CN114972562B - Fast magnetic resonance imaging method combining coil sensitivity estimation and image reconstruction - Google Patents
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Abstract
A fast magnetic resonance imaging method combining coil sensitivity estimation and image reconstruction, comprising the steps of: 1) Acquiring multi-coil magnetic resonance Fourier space data and an undersampling template, and generating undersampling zero-filling multi-coil images, a complete multi-coil sensitivity map and a magnetic resonance image to form a training set; 2) The method comprises the steps of designing a joint magnetic resonance sensitivity estimation and image reconstruction deep learning network model based on sparse model expansion, and a feedback function and a loss function of the network; 3) Solving optimal parameters of the deep learning network based on sparse model expansion by utilizing the training set obtained in the step 1); 4) The undersampled magnetic resonance fourier space data to be reconstructed is input into the trained network to reconstruct the magnetic resonance image. By combining the magnetic resonance coil sensitivity estimation and the image sparsity, the depth neural network is guided to be designed by using a traditional optimization method, and the method has the characteristics of accurate coil sensitivity estimation, high image reconstruction speed and high reconstruction quality.
Description
Technical Field
The invention relates to a reconstruction method for joint magnetic resonance coil sensitivity estimation and image sparsity, in particular to a magnetic resonance multi-coil sensitivity estimation and image reconstruction method based on deep learning, which is developed by utilizing joint estimation multi-coil sensitivity and a sparse model.
Background
Magnetic resonance imaging (Magnetic Resonance Imaging, MRI) is a medical imaging technique that is widely used for diagnosis and research. However, MRI requires a longer scan time, which can cause patient discomfort and increase the probability of motion-related artifacts in the reconstructed image. One way to reduce MRI scan time is to acquire undersampled k-space data rather than acquiring the entire k-space data. However, sampling below the nyquist rate in k-space can lead to image domain artifacts, parallel imaging and sparse sampling undersamples short scan times through fourier space, but can introduce stronger image artifacts. Therefore, the reconstruction of undersampled images containing strong artifacts is an important issue in fast magnetic resonance imaging.
Over the last three decades, a number of magnetic resonance image reconstruction methods have been proposed. Many of these approaches require relying on coil sensitivity maps that are predicted by auto-calibration signals, such as sensitivity encoding (K.P.Pruessmann,M.Weiger,M.B.Scheidegger,P.Boesiger,"SENSE:Sensitivity encoding for fast MRI,"Magnetic Resonance in Medicine,vol.42,pp.952-962,1999.),, while sparse priors (X.Qu,Y.Hou,F.Lam,D.Guo,J.Zhong,Z.Chen,"Magnetic resonance image reconstruction from undersampled measurements using a patch-basednonlocal operator,"Medical Image Analysis,vol.18,pp.843-856,2014.;Y.Liu,Z.Zhan,J.-F.Cai,D.Guo,Z.Chen,X.Qu,"Projected iterative soft-thresholding algorithm for tight frames in compressed sensing magnetic resonance imaging,"IEEE Transactions on Medical Imaging,vol.35,pp.2130-2140,2016.;X.Zhang et al.,"A guaranteed convergence analysis for the projected fast iterative soft-thresholding algorithm in parallel MRI,"Medical Image Analysis,vol.69,101987,2021.) are typically used to regularize the combined coil image to improve reconstruction performance. However, the inherent iterative process results in excessively long reconstruction time, and the algorithm parameter selection is also very dependent on experience. An algorithm (L.Ying,J.Sheng,"Joint image reconstruction and sensitivity estimation in SENSE(JSENSE),"Magnetic Resonance in Medicine,vol.57,pp.1196-1202,2007) that combines sensitivity estimation and image reconstruction is proposed to update the coil sensitivity map and image simultaneously in a conventional iteration. However, this method has low coil sensitivity estimation accuracy when the acceleration speed is high or the acquired auto-calibration signal of the multi-coil k-space data is small, which may significantly affect the reconstruction performance of the magnetic resonance image.
Recently, with powerful convolutional neural networks, deep learning has shown great potential (S.Wang et al.,"Accelerating magnetic resonance imaging via deep learning,"in 2016IEEE 13th International Symposium on Biomedical Imaging(ISBI),2016,pp.514-517.;T.Lu et al.,"pFISTA-SENSE-ResNet for parallel MRI reconstruction,"Journal of Magnetic Resonance,vol.318,106790,2020.). in fast magnetic resonance imaging but most current MR reconstruction methods based on deep learning use coil sensitivity maps that are either pre-obtained in acquisition protocols or pre-calculated by coil sensitivity estimation methods. However, for acquired multi-coil k-space data, if the acceleration doubling rate is high or the auto-calibration signal is small, the estimated coil sensitivity map may be inaccurate, which may affect the reconstruction performance of the very large magnetic resonance image.
In the reconstruction of magnetic resonance images, the reconstruction quality of the existing method is still to be improved, and a method for realizing quick and high-quality magnetic resonance intelligent imaging and coil sensitivity estimation by combining a neural network of magnetic resonance coil sensitivity estimation and sparse characteristics of images is not available.
Disclosure of Invention
The invention aims to provide a rapid magnetic resonance imaging method combining coil sensitivity estimation and image reconstruction, which has high reconstruction speed and high reconstruction quality.
The invention comprises the following steps:
1) Acquiring multi-coil magnetic resonance Fourier space data, generating a multi-coil image with undersampled zero padding through operations such as inverse Fourier transform and the like, and forming a training set by the undersampled template, the complete multi-coil sensitivity map and the magnetic resonance image;
2) The method comprises the steps of designing a joint magnetic resonance sensitivity estimation and image reconstruction deep learning network model based on sparse model expansion, and a feedback function and a loss function of the network;
3) Solving optimal parameters of the deep learning network based on sparse model expansion by utilizing the training set obtained in the step 1);
4) The undersampled magnetic resonance fourier space data to be reconstructed is input into the trained network to reconstruct the magnetic resonance image.
In step 1), the specific method for obtaining the multi-coil magnetic resonance fourier space data, generating the undersampled zero-filled multi-coil image, the undersampled template, the complete multi-coil sensitivity map and the magnetic resonance image to form the training set through operations such as fourier transformation, and the like, may be as follows:
First, a complete multi-coil magnetic resonance image is acquired from a magnetic resonance imaging apparatus Representing the complete magnetic resonance image of the j-th coil,/>Representing a complex domain, wherein M, N and J respectively represent the number of lines, the number of columns and the number of coils of an image; then use undersampling operator/>Undersampling is carried out on the Fourier space data of each coil in X, so that the multislice Fourier space data/>, which is zero-filled by undersampling, of the X can be obtainedFourier space data representing undersampled zero padding of the jth coil, defined as/>Wherein/>A fourier transform operator representing the operation on each coil data; then, carrying out inverse Fourier transform operation on the Fourier space data of each coil in the Y, so as to obtain undersampled zero-filled multi-coil magnetic resonance image/>The magnetic resonance image obtained by performing the inverse Fourier transform after the undersampled Fourier space representing the jth coil is defined asWherein superscript denotes the accompanying operator, i.e./>And/>Are respectively/>And/>Is a companion operator to; then square sum and square root of the complete multi-coil magnetic resonance image X are carried out to obtain the image/>, of the synthetic coilWherein,Representing the real number domain, defined as/>Then each pixel of X is divided by the corresponding pixel in X combined, defined as/>Representing the sensitivity map corresponding to the complete magnetic resonance image of the jth coil, i.e./>And representing a sensitivity map corresponding to the complete multi-coil magnetic resonance image. Finally, a training set is composed of X, X u and C together.
In step 2), the sparse model expansion-based combined magnetic resonance sensitivity estimation and image reconstruction deep learning network model is formed by using a sensitivity initialization module and a network main body iteration block as cores and connecting a plurality of network main body iteration blocks in series. The sensitivity initialization module comprises a coding and decoding module, a depth noise reduction module and a sensitivity characteristic extraction module; the network body iteration block comprises a sparse reconstruction module, a sensitivity updating module and a data fidelity module.
The sensitivity initialization module comprises the following structure:
a) Coding of a codon block The module mainly comprises K encoder blocks E, K with different scales, decoder blocks D with different scales and a depth representation block R; a maximum pooling layer is arranged between encoder blocks E with different scales, and an up-sampling layer is arranged between decoder blocks D with different scales; the kth encoder block E k, the decoder block D k and the depth representation block R are formed by splicing N convolution layers, wherein a nonlinear rectification function (RECTIFIED LINEAR Unit, reLU) is arranged behind each convolution layer except the last layer of the decoder block D K, and the convolution kernel of the convolution layers has the size of h multiplied by h; the complete encoded decoding sub-block is represented by the following nonlinear mapping function:
XN＝fE(Xu|ΘE) (1)
Wherein X N represents a noisy multi-coil image with image texture removed, f E (·) represents a non-linear mapping trained by the encoded decoding sub-block, Θ E represents internal parameters in the encoded decoding sub-block;
b) Deep noise reduction sub-block The module mainly comprises a coil sensitivity linear mapping item and N convolution layers, wherein a normalization function (Batch Normalization, BN) and a linear rectification function (RECTIFIED LINEAR Unit, reLU) are connected behind each convolution layer except the last layer, and the convolution kernel of the convolution layer is h multiplied by h; the first layer input of the module is that the noisy multi-coil image X N,XN passes through the linear mapping item/>, of the coil sensitivityObtaining noisy coil sensitivity C IN, i.e./>The last layer outputs coil sensitivity noise sigma, and the output of the whole module is an image C IN-σ after noise is removed; the complete depth noise reduction module is represented by the following nonlinear function:
where C IN-σ represents the coil sensitivity to remove noise, f N (·) represents the nonlinear mapping trained by the deep noise reduction sub-block, Representing a noisy multi-coil image, Θ N representing the internal parameters in the depth noise reduction sub-block,/>Is to obtain a linear mapping of coil sensitivities corresponding to a multi-coil image, i.e./>C IN is the noise coil sensitivity, i.e./>Wherein/> Representing convolutional neural networks in deep noise reduction sub-blocks,/>Representing the residual coil sensitivity learned by the network, namely noise;
c) Coil sensitivity characteristic extraction sub-block The module mainly comprises N convolution layers, wherein each convolution layer is connected with a normalization function (Batch Normalization, BN) and a linear rectification function (RECTIFIED LINEAR Unit, reLU) except the last convolution layer; the input of the module is the multi-coil sensitivity C IN-σ after denoising, and the output is the coil sensitivity C F; the complete coil sensitivity characteristic extraction sub-block is represented by the following nonlinear function:
CF＝fCF(CIN-σ,Xu|ΘCF) (3)
Wherein C F represents the coil sensitivity, f CF (·) represents the nonlinear mapping trained by the coil sensitivity feature extraction sub-block, Θ CF represents the internal parameters in the coil sensitivity feature extraction sub-block;
the sensitivity initialization module is used for cascading the three sub-modules And/>Generating initialized multi-coil magnetic resonance sensitivity of an iteration block to be input, wherein the mapping function of a complete sensitivity initialization module is as follows:
Where C I represents the initialized coil sensitivity, F sensitivity (. Cndot.) represents the mapping from the multi-coil undersampled magnetic resonance image X u to the initialized sensitivity C I, Θ C＝{ΘE,ΘN,ΘCF } is the set of training parameters for the sensitivity initialization module, and F sensitivity (. Cndot.) is the combined function of the fE(Xu|ΘE),fN(XN|ΘN),fCF(CIN-σ,Xu|ΘCF) nonlinear mapping.
The network structure of the iterative block is as follows:
The iteration block of the iteration network based on sparse model expansion comprises three sub-blocks, namely a sparse reconstruction module R, a coil sensitivity updating module RC and a data fidelity module DC, wherein the inputs of the iteration network are a multi-coil undersampled filled magnetic resonance image X u and an initialization sensitivity C I, the iteration block can be represented by a mapping function f (X u,CI|ΘS), Θ S represents a set of iteration network training parameters, and the specific contents of the single sub-blocks are as follows:
a) The sparse reconstruction module R is used for sparse reconstruction of the magnetic resonance image; it consists of data check term and forward sparse learning term Soft threshold operator T γλ, inverse sparse learning term/>A total of 4 parts are sequentially connected to form the structure;
the data check item is used for guaranteeing consistency between the reconstructed image and the measured data, and the measured data is used for carrying out data check on the output of the last iteration block, and is defined as follows:
wherein V represents an intermediate variable of the magnetic resonance image output through the data check item, Gamma is the step size and gamma e Θ S,/>Is the coil sensitivity of the last iteration block estimated by the network, when in the first iteration block/>
The forward sparse learning termConsists of L convolution layers, wherein a nonlinear rectification function (RECTIFIED LINEAR Unit, reLU) is connected behind each convolution layer except the last convolution layer, the convolution kernel size is h multiplied by h, the input of the first layer is the output of a data check term, the result of the data check term is mapped into Z by a forward sparse learning term,
The soft threshold operator T γλ carries out soft threshold operation T γλ on the pixel point of the output Z of the forward sparse learning item, wherein gamma lambda is a threshold value and gamma lambda epsilon theta S; the definition of soft threshold operation is: given a matrix Z, Z x,y =0 if the absolute value of the element Z x,y of the x-th row and y-th column of the matrix Z is |z x,y |++γλ, Z x,y＝sgn(Zx,y)(|Zx,y | - γλ if |z x,y | > γλ), where sgn (·) is a sign function; i.e., Z becomes T γλ (Z) after soft thresholding;
The reverse sparse learning term The method consists of L convolution layers, wherein except the last convolution layer, each convolution layer is connected with a nonlinear rectification function (RECTIFIED LINEAR Unit, reLU), the convolution kernels are h multiplied by h, the input of the first layer is the output of a soft threshold operator, and the result of the soft threshold operator is mapped to an image domain X c in a nonlinear way by an inverse sparse learning term, wherein/>
The three sub-items are thatT γλ and/>Cascading, a single sparse reconstruction module overall can be represented by a set of nonlinear mapping functions as follows:
Wherein, X c is a merged channel image in which the inverse sparse learning term non-linearly maps the result of the soft threshold operator to the image domain;
b) The coil sensitivity updating module RC is used for updating the coil sensitivity based on the depth noise reduction module, and mainly comprises N convolution layers, wherein a normalization function (Batch Normalization, BN) and a linear rectification function (RECTIFIED LINEAR Unit, reLU) are connected behind each convolution layer except the last convolution layer, and the convolution kernel of the convolution layers is h multiplied by h; the first layer of input of the module is a noisy reconstructed image output by the previous iteration block And coil sensitivity/>, of last iteration block outputThe last layer outputs a noise image sigma C of the coil sensitivity, and the output of the whole module is the coil sensitivity/>, after noise removalThe complete coil sensitivity update module is represented by the following nonlinear function:
Where f r (·) represents the nonlinear mapping trained by the coil sensitivity update module, Θ r represents the internal parameters in the coil sensitivity update module, Multiple coil noisy image output for last iteration block,/>Is to obtain the linear mapping of the coil sensitivity corresponding to the multi-coil image, let/>I.e.Representing a deep noise reduction module convolutional neural network;
c) The data fidelity module DC is used for keeping the values of the reconstructed image and the undersampled image at sampling points of the Fourier transform space consistent so as to ensure that an output result is aligned with the acquired data, and is defined as follows:
Wherein X DC represents a multi-coil image after data fidelity, Representing the fourier transform, X Unfold is the output of the inverse sparse learning term, X c data check term D, added to the output of the coil sensitivity update module/>The product of (a), i.eΛ is the balance parameter and λε Θ S, (m, n) represents the position of the pixel point in the Fourier transform space of X Unfold and Ω is the set of positions of the undersampled image at the Fourier transform space sampling points.
The three sub-blocks, namely the sparse reconstruction module R, the coil sensitivity updating module RC and the data fidelity module DC are cascaded, and the whole single iteration block can be represented by the following nonlinear mapping function group:
Wherein Θ S represents a set of iterative network training parameters; f (·) represents a cascade of modules of the iterative block; f sparse(Xu,CI|ΘS) represents the trained range from X u,CI to Is a nonlinear mapping of each module/> F D(XUnfold,Xu |λ)) in combination;
the sensitivity initialization module and the network iteration block based on sparse model expansion are cascaded, and the designed joint magnetic resonance sensitivity estimation based on sparse model expansion and image reconstruction deep learning network model can be integrally expressed as:
Where Θ represents the set of parameters within the overall network; f overall(Xu |Θ) represents the trained multi-coil image X u from undersampled zero padding to the net final output value F overall (·) represents a concatenation of a sensitivity initialization module and a sparse model-based expanded network iteration block.
The feedback function of the network is an important process of solving target values by the network, and in the process of constructing a network model, the output values of the network are used for solving the target valuesComparing the parameter with the complete multi-coil image and the coil sensitivities X and C, and feeding back gradients to update the parameters of the iteration module, so that the network output value is more approximate to the complete multi-coil image and the coil sensitivities;
the loss function may be defined as:
Where Θ represents a set of parameters within the overall network, |·| 2 represents a two-norm term, S represents the S-th iteration block, s=1, 2,..s, S represents the total number of iteration blocks, β represents a canonical parameter, Σ represents a summation operation.
In step 3), the solution of the optimal parameters of the joint magnetic resonance sensitivity estimation and image reconstruction deep learning network model based on sparse model expansion can adopt an Adam optimizer with better deep learning performance, perform network training by using the training set generated in step 1), and minimize the loss function in step 2)To obtain the optimal target parameter set
In step 4), the parameters of the network optimization have been obtained by step 3)The network nonlinear mapping function f overall (·) has determined that inputting the undersampled multi-coil magnetic resonance image data to be reconstructed into the trained network f overall (·) reconstructs a magnetic resonance image and estimates coil sensitivities, and the network reconstruction process can be expressed as:
The invention provides a rapid magnetic resonance imaging method combining coil sensitivity estimation and image reconstruction. The invention firstly collects complete multi-coil magnetic resonance images and coil sensitivities as training sets, then establishes a deep learning network model for magnetic resonance multi-coil sensitivity estimation and image reconstruction, trains the deep learning network model by utilizing the training sets to obtain a trained network, and finally inputs undersampled multi-channel magnetic resonance images into the network to reconstruct the complete coil sensitivities and magnetic resonance images. Compared with the prior art, the method and the device have the advantages that the reconstructed coil sensitivity and the magnetic resonance image can be obtained after the undersampled multi-coil image is subjected to forward propagation for one time by utilizing the network model obtained through training, and the reconstruction quality of the undersampled image is improved through joint estimation reconstruction.
Drawings
FIG. 1 is an undersampled template of 25% sample rate employed in an embodiment.
Fig. 2 is a schematic diagram of the overall network structure of the proposed combined magnetic resonance coil sensitivity estimation and image reconstruction method.
FIG. 3 is a detailed structure of each module of the network structure of the proposed combined MRI coil sensitivity estimation and image reconstruction method, wherein (a) is a schematic diagram of the network structure of the sensitivity initialization module; (b) a network structure schematic diagram of a sparse reconstruction module R; (c) A network structure diagram of the coil sensitivity updating module RC; (d) a network architecture schematic of the data fidelity module DC.
Fig. 4 is a full sample label image of the brain and estimated coil sensitivity and reconstructed image at 25% sample rate. Wherein, (a) is combining the full sampling label images; (b) is a reconstructed image of the present invention; (c) The four times of the reconstructed image corresponds to the four times of the amplified error map; (d) Coil sensitivity corresponding to a 5 th coil image in the multi-coil full-sampling label image; (e) Coil sensitivity corresponding to the 5 th coil image estimated for the present invention; (f) Coil sensitivity and corresponding error map estimated for the present invention.
Detailed Description
The invention will be further illustrated by the following examples in conjunction with the accompanying drawings. According to the embodiment of the invention, a training set is constructed by utilizing multi-coil brain data, optimal network parameters are obtained through a plurality of iterative training, and finally undersampled multi-channel brain data to be reconstructed are input into a trained deep learning network model to obtain estimated coil sensitivity and a reconstructed magnetic resonance image.
Specific examples are given below.
The embodiment of the invention comprises the following steps:
the first step: acquiring multi-channel magnetic resonance images as a training set
The brain of 6 volunteers was imaged using a magnetic resonance apparatus with a magnetic field strength of 3 tesla in an embodiment of the present invention. The sequence parameters used in this embodiment are: echo time te=6900 ms, repetition time tr=2500 ms, field of view 256mm256mm, layer thickness 3mm, coil channel number 12. The brain images of 6 volunteers after being scanned by the magnetic resonance instrument are used as a training set and a testing set of the network, wherein the training set is from 250 multichannel magnetic resonance images of 5 volunteers, and the testing set is from 50 multichannel magnetic resonance images of another volunteer. The training and test sets are then fourier space undersampled using a sampling template with a sampling rate of 25%.
Wherein a single multi-coil magnetic resonance imageA complete magnetic resonance image representing the jth coil; then use undersampling operator/>Undersampling operation is carried out on Fourier space data of each coil in X, an undersampling operator is shown in figure 1, white sampling points in an undersampling template represent that data corresponding to the position are sampled; black represents the point that is not sampled, and the data corresponding to the position is lost), and multi-coil Fourier space data/>, which is obtained by undersampling and zero filling, is obtainedFourier space data representing undersampled of the jth coil, defined as/>Wherein/>A fourier transform operator representing the operation on each coil data; then carrying out inverse Fourier transform operation on the Fourier space data of each coil in the Y to obtain undersampled zero-filled multi-coil magnetic resonance image/>Magnetic resonance image obtained by performing inverse fourier transform after filling zero in undersampled fourier space representing jth coil, defined as/>Then square sum and square root of the complete multi-coil magnetic resonance image X are carried out to obtain the image/>, of the synthetic coilThen dividing each pixel point of X by the corresponding pixel point in X combined, specifically/>And,/>Representing the sensitivity map corresponding to the complete magnetic resonance image of the jth coil, i.e./>And finally, forming a training set by X, X u and C together.
And a second step of: combined magnetic resonance sensitivity estimation and image reconstruction deep learning network model based on sparse model expansion, feedback function of network and loss function
The deep learning network model takes a sensitivity initialization module and a network main body iteration block as cores and is composed of a plurality of iteration blocks connected in series. The sensitivity initialization module comprises a coding and decoding module, a depth noise reduction module and a sensitivity characteristic extraction module, and the network main body iteration module comprises a sparse reconstruction module, a sensitivity updating module and a data fidelity module.
A. the sensitivity initialization module comprises the following structure:
a) Coding of a codon block The module mainly comprises 4 encoder blocks E with different scales, 4 decoder blocks D with different scales and a depth representation block R; a maximum pooling layer is arranged between encoder blocks E with different scales, and an up-sampling layer is arranged between decoder blocks D with different scales; the kth encoder block E k, the decoder block D k and the depth representation block R are formed by splicing 3 convolution layers, wherein except for the last layer of the decoder block D K, each convolution layer is followed by a nonlinear rectification function (RECTIFIED LINEAR Unit, reLU), and the convolution kernel of the convolution layers has a size of 3 multiplied by 3; the complete encoded decoding sub-block is represented by the following nonlinear mapping function:
XN＝fE(Xu|ΘE) (1)
wherein X N represents a noisy multi-coil image with image texture removed, f E (·) represents a non-linear mapping trained by the encoded decoding sub-block, Θ E represents internal parameters in the encoded decoding sub-block;
b) Deep noise reduction sub-block The module mainly comprises a coil sensitivity linear mapping item and 5 convolution layers, wherein a normalization function (Batch Normalization, BN) and a linear rectification function (RECTIFIED LINEAR Unit, reLU) are connected behind each convolution layer except the last one, and the convolution kernel of the convolution layers is 3 multiplied by 3; the first layer input of the module is that the noisy multi-coil image X N,XN passes through the linear mapping item/>, of the coil sensitivityObtaining noisy coil sensitivity C IN, i.e./>The last layer outputs coil sensitivity noise sigma, and the output of the whole module is an image C IN-σ after noise is removed; the complete depth noise reduction module is represented by the following nonlinear function:
where C IN-σ represents the coil sensitivity to remove noise, f N (·) represents the nonlinear mapping trained by the deep noise reduction sub-block, Representing a noisy multi-coil image, Θ N representing the internal parameters in the depth noise reduction sub-block,/>Is to obtain a linear mapping of coil sensitivities corresponding to a multi-coil image, i.e./>C IN is the noise coil sensitivity, i.e./>Wherein/> Representing convolutional neural networks in deep noise reduction sub-blocks,/>Representing the residual coil sensitivity learned by the network, namely noise;
d) Coil sensitivity characteristic extraction sub-block The module mainly comprises 8 convolution layers, wherein each convolution layer is connected with a normalization function (Batch Normalization, BN) and a linear rectification function (RECTIFIED LINEAR Unit, reLU) except the last convolution layer; the input of the module is the multi-coil sensitivity C IN-σ after denoising, and the output is the coil sensitivity C F; the complete coil sensitivity characteristic extraction sub-block is represented by the following nonlinear function:
CF＝fCF(CIN-σ,Xu|ΘCF) (3)
Wherein C F represents the coil sensitivity, f CF (·) represents the nonlinear mapping trained by the coil sensitivity feature extraction sub-block, Θ CF represents the internal parameters in the coil sensitivity feature extraction sub-block;
In summary, the sensitivity initialization module is implemented by cascading the three sub-modules And/>Generating initialized multi-coil magnetic resonance sensitivity of an iteration block to be input, wherein the mapping function of a complete sensitivity initialization module is as follows:
Where C I represents the initialized coil sensitivity, F sensitivity (. Cndot.) represents the mapping from the multi-coil undersampled magnetic resonance image X u to the initialized sensitivity C I, Θ C＝{ΘE,ΘN,ΘCF } is the set of training parameters for the sensitivity initialization module, and F sensitivity (. Cndot.) is the combined function of the fE(Xu|ΘE),fN(XN|ΘN),fCF(CIN-σ,Xu|ΘCF) nonlinear mapping.
B. The network structure of the iterative block is as follows
The iteration block of the iteration network based on sparse model expansion comprises three sub-blocks, namely a sparse reconstruction module R, a coil sensitivity updating module RC and a data fidelity module DC, wherein the inputs of the iteration network are a multi-coil undersampled magnetic resonance image X u and an initialization sensitivity C I, the multi-coil undersampled magnetic resonance image X u is represented by a mapping function f (X u,CI|ΘS), the theta S represents a set of iteration network training parameters, and the specific contents of the single sub-blocks are as follows:
a) The sparse reconstruction module R is used for sparse reconstruction of the magnetic resonance image; it consists of data check term and forward sparse learning term Soft threshold operator T γλ, inverse sparse learning term/>A total of 4 parts are sequentially connected to form the structure;
the data check item is used for guaranteeing consistency between the reconstructed image and the measured data, and the measured data is used for carrying out data check on the output of the last iteration block, and is defined as follows:
wherein V represents an intermediate variable of the magnetic resonance image output through the data check item, Gamma is the step size and gamma e Θ S,/>Is the coil sensitivity of the last iteration block estimated by the network, when in the first iteration block/>
The forward sparse learning termConsists of 3 convolution layers, wherein a nonlinear rectification function (RECTIFIED LINEAR Unit, reLU) is connected behind each convolution layer except the last convolution layer, the convolution kernel size is 3 multiplied by 3, the input of the first layer is the output of a data check term, the result of the data check term is mapped into Z by a forward sparse learning term,
The soft threshold operator T γλ carries out soft threshold operation T γλ on the pixel point of the output Z of the forward sparse learning item, wherein gamma lambda is a threshold value and gamma lambda epsilon theta S; the definition of soft threshold operation is: given a matrix Z, Z x,y =0 if the absolute value of the element Z x,y of the x-th row and y-th column of the matrix Z is |z x,y |++γλ, Z x,y＝sgn(Zx,y)(|Zx,y | - γλ if |z x,y | > γλ), where sgn (·) is a sign function; i.e., Z becomes T γλ (Z) after soft thresholding;
The reverse sparse learning term Consists of 3 convolution layers, wherein except the last convolution layer, each convolution layer is connected with a nonlinear rectification function (RECTIFIED LINEAR Unit, reLU), the convolution kernel size is 3 multiplied by 3, the input of the first layer is the output of a soft threshold operator, and the inverse sparse learning term is used for nonlinear mapping of the result of the soft threshold operator to an image domain X c, wherein/>
The three sub-items are thatT γλ and/>Cascading, the whole single sparse reconstruction module is represented by the following nonlinear mapping function group:
Wherein, X c is a merged channel image in which the inverse sparse learning term non-linearly maps the result of the soft threshold operator to the image domain;
b) The coil sensitivity updating module RC is used for updating the coil sensitivity based on the depth noise reduction module, the module mainly comprises 5 convolution layers, except the last convolution layer, a normalization function (Batch Normalization, BN) and a linear rectification function (RECTIFIED LINEAR Unit, reLU) are connected behind each convolution layer, and the convolution kernel of the convolution layers is 3 multiplied by 3; the first layer of input of the module is a noisy reconstructed image output by the previous iteration block And coil sensitivity/>, of last iteration block outputThe last layer outputs a noise image sigma C of the coil sensitivity, and the output of the whole module is the coil sensitivity/>, after noise removalThe complete coil sensitivity update module is represented by the following nonlinear function:
Where f r (·) represents the nonlinear mapping trained by the coil sensitivity update module, Θ r represents the internal parameters in the coil sensitivity update module, Multiple coil noisy image output for last iteration block,/>Is to obtain the linear mapping of the coil sensitivity corresponding to the multi-coil image, let/>I.e.Representing a deep noise reduction module convolutional neural network;
c) The data fidelity module DC is used for keeping the values of the reconstructed image and the undersampled image at sampling points of the Fourier transform space consistent so as to ensure that an output result is aligned with the acquired data, and is defined as follows:
Wherein X DC represents a multi-coil image after data fidelity, Representing the fourier transform, X Unfold is the output of the inverse sparse learning term, X c data check term D, added to the output of the coil sensitivity update module/>The product of (a), i.eΛ is the balance parameter and λε Θ S, (m, n) represents the position of the pixel point in the Fourier transform space of X Unfold and Ω is the set of positions of the undersampled image at the Fourier transform space sampling points.
The three sub-blocks, namely the sparse reconstruction module R, the coil sensitivity updating module RC and the data fidelity module DC are cascaded, and the whole single iteration block is represented by the following nonlinear mapping function group:
Wherein Θ S represents a set of iterative network training parameters; f (·) represents a cascade of modules of the iterative block; f sparse(Xu,CI|ΘS) represents the trained range from X u,CI to Is a nonlinear mapping of each module/> F D(XUnfold,Xu |λ)) in combination;
in summary, the sensitivity initialization module and the network iteration block based on sparse model expansion are cascaded, and the designed joint magnetic resonance sensitivity estimation based on sparse model expansion and the image reconstruction deep learning network model are integrally expressed as:
Where Θ represents the set of parameters within the overall network; f overall(Xu |Θ) represents the trained multi-coil image X u from undersampled zero padding to the net final output value F overall (·) represents a concatenation of a sensitivity initialization module and a sparse model-based expanded network iteration block.
The feedback function of the network is an important process of solving target values by the network, and in the process of constructing a network model, the output values of the network are used for solving the target valuesComparing the parameter with the complete multi-coil image and the coil sensitivities X and C, and feeding back gradients to update the parameters of the iteration module, so that the network output value is more approximate to the complete multi-coil image and the coil sensitivities;
The loss function is defined as:
Where Θ represents a set of parameters inside the overall network, |·| 2 represents a two-norm term, S represents an S-th iteration block, s=1, 2,..s, S represents the total number of iteration blocks, in this embodiment s=5, β represents a canonical parameter, in this embodiment β=0.1, and Σ represents a summation operation.
And a third step of: training optimal parameters of joint magnetic resonance sensitivity estimation and image reconstruction deep learning network model based on sparse model expansion
An Adam optimizer (DIEDERIK KINGMA AND Jimmy Ba, "Adam: A method for stochastic optimization," arXiv:1412.6980,2014) with good performance in deep learning was used, the learning rate was set to 0.0001, 100 times training was performed using the training set generated in the first step, and the loss function in the second step was minimizedTo obtain the optimal target parameter set/>
Fourth step: coil sensitivity estimation and image reconstruction are performed on the undersampled magnetic resonance image to obtain estimated coil sensitivity and a reconstructed magnetic resonance image
Inputting the undersampled multi-coil magnetic resonance image data to be reconstructed into a trained network f overall (·) to reconstruct a magnetic resonance image and estimate coil sensitivity, the network reconstruction process being represented as:
In an embodiment, the network input is 25% sampling rate (undersampled template is shown in FIG. 1. In FIG. 1, the white in the undersampled template is a sample point, indicating that the data corresponding to the location is sampled, the black indicates that the data corresponding to the location is not sampled, and the data dimension is 256×186×12 for undersampled multi-coil brain data. The complete label image of brain data and the corresponding 5 th coil sensitivity are shown in fig. 4 (a) and fig. 4 (d), respectively, and the coil sensitivity estimation and reconstruction image of the present invention at 25% sampling rate are shown in fig. 3 (e) and fig. 3 (b), respectively.
Compared with the prior art, the method and the device have the advantages that the network model obtained through training is utilized to conduct forward propagation on the undersampled multi-coil image once, the reconstructed coil sensitivity and the magnetic resonance image are obtained, and the reconstruction quality of the undersampled image is improved through joint estimation reconstruction.
Claims (8)
1. A method of fast magnetic resonance imaging combining coil sensitivity estimation and image reconstruction, comprising the steps of:
1) The method comprises the steps of obtaining multi-coil magnetic resonance Fourier space data, generating a multi-coil image with undersampled zero padding through inverse Fourier transform operation, and forming a training set by an undersampled template, a complete multi-coil sensitivity map and a magnetic resonance image, wherein the specific method comprises the following steps:
First, a complete multi-coil magnetic resonance image is acquired from a magnetic resonance imaging apparatus Representing the complete magnetic resonance image of the j-th coil,/>Representing a complex domain, wherein M, N and J respectively represent the number of lines, the number of columns and the number of coils of an image; then, undersampling operator/>, is usedUndersampling operation is carried out on the Fourier space data of each coil in X to obtain undersampled zero-filled multi-coil Fourier space data/> Fourier space data representing undersampled zero padding of the jth coil, defined as/>Wherein/>A fourier transform operator representing the operation on each coil data; then carrying out inverse Fourier transform operation on the Fourier space data of each coil in the Y to obtain undersampled zero-filled multi-coil magnetic resonance image/>Magnetic resonance image obtained by performing inverse fourier transform after filling zero in undersampled fourier space representing jth coil, defined as/>Wherein superscript denotes the accompanying operator, i.e./>And/>Are respectively/>And/>Is a companion operator to; then square sum and square root of the complete multi-coil magnetic resonance image X are carried out to obtain the image/>, of the synthetic coilWherein/>Representing the real number domain, defined as/>Then each pixel of X is divided by the corresponding pixel in X combined, defined asRepresenting the sensitivity map corresponding to the complete magnetic resonance image of the jth coil, i.e./>Representing a sensitivity map corresponding to the complete multi-coil magnetic resonance image; finally, X, X u and C together form a training set;
2) The method comprises the steps of designing a joint magnetic resonance sensitivity estimation and image reconstruction deep learning network model based on sparse model expansion, and a feedback function and a loss function of the network;
3) Solving optimal parameters of the deep learning network based on sparse model expansion by utilizing the training set obtained in the step 1);
4) The undersampled magnetic resonance fourier space data to be reconstructed is input into the trained network to reconstruct the magnetic resonance image.
2. The method for rapid magnetic resonance imaging by combining coil sensitivity estimation and image reconstruction according to claim 1, wherein in the step 2), the sparse model expansion-based combined magnetic resonance sensitivity estimation and image reconstruction deep learning network model is formed by a plurality of network body iteration blocks connected in series by taking a sensitivity initialization module and a network body iteration block as cores; the sensitivity initialization module comprises a coding and decoding module, a depth noise reduction module and a sensitivity characteristic extraction module; the network body iteration block comprises a sparse reconstruction module, a sensitivity updating module and a data fidelity module.
3. A method of fast magnetic resonance imaging combining coil sensitivity estimation and image reconstruction as recited in claim 2, wherein the sensitivity initialization module comprises the structure:
a) Coding of a codon block The module specifically comprises K encoder blocks E, K with different scales, a decoder block D with different scales and a depth representation block R; a maximum pooling layer is arranged between encoder blocks E with different scales, and an up-sampling layer is arranged between decoder blocks D with different scales; the kth encoder block E k, the decoder block D k and the depth representation block R are formed by splicing N convolution layers, except for the last layer of the decoder block D K, each convolution layer is provided with a nonlinear rectification function, and the convolution kernel of the convolution layer has the size of h multiplied by h; the complete encoded decoding sub-block is represented by the following nonlinear mapping function:
XN＝fE(Xu|ΘE) (1)
wherein X N represents a noisy multi-coil image with image texture removed, f E (·) represents a non-linear mapping trained by the encoded decoding sub-block, Θ E represents internal parameters in the encoded decoding sub-block;
b) Deep noise reduction sub-block The module mainly comprises a coil sensitivity linear mapping item and N convolution layers, wherein a normalization function and a linear rectification function are connected behind each convolution layer except the last layer, and the convolution kernel of the convolution layer is h multiplied by h; the first layer input of the module is that the noisy multi-coil image X N,XN passes through the linear mapping item/>, of the coil sensitivityObtaining noisy coil sensitivity C IN, i.e./>The last layer outputs coil sensitivity noise sigma, and the output of the whole module is coil sensitivity C IN-σ with noise removed; the complete depth noise reduction module is represented by the following nonlinear function:
where C IN-σ represents the coil sensitivity to remove noise, f N (·) represents the nonlinear mapping trained by the deep noise reduction sub-block, Representing a noisy multi-coil image, Θ N representing the internal parameters in the depth noise reduction sub-block,/>Is to obtain a linear mapping of coil sensitivities corresponding to a multi-coil image, i.e./>C IN is the coil sensitivity with noise, i.e./>Wherein/> Representing convolutional neural networks in deep noise reduction sub-blocks,/>Representing the residual coil sensitivity learned by the network, namely noise;
c) Coil sensitivity characteristic extraction sub-block The module mainly comprises N convolution layers, wherein each convolution layer is connected with a normalization function and a linear rectification function except the last convolution layer; the input of the module is coil sensitivity C IN-σ for removing noise, and the output is coil sensitivity C F; the complete coil sensitivity characteristic extraction sub-block is represented by the following nonlinear function:
CF＝fCF(CIN-σ,Xu|ΘCF) (3)
Wherein C F represents the coil sensitivity, f CF (·) represents the nonlinear mapping trained by the coil sensitivity feature extraction sub-block, Θ CF represents the internal parameters in the coil sensitivity feature extraction sub-block;
the sensitivity initialization module is used for cascading the three sub-modules And/>Generating initialized multi-coil magnetic resonance sensitivity of an iteration block to be input, wherein the mapping function of a complete sensitivity initialization module is as follows:
Where C I represents the initialized coil sensitivity, F sensitivity (. Cndot.) represents the mapping from the multi-coil undersampled magnetic resonance image X u to the initialized sensitivity C I, Θ C＝{ΘE,ΘN,ΘCF } is the set of training parameters for the sensitivity initialization module, and F sensitivity (. Cndot.) is the combined function of the fE(Xu|ΘE),fN(XN|ΘN),fCF(CIN-σ,Xu|ΘCF) nonlinear mapping.
4. A method of fast magnetic resonance imaging combining coil sensitivity estimation and image reconstruction as claimed in claim 2, wherein the network structure of the iterative block is as follows:
The iteration block of the iteration network based on sparse model expansion comprises three sub-blocks, namely a sparse reconstruction module R, a coil sensitivity updating module RC and a data fidelity module DC, wherein the inputs of the iteration network are a multi-coil undersampled magnetic resonance image X u and an initialization sensitivity C I, the multi-coil undersampled magnetic resonance image X u is represented by a mapping function f (X u,CI|ΘS), the theta S represents a set of iteration network training parameters, and the specific contents of the single sub-blocks are as follows:
a) The sparse reconstruction module R is used for sparse reconstruction of the magnetic resonance image; it consists of data check term and forward sparse learning term Soft threshold operator T γλ, inverse sparse learning term/>A total of 4 parts are sequentially connected to form the structure;
the data check item is used for guaranteeing consistency between the reconstructed image and the measured data, and the measured data is used for carrying out data check on the output of the last iteration block, and is defined as follows:
wherein V represents an intermediate variable of the magnetic resonance image output through the data check item, Gamma is the step size and gamma e Θ S,/>Is the coil sensitivity of the last iteration block estimated by the network, when in the first iteration block/>
The forward sparse learning termConsists of L convolution layers, wherein a nonlinear rectification function (RECTIFIED LINEAR Unit, reLU) is connected behind each convolution layer except the last convolution layer, the convolution kernel size is h multiplied by h, the input of the first layer is the output of a data check term, the result of the data check term is mapped into Z by a forward sparse learning term,
The soft threshold operator T λγ carries out soft threshold operation on pixel points of the output Z of the forward sparse learning item point by point, wherein gamma lambda is a threshold value and gamma lambda epsilon theta S; the definition of soft threshold operation is: given a matrix Z, Z x,y =0 if the absolute value of the element Z x,y of the x-th row and y-th column of the matrix Z is |z x,y |++γλ, Z x,y＝sgn(Zx,y)(|Zx,y | - γλ if |z x,y | > γλ), where sgn (·) is a sign function; i.e., Z becomes T γλ (Z) after soft thresholding;
The reverse sparse learning term The method comprises the steps of forming L convolution layers, connecting a nonlinear rectification function after each convolution layer except the last convolution layer, wherein the convolution kernel is h multiplied by h, the input of the first layer is the output of a soft threshold operator, and the result of the soft threshold operator is mapped to an image domain X c in a nonlinear way by an inverse sparse learning term, wherein/>
The three sub-items are thatT γλ and/>Cascading, wherein the whole single sparse reconstruction module is represented by the following nonlinear mapping function group:
Wherein, X c is a merged channel image in which the inverse sparse learning term non-linearly maps the result of the soft threshold operator to the image domain;
b) The coil sensitivity updating module RC is used for updating the coil sensitivity based on the depth noise reduction module, and mainly comprises N convolution layers, wherein a normalization function (Batch Normalization, BN) and a linear rectification function (RECTIFIED LINEAR Unit, reLU) are connected behind each convolution layer except the last convolution layer, and the convolution kernel of the convolution layers is h multiplied by h; the first layer of input of the module is a noisy multi-coil reconstructed image output by the last iteration block And coil sensitivity/>, of last iteration block outputThe last layer outputs a noise image sigma C of the coil sensitivity, and the output of the whole module is the coil sensitivity/>, after noise removalThe complete coil sensitivity update module is represented by the following nonlinear function:
Where f r (·) represents the nonlinear mapping trained by the coil sensitivity update module, Θ r represents the internal parameters in the coil sensitivity update module, Multiple coil noisy image output for last iteration block,/>Is to obtain the linear mapping of the coil sensitivity corresponding to the multi-coil image, let/>I.e./> Representing a deep noise reduction module convolutional neural network;
c) The data fidelity module DC is used for keeping the values of the reconstructed image and the undersampled image at sampling points of the Fourier transform space consistent so as to ensure that an output result is aligned with the acquired data, and is defined as follows:
Wherein X DC represents a multi-coil image after data fidelity, Representing the fourier transform, X Unfold is the output/>, of the inverse sparse learning term after adding the merged channel image X c data check term D, which non-linearly maps the result of the soft threshold operator to the image domain, to the coil sensitivity update moduleProduct of/>, i.e.)Λ is a balance parameter and λe Θ S, (m, n) represents the position of a pixel point in the fourier transform space of X Unfold, Ω is a set of positions of undersampled images at the fourier transform space sampling points;
the three sub-blocks, namely the sparse reconstruction module R, the coil sensitivity updating module RC and the data fidelity module DC are cascaded, and the whole single iteration block is represented by the following nonlinear mapping function group:
Wherein Θ S represents a set of iterative network training parameters; f (·) represents a cascade of modules of the iterative block; f sparse(Xu,CI|ΘS) represents the trained range from X u,CI to Is a nonlinear mapping of each module/> F D(XUnfold,Xu |λ);
The sensitivity initialization module and the network iteration block based on sparse model expansion are cascaded, and the designed joint magnetic resonance sensitivity estimation based on sparse model expansion and the image reconstruction deep learning network model are integrally expressed as:
Where Θ represents the set of parameters within the overall network; f overall(Xu |Θ) represents the trained multi-coil image X u from undersampled zero padding to the net final output value And F overall (g) represents a cascade of a sensitivity initialization module and a sparse model-based expanded network iteration block.
5. A method of fast magnetic resonance imaging combining coil sensitivity estimation and image reconstruction as recited in claim 1, wherein in step 2) the feedback function of the network is performed by combining the output values of the network during the network model construction processAnd comparing the network output value with the complete multi-coil image and the coil sensitivities X and C, and feeding back gradients to update parameters of the iteration module so that the network output value is more approximate to the complete multi-coil image and the coil sensitivities.
6. A fast magnetic resonance imaging method combining coil sensitivity estimation and image reconstruction as claimed in claim 1, wherein in step 2) the loss function is defined as:
Where Θ represents a set of parameters within the overall network, |·| 2 represents a two-norm term, S represents the S-th iteration block, s=1, 2,..s, S represents the total number of iteration blocks, β represents a canonical parameter, Σ represents a summation operation.
7. The rapid magnetic resonance imaging method combining coil sensitivity estimation and image reconstruction as set forth in claim 1, wherein in step 3), the optimal parameters for solving the sparse model based developed deep learning network employ Adam optimizer in deep learning, network training using the training set generated in step 1), by minimizing the loss function in step 2)To obtain the optimal target parameter set/>
8. A fast magnetic resonance imaging method combining coil sensitivity estimation and image reconstruction as set forth in claim 1, wherein in step 4) the reconstructed undersampled magnetic resonance fourier space data is input to a trained network f overall (·) to reconstruct magnetic resonance images and estimate coil sensitivity, the network reconstruction process being expressed as:
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