs and tissues of a human body. However, conventional scanning of magnetic resonance signals and reconstruction of images requires a long time. For example: cardiac, perfusion, and functional imaging, which are relatively real-time demanding items, are often not satisfactory for magnetic resonance imaging. Further, due to the long scan time, the patient may feel uncomfortable and introduce motion artifacts.
However, the above proposed effective solutions to how to shorten the time of the magnetic resonance scan to improve the accuracy of the reconstructed image.
Disclosure of Invention
The application aims to provide a dynamic magnetic resonance image reconstruction method and device for adaptive parameter learning, which can efficiently reconstruct an undersampled image through an established magnetic resonance image reconstruction model to obtain a required image, so that the time of magnetic resonance scanning can be effectively shortened. The application provides a dynamic magnetic resonance image reconstruction method and a device for adaptive parameter learning, which are realized by the following steps:
a method of adaptive parameter learning dynamic magnetic resonance image reconstruction, the method comprising:
taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization items of CS-MRI;
establishing a magnetic resonance image reconstruction model according to regularization terms of a DCT filter operator and a TV filter operator;
reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
calculating the difference value between the fully sampled image corresponding to the sample image and the reconstructed image;
updating a DCT filter operator, a TV filter operator and a regularization parameter in the magnetic resonance reconstruction model by using a back propagation algorithm in a network according to the difference value, so as to realize the optimization training of the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets the preset precision requirement;
and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
In one embodiment, the magnetic resonance image reconstruction model is established according to a regularization term which introduces a DCT filter operator and a TV filter operator, and comprises the following steps:
utilizing a joint sparse model, utilizing DCT filtering in a spatial domain, and utilizing TV filtering in a time domain to enhance the sparsity of an image to obtain a sparsity expression formula;
performing fusion conversion on the sparse expression formula to obtain a target formula;
converting the target formula into a plurality of subproblem solving formulas by using an alternating direction multiplier method;
and networking the plurality of sub-problem solving formulas to obtain a magnetic resonance image reconstruction model.
In one embodiment, the joint sparse model is used, DCT filtering is used in a spatial domain, TV filtering is used in a time domain to enhance the sparsity of the image, and a sparsity expression formula is obtained, wherein the sparsity expression formula comprises:
setting the filter operator of the following formula as a DCT operator and a TV operator:
wherein arg min f (x) represents the set of all arguments x that make the function f (x) take its minimum,
is a reconstructed magnetic resonance image, N t ＝{x 1 ,x 2 ,...,x T And represents a time direction common T frame image, y represents undersampled k-space data, A = PF, wherein P is an undersampled matrix, F represents a Fourier transform, phi represents a filter operator, and lambda represents a parameter.
The following equation is obtained:
wherein, the first and the second end of the pipe are connected with each other,
an image representing a spatial domain is provided,
image representing the time domain,. Phi 1 Representing DCT filter operator, phi 2 Representing TV filter operator, | · Limu DCT Representing discrete cosine transform, | · | | non-calculation TV Representing total variation transformation, λ 1 、λ 2 To balance the parameters of the data fidelity term with the regularization term.
In one embodiment, the target formula is:
wherein z represents an auxiliary variable, α represents a Lagrangian multiplier, and g (·) represents l 2,p An approximation function of the norm, p, represents a penalty parameter.
In one embodiment, the plurality of sub-problem solving equations are:
where T denotes transposition, β denotes the scaling factor of the Lagrangian multiplier, and k is {1,2 t Denotes the number of iterations in the gradient descent, n denotes the nth layer, μ 1 ＝(1-l r ρ)，μ 2 ＝l r ρ representing learnable weight parameters, respectively,
l r the size of the step size is indicated,
represents the update rate, H (-) represents the gradient of g (-), D (-) represents the gradient of g (-), D 1 Representing a transformation matrix.
In one embodiment, the plurality of sub-problem solving formulas are networked to obtain:
wherein I represents an identity matrix, C 1 、C 2 Respectively represent two convolution layers, w 1 Corresponding to the combination of DCT and TV filters, size 3 x 1 x L, b 1 Representing an L-dimensional offset vector. w is a 2 Corresponding to the combination of DCT and TV filters, size 3 x l, b 2 Represents a 1-dimensional offset vector, S PLF (. Represents a point of
Piecewise linear function of control, N C Is a parameter for controlling a point in a piecewise linear function, recon denotes a reconstruction layer, addition denotes an overlay layer, conv1 denotes a convolution layer, nonlinear denotes a Nonlinear transformation layer, conv2 denotes a convolution layer, and Multi denotes a multiplier update layer.
An adaptive parameter learning dynamic magnetic resonance image reconstruction apparatus, the apparatus comprising:
the replacing module is used for taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization terms of CS-MRI;
the establishing module is used for establishing a magnetic resonance image reconstruction model according to the regularization items of the introduced DCT filter operator and the introduced TV filter operator;
the reconstruction module is used for reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
the calculation module is used for calculating the difference value between the fully sampled image corresponding to the sample image and the reconstructed image;
the iteration updating module is used for updating a DCT (discrete cosine transform) filter operator, a TV (television) filter operator and a regularization parameter in the magnetic resonance reconstruction model by using a back propagation algorithm in a network according to the difference value so as to realize optimization training of the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets a preset precision requirement;
and the application module is used for reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
In one embodiment, the establishing module comprises;
the generating unit is used for utilizing the joint sparse model, utilizing DCT filtering in a space domain and utilizing TV filtering in a time domain to enhance the sparsity of the image and obtain a sparsity expression formula;
the first conversion unit is used for carrying out fusion conversion on the sparse expression formula to obtain a target formula;
a second conversion unit, configured to convert the target formula into a plurality of subproblem solution formulas by using an alternating direction multiplier method;
and the networking unit is used for networking the plurality of subproblem solving formulas to obtain a magnetic resonance image reconstruction model.
In an embodiment, the generating unit is specifically configured to set a filter operator of the following formula as a DCT operator and a TV operator:
wherein arg min f (x) represents the set of all arguments x that make the function f (x) take its minimum,
is the reconstructed magnetic resonance image, y represents undersampled k-space data, a = PF, where P is an undersampled matrix, F represents the fourier transform, Φ represents the filter operator, and λ represents the parameter.
The following equation is obtained:
wherein the content of the first and second substances,
an image representing a spatial domain is provided,
image representing the time domain, N t ＝{x 1 ,x 2 ,...,x T And indicates a T-frame image in the time direction. Phi 1 Representing DCT filter operator, phi 2 Representing the TV filter operator, | · | | ventilation DCT Representing discrete cosine transform, | · | non-conducting phosphor TV Representing total variation transformation, λ 1 、λ 2 To balance the parameters of the data fidelity term with the regularization term.
In one embodiment, the target formula is:
wherein z represents an auxiliary variable, α represents a Lagrangian multiplier, and g (·) represents l 2,p An approximation function of the norm, p, represents a penalty parameter.
In one embodiment, the plurality of sub-problem solving equations are:
where T represents the transpose, β represents the scaling factor of the Lagrangian multiplier, and k ∈ {1,2 t Denotes the number of iterations in the gradient descent, n denotes the nth layer, μ 1 ＝(1-l r ρ)，μ 2 ＝l r ρ representing learnable weight parameters, respectively,
l r the size of the step size is indicated,
represents the update rate, H (-) represents the gradient of g (-), D (-) represents the gradient of g (-), D 1 Representing a transformation matrix.
In one embodiment, the plurality of sub-problem solving formulas are networked to obtain:
wherein I represents an identity matrix, C 1 、C 2 Respectively represent two convolution layers, w 1 Corresponding to the combination of DCT and TV filters, size 3 x 1 x l, b 1 Representing an L-dimensional offset vector. w is a 2 Corresponding to the combination of DCT and TV filters, size 3 x L, b 2 Represents a 1-dimensional offset vector, S PLF (. Represents a point of
Piecewise linear function of control, N C Is a parameter for controlling a point in a piecewise linear function, recon denotes a reconstruction layer, addition denotes an overlay layer, conv1 denotes a convolution layer, nonlinear denotes a Nonlinear transformation layer, conv2 denotes a convolution layer, and Multi denotes a multiplier update layer.
A terminal device comprising a processor and a memory for storing processor-executable instructions, the instructions when executed by the processor performing the steps of:
taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization parameters;
establishing a magnetic resonance image reconstruction model according to regularization terms of a DCT filter operator and a TV filter operator;
reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
calculating the difference value between the fully sampled image corresponding to the sample image and the reconstructed image;
according to the difference value, performing reverse iteration on the magnetic resonance reconstruction model to update the values of a DCT filter operator and a TV filter operator, and realizing optimization training on the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets the preset precision requirement;
and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
A computer readable storage medium having stored thereon computer instructions that when executed perform the steps of:
taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization parameters;
establishing a magnetic resonance image reconstruction model according to regularization terms of a DCT filter operator and a TV filter operator;
reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
calculating a difference value between a fully sampled image corresponding to the sample image and the reconstructed image;
according to the difference value, performing reverse iteration on the magnetic resonance reconstruction model to update the values of a DCT filter operator and a TV filter operator, and realizing optimization training on the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets the preset precision requirement;
and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
According to the dynamic magnetic resonance image reconstruction method and device based on adaptive parameter learning, due to the fact that the magnetic resonance image is sparse and has noise, the magnetic resonance image reconstruction model is established by taking the DCT filter operator in the space domain and the TV filter operator in the time domain as regularization parameters, and redundancies can be removed in the space direction and the time direction respectively, and therefore the reconstruction effect can be effectively improved. Furthermore, the DCT filter operator and the TV filter operator in the time domain are adjusted in a network autonomous learning mode, so that the precision of a magnetic resonance image reconstruction model can be effectively improved, the magnetic resonance image reconstruction model established in the mode can be used for efficiently reconstructing highly undersampled images to obtain images with high reconstruction precision and reconstruction speed, and the time of magnetic resonance scanning can be effectively shortened under the condition of not losing spatial resolution.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and for those skilled in the art, other drawings can be obtained according to the drawings without any creative effort.
FIG. 1 is a flowchart of a method of an embodiment of a method for reconstructing a dynamic magnetic resonance image with adaptive parameter learning provided herein;
figure 2 is a schematic diagram of the adaptive parameter learning dynamic magnetic resonance image sparseness processing provided by the present application;
FIG. 3 is a schematic diagram of a model of a neural network obtained after the networking provided by the present application;
fig. 4 is a schematic architecture diagram of a terminal device provided in the present application;
fig. 5 is a block diagram of a dynamic magnetic resonance image reconstruction apparatus for adaptive parameter learning according to the present application.
Detailed Description
In order to make those skilled in the art better understand the technical solutions in the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making creative efforts shall fall within the protection scope of the present application.
At present, the magnetic resonance imaging speed is accelerated mainly by the following modes: parallel magnetic resonance imaging (Parallel MR imaging) and k-space undersampling. The present example is mainly directed to the study of k-space undersampling to improve the magnetic resonance imaging speed. Considering that Compressed Sensing-Magnetic Resonance Imaging (CS-MRI) consists of a data fidelity term and a regularization term, and the study on the regularization term includes wavelet sparse regularization, total variation sparse regularization and adaptive dictionary learning; further, there are studies showing that low rank models are effective for dynamic magnetic resonance imaging. Although the existing methods based on sparseness and low rank have good reconstruction effect, signals cannot be reconstructed well, noise in images is not considered based on the low rank method, the selection of a filter is artificially selected and is not representative based on the sparseness method, and the reconstruction time of the method based on dictionary learning is long.
Based on this, in the present example, from the practical application point of view, the magnetic resonance imaging is rapidly realized based on the compressed sensing theory reconstruction algorithm. Since the magnetic resonance image is sparse and has noise, in this example, a Discrete Cosine Transform (DCT) filter is used in space, and a Total Variation (TV) filter is used in a time direction, which removes redundancy in the space direction and the time direction, respectively, so that the reconstruction effect can be effectively improved.
Specifically, the magnetic resonance image is sparse, the image is transformed to a sparse domain by discrete cosine transform, and the value of the filter can be obtained by network autonomous learning without manual selection. And the TV is used for filtering in the time direction, so that not only can noise be removed, but also the sparsity of the MR image can be further enhanced, and the reconstruction quality of the image is improved.
Aiming at the problem of slow scanning speed of magnetic resonance imaging, particularly dynamic magnetic resonance imaging, the scanning speed of the dynamic magnetic resonance imaging is increased by an undersampling method in the embodiment. In the embodiment, by using the CS-MRI technology, a regularization term in the under-sampled magnetic resonance image is explored, and combining with a deep learning adaptive learning method, so that an image with high resolution and approximate to full sampling can be quickly reconstructed from the under-sampled magnetic resonance image.
Fig. 1 is a flowchart illustrating a method of an embodiment of a dynamic magnetic resonance image reconstruction method based on adaptive parameter learning according to the present application. Although the present application provides method operational steps or apparatus configurations as illustrated in the following examples or figures, more or fewer operational steps or modular units may be included in the methods or apparatus based on conventional or non-inventive efforts. In the step or structure in which the necessary cause and effect relationship does not logically exist, the execution sequence of the steps or the module structure of the apparatus is not limited to the execution sequence or the module structure described in the embodiment of the present application and shown in the drawings. When the described methods or modular structures are applied in a practical device or end product, they can be executed sequentially or in parallel according to the embodiments or the methods or modular structures shown in the figures (for example, in the environment of parallel processors or multi-thread processing, or even in the environment of distributed processing).
Specifically, as shown in fig. 1, a dynamic magnetic resonance image reconstruction method for adaptive parameter learning according to an embodiment of the present application may include (step 101 to step 106):
step 101: taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization items of CS-MRI;
step 102: establishing a magnetic resonance image reconstruction model according to regularization terms of a DCT filter operator and a TV filter operator;
specifically, according to the regularization term introduced with the DCT filter operator and the TV filter operator, establishing the magnetic resonance image reconstruction model may include:
s1: utilizing a joint sparse model, utilizing DCT (discrete cosine transform) filtering in a spatial domain and utilizing TV (television) filtering in a time domain to enhance the sparsity of an image and obtain a sparsity expression formula;
for example: the filter operators of the following formula can be set as a DCT filter operator and a TV filter operator:
wherein arg min f (x) represents the set of all arguments x that make the function f (x) take its minimum,
is the reconstructed magnetic resonance image, y represents undersampled k-space data, a = PF, where P is an undersampled matrix, F represents the fourier transform, Φ represents the filter operator, and λ represents the parameter.
The following equation is obtained:
wherein the content of the first and second substances,
an image representing a spatial domain is provided,
image representing the time domain, N t ＝{x 1 ,x2,...,x T And represents a T-frame image in the time direction. Phi (phi) of 1 Representing DCT filter operator, phi 2 Representing TV filter operator, | · Limu DCT Representing discrete cosine transform, | · | non-conducting phosphor TV Representing total variation transformation, λ 1 、λ 2 To balance the parameters of the data fidelity term with the regularization term.
That is, the filter operators in the original formula are selected as the DCT filter operator and the TV filter operator, so that the redundancy can be removed in time and space.
S2: performing fusion conversion on the sparse expression formula to obtain a target formula;
wherein the target formula can be expressed as:
wherein z represents an auxiliary variable, α represents a Lagrangian multiplier, and g (·) represents l 2,p An approximation function of the norm, p, represents a penalty parameter.
Specifically, the target formula may be converted as follows:
considering that in practical applications, the sparse induction norm for sparse regularization includes: l 0 Norm,/, of 1 Norm,/, of 2,1 Norm is defined as l of the row vector 2 Sum of norm, minimum l 2,1 The norm aims to select as few non-zero rows as possibleAnd (5) vector quantity. For example: by means of 2 , p Matrix norm (0)<p<1) A more sparse solution can be achieved by making feature choices, and therefore, choose l 2,p Norm, and further α = β. Accordingly, the above formula:
can be simplified as follows:
wherein Φ represents Φ 1 And phi 2 Fusion of (a) l ＝λ 1 ＝λ 2 For regularization parameters, g (-) is l 2,p An approximation function of the norm.
The above method is solved by using an expansion iteration method, and an auxiliary variable z is introduced into an image domain, so that a formula:
to convert to:
s.t.z＝x
wherein, the augmented Lagrangian function is:
the augmented Lagrangian function is the target formula. The conversion from the base formula to the target formula is accomplished in the manner described above.
S3: converting the target formula into a plurality of subproblem solving formulas by using an alternating direction multiplier method;
the Alternating Direction Method of Multipliers (ADMM for short) is a computing framework for solving optimization problems, and is suitable for solving distributed convex optimization problems, especially statistical learning problems. ADMM decomposes a large global problem into a number of smaller, more easily solved local sub-problems by a Decomposition-Coordination (Decomposition-Coordination) process, and obtains a solution to the large global problem by coordinating the solutions of the sub-problems.
In this example, the above target formula can be converted into:
the multiple subproblem solving equations are:
where T denotes transposition, β denotes the scaling factor of the Lagrangian multiplier, and k is {1,2 t Denotes the number of iterations in the gradient descent, n denotes the nth layer, μ 1 ＝(1-l r ρ)，μ 2 ＝l r ρ representing learnable weight parameters, respectively,
l r which represents the size of the step size,
is the update rate, H (-) denotes the gradient of g (-) and D 1 Representing a transform matrix (e.g., DCT, wavelet transform, etc.).
S4: and networking the plurality of sub-problem solving formulas to obtain a magnetic resonance image reconstruction model.
Specifically, the plurality of sub-problem solving formulas are networked to obtain:
wherein I represents an identity matrix. C 1 、C 2 Two convolutional layers are shown separately. w is a 1 Corresponding to the combination of DCT and TV filters, size 3 x 1 x L, b 1 Representing an offset vector of dimension L, w 2 Corresponding to the combination of DCT and TV filters, size 3 x L, b 2 Representing a 1-dimensional offset vector. S. the PLF (. Represents a point of
Piecewise linear function of control, N C Is a parameter for controlling a point in a piecewise linear function, recon denotes a reconstruction layer, addition denotes an overlay layer, conv1 denotes a convolution layer, nonlinear denotes a Nonlinear transformation layer, conv2 denotes a convolution layer, and Multi denotes a multiplier update layer.
Step 103: reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
after networking is carried out in the mode, the neural network of the magnetic resonance reconstruction model can be obtained, and the sample image can be reconstructed based on the neural network so as to obtain a reconstructed image.
Step 104: calculating a difference value between a fully sampled image corresponding to the sample image and the reconstructed image;
step 105: updating a DCT filter operator, a TV filter operator and a regularization parameter in the magnetic resonance reconstruction model by using a back propagation algorithm in a network according to the difference value, so as to realize the optimization training of the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets the preset precision requirement;
further, after reconstruction, a loss value can be calculated by a standard mean square error between the reconstructed image and the original image, and the expression is as follows:
the lambda represents the number of the training sets, and the parameters of the network model can be updated through back propagation based on the loss value, so that each parameter in the network model can be updated optimally based on the loss value, and the finally determined parameters of the network model can be guaranteed to be higher in reconstruction accuracy.
The update process of the back propagation parameter may be a Loss layer gradient update, and may be represented as:
step 106: and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
In the above example, the regularization term in the CS-MRI model is improved, including using discrete cosine filter operator (DCT) in the spatial domain and total variation filter operator (TV) in the time domain to perform de-redundancy on the dynamic magnetic resonance image, and using convolutional neural network to perform adaptive learning on a large number of parameters in the CS-MRI, and building a magnetic resonance image reconstruction model; reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image; calculating the difference value of the fully sampled image and the reconstructed image; updating parameters in the model, including DCT, TV filter operator, regularization parameter and the like, by using a back propagation algorithm in the network according to the difference value to realize optimization training of the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets the preset precision requirement; and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement. The magnetic resonance image reconstruction model established by the method can efficiently reconstruct the highly undersampled image to obtain an image with high reconstruction precision and reconstruction speed, so that the time of magnetic resonance scanning can be effectively shortened under the condition of not losing the spatial resolution.
The above method is described below with reference to a specific embodiment, however, it should be noted that the specific embodiment is only for better describing the present application and is not to be construed as a limitation of the present application.
In order to reconstruct an image, a regularization term is introduced, and in order to construct a good regularization term, it is often necessary to acquire feature information and prior knowledge of the image. However, the existing iterative method needs to artificially design the weight parameters of the regularization term, and the optimal parameters corresponding to different images may be different, so that the universality of the method is not very strong, and the time required by the existing iterative method is relatively long.
In this example, as shown in fig. 2, the magnetic resonance image is sparse, DCT filtering is introduced in the spatial domain and TV filtering is introduced in the temporal domain in the regularization term by using prior information such as sparse low rank specific to the Magnetic Resonance Image (MRI) itself, and the combination of the two can greatly reduce the redundancy of the image. Further, the solution is performed by using an iterative reconstruction method, because real projection data are used in the iterative process, the reconstruction result is theoretically more accurate. The iterative process is networked, and the regularization parameters of the image can be automatically learned without manual setting.
Specifically, with the joint sparse model, DCT filtering is used in the spatial domain, and TV filtering is used in the temporal domain to enhance the sparsity of the image, which can be performed according to the following formula:
wherein the content of the first and second substances,
is the reconstructed MRI image, y is undersampled k-space data, a = PF, where P is an undersampled matrix and F is the fourier transform. Phi denotes the filter operator (e.g. wavelet transform DWT, discrete cosine transform DCT, total variation TV), lambda 1 、λ 2 Are parameters that balance the data fidelity term with the regularization term.
According to the sparsity of the image, the above formula 1 can be changed to:
wherein the content of the first and second substances,
an image representing a spatial domain is provided,
representing the image in the time domain, α and β are two regularization parameters. Phi 1 Filter operator, phi, representing a DCT 2 Representing the filter operator of the TV. I | · | purple wind DCT Representing discrete cosine transform, | · | non-conducting phosphor TV Representing the total variation transformation.
Wherein, the first and the second end of the pipe are connected with each other,
finite difference operator representing previous frame and
representing the finite difference operator for the next frame.
In practical applications, the sparse induction norm for sparse regularization includes: l 0 Norm,/, of 1 Norm,/, of 2,1 Norm is defined as l of the row vector 2 Sum of norm, minimum l 2,1 The purpose of the norm is to select as few non-zero row vectors as possible. However, this can only be applied to vector norms. Researchers in the fields of deep learning, feature selection, multi-view learning, etc. propose to use matrix norms for sparse regularization, for example: by means of 2,p Matrix norm (0)<p<1) A more sparse solution can be obtained by making feature selection. In this example, select l 2,p Norm, for simplicity of illustration, further α = β. Accordingly, the above equation 2 can be simplified as:
wherein Φ represents Φ 1 And phi 2 Fusion of (a) ("lambda l ＝λ 1 ＝λ 2 For the regularization parameter, g (-) is l 2,p An approximation function of the norm.
By using an expansion iteration method to solve the above equation 3 and introducing an auxiliary variable z in the image domain, the above equation 3 can be converted into:
s.t.z = x (formula 4)
Wherein the augmented lagrange function of equation 4 above is:
the above formula 5 is converted into a plurality of subproblems to solve by using an alternating direction multiplier method, and the result is as follows:
wherein the content of the first and second substances,
beta is the scaling factor of Lagrange multiplier, k is an element of {1,2 t Denotes the number of iterations in the gradient descent, n denotes the nth layer, μ 1 ＝(1-l r ρ)，μ 2 ＝l r ρ representing learnable weight parameters, respectively,
l r which represents the size of the step size,
represents the update rate, H (-) represents the gradient of g (-), D (-) represents the gradient of g (-), D 1 Representing a transformation matrix.
To network the above equation 6, the above equation 6 may be modified as follows:
the formula is a reconstruction process of a forward propagation image, I represents an identity matrix, C 1 、C 2 Respectively represent two convolution layers, w 1 Corresponding to the combination of DCT and TV filters, size 3 x 1 x L, b 1 Representing an L-dimensional offset vector. w is a 2 Corresponding to the combination of DCT and TV filters, size 3 x L, b 2 Represents a 1-dimensional offset vector, S PLF (. Represents a point of
Piecewise linear function of control, N C Is a parameter for controlling a point in a piecewise linear function, as shown in fig. 3, DCTV-Net in fig. 3 represents a network flow chart, in which Recon represents a reconstruction layer, addition represents an overlay layer, conv1 represents a convolutional layer, nonlinear represents a Nonlinear transformation layer, conv2 represents a convolutional layer, and Multi represents a multiplier update layer.
After reconstruction, the reconstructed image and the original image can calculate the loss value through the standard mean square error, and the expression is as follows:
wherein Λ represents the number of training sets, a forward arrow in fig. 2 is a result of one-time iterative reconstruction, and a backward arrow represents a process of propagating update parameters backward.
The update process of the back propagation parameter may be Loss layer gradient update, and may be represented as:
in the above example, the magnetic resonance image is sparsely constrained by time-frequency domain sparse networking, so that a higher acceleration factor is obtained without losing spatial resolution. Furthermore, a large number of solution parameters in CS-MRI are replaced by CNN by using a self-adaptive learning method, so that the contingency caused by manual selection can be avoided. Compared with the deep learning reconstruction method, when the data size is limited, the method used in this example has higher reconstruction accuracy compared with the conventional deep learning method. Under the condition of the same acceleration multiple, the reconstruction precision is higher and the reconstruction effect is better in the mode of the embodiment. In this example, a neural network is used to learn these regularization parameters, and a trained model is obtained by offline training, and the online test requires only about 3 seconds to obtain a highly undersampled MRI reconstructed image.
The method embodiments provided in the above embodiments of the present application may be executed in a terminal device, a computer terminal, or a similar computing device. Taking the example of running on a terminal device, fig. 4 is a block diagram of a hardware structure of a computer terminal of the dynamic magnetic resonance image reconstruction method for adaptive parameter learning according to the embodiment of the present invention. As shown in fig. 4, terminal device 10 may include one or more (only one shown) processors 102 (processor 102 may include, but is not limited to, a processing device such as a microprocessor MCU or a programmable logic device FPGA, etc.), a memory 104 for storing data, and a transmission module 106 for communication functions. It will be understood by those skilled in the art that the structure shown in fig. 4 is only an illustration and is not intended to limit the structure of the electronic device. For example, the computer terminal 10 may also include more or fewer components than shown in FIG. 4, or have a different configuration than shown in FIG. 4.
The memory 104 can be used to store software programs and modules of application software, such as program instructions/modules corresponding to the dynamic magnetic resonance image reconstruction method for adaptive parameter learning in the embodiment of the present invention, and the processor 102 executes various functional applications and data processing by running the software programs and modules stored in the memory 104, that is, the dynamic magnetic resonance image reconstruction method for adaptive parameter learning described above is implemented. The memory 104 may include high speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include memory located remotely from the processor 102, which may be connected to the computer terminal 10 over a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The transmission module 106 is used to receive or transmit data via a network. Specific examples of the network described above may include a wireless network provided by a communication provider of the computer terminal 10. In one example, the transmission module 106 includes a Network adapter (NIC) that can be connected to other Network devices through a base station to communicate with the internet. In one example, the transmission module 106 may be a Radio Frequency (RF) module, which is used to communicate with the internet in a wireless manner.
At a software level, the apparatus may be as shown in fig. 5, and may include:
a replacing module 501, configured to use a DCT filter operator in a spatial domain and a TV filter operator in a time domain as regularization terms of CS-MRI;
a building module 502, configured to build a magnetic resonance image reconstruction model according to the regularization terms introduced with the DCT filter operator and the TV filter operator;
the reconstruction module 503 is configured to reconstruct the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
a calculating module 504, configured to calculate a difference between a fully sampled image corresponding to the sample image and the reconstructed image;
an iterative updating module 505, configured to update a DCT filter operator, a TV filter operator, and a regularization parameter in the magnetic resonance reconstruction model by using a back propagation algorithm in a network according to the difference value, so as to implement optimization training on the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets a preset precision requirement;
and the application module 506 is configured to perform magnetic resonance image reconstruction according to the magnetic resonance image reconstruction model meeting the preset accuracy requirement.
In one embodiment, the establishing module 502 may include: the generating unit is used for utilizing the joint sparse model, utilizing DCT filtering in a space domain and utilizing TV filtering in a time domain to enhance the sparsity of the image and obtain a sparsity expression formula; the first conversion unit is used for carrying out fusion conversion on the sparse expression formula to obtain a target formula; a second conversion unit for converting the target formula into a plurality of subproblem solving formulas by using an alternating direction multiplier method; and the networking unit is used for networking the plurality of subproblem solving formulas to obtain a magnetic resonance image reconstruction model.
In an embodiment, the generating unit may be specifically configured to set a filter operator of the following formula as a DCT operator and a TV operator:
wherein arg min f (x) represents the set of all arguments x that make the function f (x) take its minimum,
is the reconstructed magnetic resonance image, y represents undersampled k-space data, a = PF, where P is an undersampled matrix, F represents the fourier transform, Φ represents the filter operator, and λ represents the parameter.
The following equation is obtained:
wherein the content of the first and second substances,
an image representing a spatial domain is provided,
image representing the time domain, N t ＝{x 1 ,x2,...,x T Denotes a time-wise common T-frame image, phi 1 Representing DCT filter operator, phi 2 Representing TV filter operators，||·|| DCT Representing discrete cosine transform, | · | non-conducting phosphor TV Representing total variation transformation, λ 1 、λ 2 To balance the parameters of the data fidelity term with the regularization term.
In one embodiment, the target formula may be expressed as:
wherein z represents an auxiliary variable, α represents a Lagrangian multiplier, and g (·) represents l 2,p An approximation function of the norm, p, represents a penalty parameter.
In one embodiment, the above-mentioned plurality of sub-problem solving equations can be expressed as:
where T represents the transpose, β represents the scaling factor of the Lagrangian multiplier, and k ∈ {1,2 t Denotes the number of iterations in the gradient descent, n denotes the nth layer, μ 1 ＝(1-l r ρ)，μ 2 ＝l r ρ representing learnable weight parameters, respectively,
l r the size of the step size is indicated,
denotes the update rate, H (-) denotes the gradient of g (-), D 1 Representing a transformation matrix.
In one embodiment, networking the plurality of sub-problem solving equations may result in:
wherein I represents an identity matrix, C 1 、C 2 Respectively representTwo convolutional layers, w 1 Corresponding to the combination of DCT and TV filters, size 3 x 1 x L, b 1 Representing an L-dimensional offset vector. w is a 2 Corresponding to the combination of DCT and TV filters, size 3 x L, b 2 Represents a 1-dimensional offset vector, S PLF (. Represents a point of
Piecewise linear function of control, N C Is a parameter for controlling a point in a piecewise linear function, recon denotes a reconstruction layer, addition denotes an overlay layer, conv1 denotes a convolution layer, nonlinear denotes a Nonlinear transformation layer, conv2 denotes a convolution layer, and Multi denotes a multiplier update layer.
An embodiment of the present application further provides a specific implementation manner of an electronic device, which is capable of implementing all steps in the dynamic magnetic resonance image reconstruction method for adaptive parameter learning in the foregoing embodiment, where the electronic device specifically includes the following contents:
a processor (processor), a memory (memory), a communication Interface (Communications Interface), and a bus;
the processor, the memory and the communication interface complete mutual communication through the bus; the processor is configured to call a computer program in the memory, and the processor implements all the steps of the dynamic magnetic resonance image reconstruction method of adaptive parameter learning in the above embodiments when executing the computer program, for example, the processor implements the following steps when executing the computer program:
step 1: taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization items of CS-MRI;
step 2: establishing a magnetic resonance image reconstruction model according to regularization terms of a DCT filter operator and a TV filter operator;
and step 3: reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
and 4, step 4: calculating the difference value between the fully sampled image corresponding to the sample image and the reconstructed image;
and 5: updating a DCT filter operator, a TV filter operator and a regularization parameter in the magnetic resonance image reconstruction model by using a back propagation algorithm in a network according to the difference until the magnetic resonance image reconstruction model meets a preset precision requirement;
step 6: and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
From the above description, since the magnetic resonance image is sparse and has noise, the DCT filter operator in the spatial domain and the TV filter operator in the time domain are used as regularization parameters to establish a magnetic resonance image reconstruction model, which can remove redundancy in the spatial direction and the time direction, respectively, thereby effectively improving the reconstruction effect. Furthermore, the DCT filter operator and the TV filter operator in the time domain are adjusted in a network autonomous learning mode, so that the precision of a magnetic resonance image reconstruction model can be effectively improved, the magnetic resonance image reconstruction model established in the mode can be used for efficiently reconstructing highly undersampled images, images with high reconstruction precision and reconstruction speed are obtained, and the time of magnetic resonance scanning can be effectively shortened under the condition of not losing spatial resolution.
Embodiments of the present application further provide a computer-readable storage medium capable of implementing all the steps in the dynamic magnetic resonance image reconstruction method for adaptive parameter learning in the above embodiments, where the computer-readable storage medium stores thereon a computer program, and when the computer program is executed by a processor, the computer program implements all the steps in the dynamic magnetic resonance image reconstruction method for adaptive parameter learning in the above embodiments, for example, when the processor executes the computer program, the processor implements the following steps:
step 1: taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization items of CS-MRI;
step 2: establishing a magnetic resonance image reconstruction model according to regularization terms of a DCT filter operator and a TV filter operator;
and step 3: reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
and 4, step 4: calculating a difference value between a fully sampled image corresponding to the sample image and the reconstructed image;
and 5: updating a DCT (discrete cosine transform) filter operator, a TV (television) filter operator and a regularization parameter in the magnetic resonance reconstruction model by using a back propagation algorithm in a network according to the difference value to realize optimization training of the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets a preset precision requirement;
step 6: and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
From the above description, since the magnetic resonance image is sparse and has noise, the DCT filter operator in the spatial domain and the TV filter operator in the time domain are used as regularization parameters to establish a magnetic resonance image reconstruction model, which can remove redundancy in the spatial direction and the time direction, respectively, and thus, the reconstruction effect can be effectively improved. Furthermore, the DCT filter operator and the TV filter operator in the time domain are adjusted in a network autonomous learning mode, so that the precision of a magnetic resonance image reconstruction model can be effectively improved, the magnetic resonance image reconstruction model established in the mode can be used for efficiently reconstructing highly undersampled images to obtain images with high reconstruction precision and reconstruction speed, and the time of magnetic resonance scanning can be effectively shortened under the condition of not losing spatial resolution.
All the embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the hardware + program class embodiment, since it is substantially similar to the method embodiment, the description is simple, and the relevant points can be referred to the partial description of the method embodiment.
The foregoing description has been directed to specific embodiments of this disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.
Although the present application provides method steps as described in an embodiment or flowchart, additional or fewer steps may be included based on routine or non-inventive labor. The order of steps recited in the embodiments is merely one manner of performing the steps in a multitude of orders and does not represent the only order of execution. When an actual apparatus or client product executes, it may execute sequentially or in parallel (e.g., in the context of parallel processors or multi-threaded processing) according to the embodiments or methods shown in the figures.
The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. One typical implementation device is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a vehicle-mounted human-computer interaction device, a cellular telephone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.
Although embodiments of the present description provide method steps as described in embodiments or flowcharts, more or fewer steps may be included based on conventional or non-inventive means. The order of steps recited in the embodiments is merely one manner of performing the steps in a multitude of orders and does not represent the only order of execution. When an actual apparatus or end product executes, it may execute sequentially or in parallel (e.g., parallel processors or multi-threaded environments, or even distributed data processing environments) according to the method shown in the embodiment or the figures. The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, the presence of additional identical or equivalent elements in a process, method, article, or apparatus that comprises the recited elements is not excluded.
For convenience of description, the above devices are described as being divided into various modules by functions, and are described separately. Of course, in implementing the embodiments of the present description, the functions of each module may be implemented in one or more software and/or hardware, or a module implementing the same function may be implemented by a combination of multiple sub-modules or sub-units, and the like. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
Those skilled in the art will also appreciate that, in addition to implementing the controller as pure computer readable program code, the same functionality can be implemented by logically programming method steps such that the controller is in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Such a controller may therefore be considered as a hardware component, and the means included therein for performing the various functions may also be considered as a structure within the hardware component. Or even means for performing the functions may be regarded as being both a software module for performing the method and a structure within a hardware component.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
As will be appreciated by one skilled in the art, embodiments of the present description may be provided as a method, system, or computer program product. Accordingly, embodiments of the present description may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the present description may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The embodiments of this specification may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The specification embodiments may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, as for the system embodiment, since it is substantially similar to the method embodiment, the description is relatively simple, and reference may be made to the partial description of the method embodiment for relevant points. In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of an embodiment of the specification. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
The above description is only an example of the embodiments of the present disclosure, and is not intended to limit the embodiments of the present disclosure. Various modifications and variations to the embodiments described herein will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the embodiments of the present specification should be included in the scope of the claims of the embodiments of the present specification.
Claims (14)
1. A method for adaptive parameter learning dynamic magnetic resonance image reconstruction, the method comprising:
taking a discrete cosine DCT filter operator of a spatial domain and a total variation TV filter operator of a time domain as regularization items of compressed sensing-magnetic resonance imaging CS-MRI;
establishing a magnetic resonance image reconstruction model according to regularization terms of a DCT filter operator and a TV filter operator;
reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
calculating a difference value between a fully sampled image corresponding to the sample image and the reconstructed image;
updating a DCT filter operator, a TV filter operator and a regularization parameter in the magnetic resonance reconstruction model by using a back propagation algorithm in a network according to the difference value, so as to realize the optimization training of the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets the preset precision requirement;
and reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
2. The method of claim 1, wherein establishing a magnetic resonance image reconstruction model based on a regularization term that incorporates a DCT filter operator and a TV filter operator comprises:
utilizing a joint sparse model, utilizing DCT (discrete cosine transform) filtering in a spatial domain and utilizing TV (television) filtering in a time domain to enhance the sparsity of an image and obtain a sparsity expression formula;
performing fusion conversion on the sparse expression formula to obtain a target formula;
converting the target formula into a plurality of subproblem solving formulas by using an alternating direction multiplier method;
and networking the plurality of sub-problem solving formulas to obtain a magnetic resonance image reconstruction model.
3. The method of claim 2, wherein the joint sparse model is used, DCT filtering is used in a spatial domain, and TV filtering is used in a time domain to enhance the sparsity of the image, and a sparsity expression formula is obtained, and the method comprises the following steps:
setting the filter operators of the following formulas as a DCT filter operator and a TV filter operator:
wherein argminf (x) represents the set of all arguments x that make the function f (x) take its minimum,
is a reconstructed magnetic resonance image, N t ＝{x 1 ,x 2 ,...,x T The method comprises the following steps of (1) representing a T-frame image in the time direction, y representing undersampled k-space data, A = PF, wherein P is an undersampled matrix, F represents Fourier transform, phi represents a filter operator, and lambda represents a parameter;
the following equation is obtained:
wherein the content of the first and second substances,
an image representing a spatial domain is provided,
image representing the time domain,. Phi 1 Representing DCT filter operator, phi 2 Representing TV filter operator, | · Limu DCT Representing discrete cosine transform, | · | non-conducting phosphor TV Representing total variation transformation, λ 1 、λ 2 To balance the parameters of the data fidelity term with the regularization term.
4. The method of claim 3, wherein the target formula is:
wherein z represents an auxiliary variable, α represents a Lagrangian multiplier, and g (·) represents l 2,p An approximation function of the norm, p, represents a penalty parameter.
5. The method of claim 4, wherein the plurality of sub-problem solving equations are:
where T denotes transposition, β denotes the scaling factor of the Lagrangian multiplier, and k is {1,2 t Denotes the number of iterations in the gradient descent, n denotes the nth layer, μ 1 ＝(1-l r ρ)，μ 2 ＝l r ρ representing learnable weight parameters, respectively,
l r which represents the size of the step size,
represents the update rate, H (-) represents the gradient of g (-), D (-) represents the gradient of g (-), D 1 Representing a transformation matrix.
6. The method of claim 5, wherein the plurality of sub-problem solving equations are networked to obtain:
wherein I represents an identity matrix, C 1 、C 2 Respectively represent two convolution layers, w 1 Corresponding to the combination of DCT and TV filters, size 3 x 1 x l, b 1 Offset vector, w, representing dimension L 2 Corresponding to the combination of DCT and TV filters, size 3 x l, b 2 Represents a 1-dimensional offset vector, S PLF (. Represents a point of
Piecewise linear function of control, N C Is a parameter for controlling a point in a piecewise linear function, recon denotes a reconstruction layer, addition denotes an overlay layer, conv1 denotes a convolution layer, nonlinear denotes a Nonlinear transformation layer, conv2 denotes a convolution layer, and Multi denotes a multiplier update layer.
7. An adaptive parameter learning dynamic magnetic resonance image reconstruction apparatus, comprising:
the replacing module is used for taking a DCT filter operator of a spatial domain and a TV filter operator of a time domain as regularization items of CS-MRI;
the establishing module is used for establishing a magnetic resonance image reconstruction model according to the regularization items of the introduced DCT filter operator and the introduced TV filter operator;
the reconstruction module is used for reconstructing the sample image through the established magnetic resonance reconstruction model to obtain a reconstructed image;
the calculation module is used for calculating the difference value between the fully sampled image corresponding to the sample image and the reconstructed image;
the iterative updating module is used for updating a DCT (discrete cosine transform) filter operator, a TV (television) filter operator and a regularization parameter in the magnetic resonance reconstruction model by using a back propagation algorithm in a network according to the difference value so as to realize optimization training of the magnetic resonance reconstruction model until the magnetic resonance image reconstruction model meets a preset precision requirement;
and the application module is used for reconstructing the magnetic resonance image according to the magnetic resonance image reconstruction model meeting the preset precision requirement.
8. The apparatus of claim 7, wherein the establishing module comprises:
the generating unit is used for utilizing the joint sparse model, utilizing DCT filtering in a spatial domain and utilizing TV filtering in a time domain to enhance the sparsity of the image and obtain a sparsity expression formula;
the first conversion unit is used for carrying out fusion conversion on the sparse expression formula to obtain a target formula;
a second conversion unit for converting the target formula into a plurality of subproblem solving formulas by using an alternating direction multiplier method;
and the networking unit is used for networking the plurality of sub-problem solving formulas to obtain a magnetic resonance image reconstruction model.
9. The apparatus according to claim 8, wherein the generating unit is specifically configured to set the filter operators of the following formulas as a DCT filter operator and a TV filter operator:
wherein argminf (x) represents the set of all arguments x that make the function f (x) take its minimum,
is a reconstructed magnetic resonance image, y represents undersampled k-space data, a = PF, wherein P is an undersampled matrix, F represents fourier transform, Φ represents a filter operator, λ represents a parameter;
the following equation is obtained:
wherein the content of the first and second substances,
an image representing a spatial domain is provided,
image representing a time domain, N t ＝{x 1 ,x2,...,x T T denotes a common T frame image, Φ 1 Representing DCT filter operator, phi 2 Representing the TV filter operator, | · | | ventilation DCT Representing discrete cosine transform, | · | non-conducting phosphor TV Representing total variation transformation, λ 1 、λ 2 To balance the parameters of the data fidelity term with the regularization term.
10. The apparatus of claim 9, wherein the target formula is:
wherein z represents an auxiliary variable, α represents a Lagrangian multiplier, and g (·) represents l 2,p An approximation function of the norm, p, represents a penalty parameter.
11. The apparatus of claim 10, wherein the plurality of sub-problem solving equations are:
where T denotes transposition, β denotes the scaling factor of the Lagrangian multiplier, and k is {1,2 t Denotes the number of iterations in the gradient descent, n denotes the nth layer, μ 1 ＝(1-l r ρ)，μ 2 ＝l r ρ representing learnable weight parameters, respectively,
l r which represents the size of the step size,
represents the update rate, H (-) represents the gradient of g (-), D (-) represents the gradient of g (-), D 1 Representing a transformation matrix.
12. The apparatus of claim 11, wherein the plurality of sub-problem solving equations are networked to obtain:
wherein I represents an identity matrix, C 1 、C 2 Respectively represent two convolution layers, w 1 Corresponding to the combination of DCT and TV filters, size 3 x 1 x L, b 1 Representing an offset vector of dimension L, w 2 Set of DCT and TV filtersAnd the size is 3 x L, b 2 Represents a 1-dimensional offset vector, S PLF (. Represents a point of
Piecewise linear function of control, N C Is a parameter for controlling a point in a piecewise linear function, recon denotes a reconstruction layer, addition denotes an overlay layer, conv1 denotes a convolution layer, nonlinear denotes a Nonlinear transformation layer, conv2 denotes a convolution layer, and Multi denotes a multiplier update layer.
13. A terminal device comprising a processor and a memory for storing processor-executable instructions which, when executed by the processor, implement the steps of the method of any one of claims 1 to 6.
14. A computer readable storage medium having stored thereon computer instructions which, when executed, implement the steps of the method of any one of claims 1 to 6.
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