CN108335339A - A kind of magnetic resonance reconstruction method based on deep learning and convex set projection - Google Patents
A kind of magnetic resonance reconstruction method based on deep learning and convex set projection Download PDFInfo
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Abstract
The present invention discloses a kind of magnetic resonance reconstruction method based on deep learning and convex set projection, is related to magnetic resonance arts, including：S1：Network is built according to the overlay structure and shared data of multiple convolutional neural networks modules and multiple convex set projection layers, the shared data includes the K space data acquired and Coil sensitivity information, and the projection layer that highlights is obtained based on shared data；S2：After the completion of network struction, all-network parameter is trained by back-propagation process, and verify to network parameter；S3：The structure and operating characteristic of network are determined according to the network parameter after inspection, are inputted known test set data, are carried out the propagated forward of network, obtain unknown mappings data, complete the reconstruction of magnetic resonance.The present invention solves the problem of current magnetic resonance reconstruction technology based on deep learning can only support single channel MR data, can not handle multi-channel magnetic resonance data.
Description
Technical field
The present invention relates to magnetic resonance arts more particularly to a kind of magnetic resonance reconstruction sides based on deep learning and convex set projection
Method.
Background technology
Mr imaging technique is a kind of technology being imaged using the nmr phenomena of Hydrogen Proton.Include odd number in human body
The atomic nucleus of proton, such as the hydrogen nuclei that is widely present, proton have spin motion.The spin motion of charge atom core,
Physically be similar to individual small magnet, and under the influence of no external condition the directional distribution of these small magnets be with
Machine.When human body is placed in external magnetic field, these small magnets will be rearranged according to the magnetic line of force of external magnetic field specially to exist
Either parallel or anti-parallel to the both direction arrangement of the exterior magnetic field magnetic line of force, by the above-mentioned direction for being parallel to the exterior magnetic field magnetic line of force
The above-mentioned direction for being antiparallel to the exterior magnetic field magnetic line of force is known as negative longitudinal axis by referred to as positive longitudinal axis, and atomic nucleus only has longitudinal
Magnetization component, the longitudinal magnetization component is not only with direction but also with amplitude.
It is in the atomic nucleus in exterior magnetic field with radio frequency (RF, Radio Frequency) pulse excitation of specific frequency, makes these
Nuclear spin axis deviates positive longitudinal axis or negative longitudinal axis, generates resonance, here it is electromagnetic induction phenomenons.The above-mentioned atom that is excited
After the spin axis of core deviates positive longitudinal axis or negative longitudinal axis, atomic nucleus is provided with component of transverse magnetisation.
After stopping transmitting radio-frequency pulse, the atomic nucleus transmitting echo-signal being excited, by the energy of absorption gradually with electromagnetism
The form of wave releases, and phase and energy level are all restored to the state before excitation, by the echo-signal of atom nuclear emission
Being further processed by space encoding etc. can reconstruction image.
It is limited by magnetic resonance physical characteristic and scanned human body, MRI scan needs long time to acquire foot
Enough signals (K space data) carry out image reconstruction.Long sweep time leads to the less efficient of hospital's diagnosis of scans, and
And patient's discomfort is easily caused in scanning process.In addition, longer sweep time, causes magnetic resonance imaging to be difficult to handle human body
The imaging at the positions such as motor tissue, such as abdomen, heart.Therefore, how on the basis for ensureing picture quality needed for clinical diagnosis
On, shorten sweep time as magnetic resonance imaging and one of the core research in reconstruction field.Parallel imaging technique is dependent on multiple
The signal of lack sampling restore or will be due to owing by effective parallel imaging Processing Algorithm by phased array receiving coil
Image aliasing is unlocked caused by sampling, finally realizes shorter image acquisition time.
1999, K.P.Pruessmann et al. proposed SENSE (SENSE:Sensitivity Encoding for Fast
MRI) technology.The technology depends on multichannel phased-array coil, by the space encoding ability of coil sensitivity and gradient pulse
Code capacity is combined, and then reduces the acquisition of data, shortens sweep time.SENSE technologies are firstly the need of all receptions of calculating
The coil sensitivity profiles in channel, this information can be by realizing independently of the prescan formally scanned；Then, formal
Lack sampling K space data is obtained in scanning, and then effectively shortens sweep time.The K space data of these lack samplings is being schemed
Corresponding image field is exactly the image for occurring volume pleat.Finally, by coil sensitivity and uncoiling pleat algorithm, will can effectively occur
The image of volume pleat is unlocked, and the image of pleat is not rolled up.From technical principle, to minimize mean square error as target, base
Optimal result can be obtained in the SENSE algorithms of known coil sensitivity.Meanwhile SENSE technologies also have broad applicability,
It can readily can merge suitable for a variety of K spacescans track and reconstruction process a variety of Given informations raising reconstructions
Quality.But be but not easy to the stable accurate coil sensitivity profiles of acquisition, even and very small coil
Sensitivity error can also introduce on image obviously artifact.
2002, M.A.Griswold et al. proposed GRAPPA (Generalized Auto-calibrating
Partially Parallel Acquisitions) technology.GRAPPA technologies are not also with multichannel phased-array coil, but not
The spatial sensitivity profile of extra computation coil is needed, but utilizes the data of the correlation recovery lack sampling of K space data.
For GRAPPA technologies while carrying out lack sampling to the spaces K, the data that can retain K space center are fully sampled, this partial data
It is called ACS signals (auto-calibrating signal)；Then, it is calculated according to ACS signals between representing K space data
The convolution kernel (GRAPPA kernel) of correlation；Finally, it owes to adopt using the convolution kernel estimated and gathered data, reconstruction
The data of sample, and then complete K space data is obtained, corresponding is exactly the image without rolling up pleat.GRAPPA technologies avoid essence
The spatial distribution of true estimation coil sensitivity, reconstruction quality is relatively stable, still, the effect in the case of accelerated factor is higher
Decline apparent.
2004, A.A.Samsonov et al. proposed the SENSE (POCSENSE based on convex set projection： POCS-based
Reconstruction for sensitivity encoded magnetic resonance imaging.) technology.With warp
The SENSE of allusion quotation is different, the recovery problem of technology pleat image to be rolled up from the point of view of subspace, it is indicated that the weight of lack sampling magnetic resonance
The problem of building can be to seek the non-volume pleat image problem in all single channels by definition of equal value.The non-volume pleat image in single channel
It is constrained by coil sensitivity and general image, that is to say, that single channel image comes from sub defined in coil sensitivity
In space.Convex set projection SENSE technologies still need the coil sensitivity profiles for obtaining each channel first, then by convex
Collect projection process and the consistency constraint of gathered data, obtains the non-volume pleat image in all single channels.POCSENSE skills
Art further simplifies the reconstruction process of SENSE, and more easily incorporates and linearly or nonlinearly constrain.
2014, Martin Uecker, Peng Lai et al. proposed ESPIRiT (the An Eigenvalue of hybrid domain
Approach to Autocalibrating Parallel MRI:Where SENSE Meets GRAPPA) technology.The technology
Attempt angle fusion SENSE and the GRAPPA two methods from subspace.Authors point out that SENSE technologies pass through known line
Lack sampling data are limited to a specific subspace by circle sensitivity profile, and GRAPPA technologies are then by correction matrix certainly
Defined kernel restores lack sampling data.Based on above-mentioned relation, ESPIRiT technologies are constructed specific by ACS signals
K spatial correlation matrixs, then pass through the Eigenvalues Decomposition method of image area generate stablize, accurate coil sensitivity space point
Cloth.Simultaneously this method in phase of regeneration, can introduce multigroup coil sensitivity soft-constraint condition replace tradition SENSE firmly about
Beam evades the hierarchy of coil sensitivity profiles.This method combines the respective advantage of SENSE and GRAPPA technologies, can obtain
It is more stable, accurately rebuild effect.
In order to which on the basis of parallel imaging, further to shorten sweep time, 2007, Michael Lustig et al. were carried
The magnetic resonance imaging based on compressed sensing technology is gone out.Compressive sensing theory is thought, if specific at some by processing signal
There are sparsities in domain, then can under conditions of much smaller than nyquist sampling rate, with stochastical sampling signal acquisition signal from
Sample is dissipated, original signal is then recovered by non-linear algorithm for reconstructing.In clinic, especially dynamic scan (such as heart)
Either space sparsity structure (such as blood vessel imaging), compressed sensing technology pass through the sweep speed being exceedingly fast and good reconstruction energy
Power obtains good effect.
Compressed sensing technology has specific requirement to the acquisition of signal and reconstruction process, and main includes four aspects.First,
The acquisition of K spacing waves must be by the way of random or non-Cartesian, to ensure that the image caused by lack sampling is pseudo-
Shadow is incoherent in transform domain.But in clinic especially in most widely used magnetic resonance two-dimensional scan, rail is scanned
Mark is difficult to be randomized or non-Cartesian.Second, compressed sensing technology requires image to be reconstructed to have in specific transform domain
One sparse expression.Usually used rarefaction representation includes wavelet transformation or full variation.It is usually used in these transform domains
L1 norms carry out approximate expression sparsity.But above-mentioned approximate transform is difficult to describe complicated subtle biological structure, and then lead to weight
Build that image is fuzzy or mosaic effect.Magnetic resonance reconstruction is defined as nonlinear optimal problem by third, compressed sensing technology, because
This causes reconstruction time very long.Finally, there is the hyper parameter for much having significant impact to reconstructed results in compressed sensing algorithm, this
The definition and debugging of a little hyper parameters tend to rely on experience, it is difficult to the hyper parameter definition for obtaining generalization and stablizing.
In recent years, using convolutional neural networks as the deep learning of representative weight was obtained in fields such as computer vision, language understandings
Big progress.Nearly 2 years, in order to obtain higher speed-up ratio and preferably rebuild effect, the thought of deep learning is total to for magnetic
Sparse reconstruction of shaking is shortened the technology of sweep time and is continued to bring out in turn.It, can be by phase according to the net structure mode of deep learning
The technology of pass is divided into two classes：Reconstruction technique based on deep learning and the reconstruction technique based on discriminate study.Based on depth
The reconstruction technique of habit can be extracted, identify, be restored image using multiple network building method using learning method end to end
And data, used network structure are more flexible.Reconstruction technique based on discriminate study is between the reconstruction skill based on model
Between art and reconstruction technique based on deep learning, on the one hand, the technology to the definition of magnetic resonance reconstruction problem be based on model
Method it is consistent, on the other hand, which attempts to solve the problems, such as that the method based on model encounters by convolutional neural networks, example
The defining of such as more accurate hyper parameter, faster reconstruction time.
2017, it is quick for magnetic resonance that Kerstin Hammernik et al. will become subnetwork (variational network)
It rebuilds.This method uses the method based on model first, and the sparse Problems of Reconstruction of magnetic resonance is defined as to use gradient descent algorithm
The Variation Model of solution；Then, by the iterative process networking of gradient descent algorithm, ensure that the parameter in algorithm is no longer artificial
It is arranged but is generated by training.In the network generated in this way, duplication stages correspond to traditional reconstruction based on model each time
In an iteration calculate.2017, Yan Yang et al. proposed ADMM networks (ADMM-Net:A Deep Learning
Approach for Compressive Sensing MRI) it is used for the sparse reconstruction of magnetic resonance.This method is equally using based on mould
The sparse Problems of Reconstruction of magnetic resonance is defined as the iterative process solved using ADMM algorithms by the method for type first；Then, it defines
Data flow based on the iterative process；Finally, by network structure by the generalization of above-mentioned data flow architecture, and ensure network
In parameter can train.Above two method belongs to the reconstruction technique learnt based on discriminate, and achieves compared to simultaneously
Row imaging and the higher reconstruction quality of compressed sensing reconstruction technique.
2016, Wang et al. proposed the technology that deep learning is used for the sparse reconstruction of magnetic resonance.The technology constructs one first
Convolutional neural networks, then use end to end training mode the network is converted full the lack sampling data of input to
Sampled data finally the initial value rebuild using the output result of network as compressed sensing or is rebuild as compressed sensing
The regularization term newly introduced in equation.2017, Jo Schlemper et al. proposed a kind of concatenated deep learning network mode
For the sparse reconstruction of magnetic resonance.The sparse reconstruction of magnetic resonance is defined as the learning process that image area eliminates artifact, construction by the technology
Convolutional neural networks can be learned how by training process eliminate caused by lack sampling image artifacts.The technology is first
Shallower convolutional neural networks are first constructed, the data consistency layer (data being specially arranged then is added behind the network
Consistency layer), the information for providing sampled data；Finally, series connection above-mentioned two basic structure repeated
Get up, constructs deeper convolutional network.The characteristics of technology is, based on convolutional neural networks reconstruction and hits
According to consistency both independent factors combine, construct more stable, efficient network structure.Experiment shows phase
Than in method for reconstructing dictionary-based learning, this method is faster, more precisely.But the technology only supports that single channel magnetic is total at present
It shakes data, multi-channel magnetic resonance data can not be handled.
Invention content
It is an object of the invention to：The current magnetic resonance reconstruction technology based on deep learning can only support single channel magnetic resonance number
According to the problem of can not handling multi-channel magnetic resonance data, the present invention provides a kind of magnetic based on deep learning and convex set projection
Resonate method for reconstructing.
A kind of magnetic resonance reconstruction method based on deep learning and convex set projection, includes the following steps：
S1：It is built and is rebuild according to the overlay structure and shared data of multiple convolutional neural networks modules and multiple convex set projection layers
Network, the shared data include the K space data acquired and Coil sensitivity information, and the projection layer that highlights is based on sharing
Data obtain.
S2：After the completion of network struction, all-network parameter is trained by back-propagation process, and school is carried out to network parameter
It tests；
S3：The structure and operating characteristic of network are determined according to the network parameter after inspection, are inputted known test set data, are carried out
The propagated forward of network obtains unknown mappings data, completes the reconstruction of magnetic resonance.
Further, the S1 includes the following steps：
S1.1：Lack sampling multi-channel data and self calibration data in the spaces K are acquired, with the center in K spatial multichannel data
Domain is self calibration data, and the part removed other than self calibration data is lack sampling multi-channel data.
S1.2:The corresponding multichannel of lack sampling multi-channel data is generated by inverse fourier transform and rolls up pleat image, by the multichannel
Pleat image is rolled up as the input for rebuilding network.
S1.3：Multi-channel coil sensitivity profile information is obtained from self calibration data.
S1.4：Based on multi-channel coil sensitivity profile information, multichannel is rolled up by channel composite operator by pleat image and is synthesized
Image Icomb；
S1.5：By convolutional neural networks module CNN1, by image IcombIt is mapped as not rolling up pleat artifact or volume pleat artifact subtracts
Weak output image Icnn1；
S1.6：It will output image Icnn1Incoming convex set projection layer POCS, according to coil sensitivity point in convex set projection layer POCS
Cloth information and the K spatial multichannel data acquired complete convex set projection process and obtain image Ipocs1；
S1.7：By image Ipocs1Convolutional neural networks module CNN2 is inputted, by image Ipocs1Be mapped as not rolling up pleat artifact or
Roll up the output image I that pleat artifact weakenscnn2；Again by image Icnn2Incoming convex set projection layer POCS, in convex set projection layer POCS
Convex set projection process, which is completed, according to coil sensitivity profiles information and the K spatial multichannel data acquired obtains image Ipocs2；
S1.8：S1.7 is repeated, profound network structure is constructed, it includes N to amount tocA CNN layers and NcIt is POCS layers a, so far, net
Network structure is completed.
Specifically, in the S1.1, the S 1.3 includes the following steps：
S1.3.1：Correction matrix A is generated according to the self calibration data in K spatial multichannel data；
S1.3.2：A is put to the proof to correction and carries out singular value decomposition, obtains right singular matrix V, decomposition formula is：A=U Σ VH,
In, U is left singular matrix, and V is right singular matrix, and singular value is according to the descending leading diagonal for being arranged sequentially matrix Σ
On；
S1.3.3：The sensitivity matrix on each spatial position of image area is constructed according to all column vectors of right singular matrix V；
S1.3.4：Eigenvalues Decomposition is carried out to each sensitivity matrix, it is sensitive to obtain the corresponding multi-channel coil in the spatial position
Spend distributed intelligence.
Specifically, the formula that the synthesis of the S1.4 uses for：
Wherein, NcFor number of active lanes, CiFor the coil sensitivity in i-th of channel,For CiConjugate matrices,Indicate normalization
I-th of channel coil sensitivity,ForConjugate matrices,For the figure in i-th of channel with volume pleat of input
Picture, IcombFor the image after synthesis.
Preferably, the convolutional neural networks module in the S1.5 includes multiple CBR units, and each unit includes at least 1 volume
Lamination, 1 standardization layer and 1 nonlinear activation layer.
Further, in the convolutional neural networks further include convergence-level and anti-convergence-level.
Further, residual error connection is also introduced in the convolutional neural networks module, by the input data of convolutional neural networks
IcombOr IpocsIt is connected by residual error, residual error connection is Chong Die with the output of CBR units again, constitutes convolutional neural networks module
Final output Icnn。
Specifically, the convex set projection process of the S1.6 is specially：
fcsm(i)=CiIcnn|1≤i≤Nc (5-1)
Scsm(i)=Ffcsm(i)|1≤i≤Nc (5-2)
Idp=F-1fdp(Scsm,Sacq,k) (5-4)
NcFor number of active lanes, i is the serial number in channel,ForConjugate matrices, in equation (5-1), IcnnIt is defeated for CNN modules
The composograph entered, CiFor coil sensitivity, which is to be based on composograph and coil sensitivity, is generated multiple single pass
Image fcsm(i)；F is Fourier transform in equation (5-2), and multiple single pass images are converted to K spacing waves Scsm(i)；
Equation (5-3) is data projection process, and Ω represents the data acquisition system acquired, i.e., if the data on some spatial position K
Through being collected, then gathered data S is filled withacq, otherwise fill according to the calculated data S of the above processcsm, and then construct
Go out new complete K spatial datas fdp；F in equation [5-4]-1For inverse Fourier transform, by new K space data fdpBe converted to figure
The multichannel image I of image fielddp；Equation [5-5] executes the multichannel synthesis based on coil sensitivity, and the image in multiple channels is closed
And I is obtained togetherpocs。
Specifically, the loss function uses the L2 norms of image area：
Wherein, input data is known volume pleat image X, and flag data is the complete image Y synthesized based on coil sensitivity.
After adopting the above scheme, beneficial effects of the present invention are as follows：
(1) of the invention, it is proposed that a kind of brand-new convolutional neural networks structure, the network structure are to have merged the priori of magnetic resonance
The learning ability of depth convolutional network is utilized in knowledge again.Creativeness about depth convolutional network part.First：Based on depth
The convolutional neural networks field of structural design for spending study is to be directed to multi-channel magnetic resonance design data there is presently no a kind of network
, and the convex set projection layer proposed in this paper newly increased is a kind of unprecedented result.It is general next in deep learning field
It says, a kind of new network structure is inherently creative；Second：Traditional convolutional neural networks structure need to only be carried out in image area
Calculate, and network structure proposed by the present invention need image area and K spatial signal domains alternately, this is also the core of the present invention
The heart is created.Wherein, the creativeness for having merged magnetic resonance priori this point is, traditionally has existed convex set projection really
This algorithm, but the present invention is then to construct a convex set projection layer, and which needs to blend with convolutional neural networks, therefore this
In image area and K spatial signal domains, (POCS processes need to transform to the spaces K the convolutional neural networks that solve of innovation and creation
Signal domain) work (including propagated forward and backpropagation) the technical issues of.
(2) of the invention " band-wise processing ability " allows the invention to use less signal, compared to single-channel algorithm or
Network, the present invention can more effectively utilize the redundancy between multiple channels.It has been generated using less magnetic resonance signal
Whole image, therefore can further shorten sweep time, clinical scanning efficiency is improved, locomotory apparatus is preferably mitigated or evade
The artifact that official introduces, using same magnetic resonance signal, the present invention can generate more accurately image, improve clinical diagnosis
Validity；The reconstruction time of the present invention greatly shortens compared to conventional method, contributes to clinical real time imagery and diagnosis.
(3) present invention there is no special requirement for the sample track of magnetic resonance imaging, can with stochastical sampling can also rule adopt
Therefore sample has wide applicability for clinical a variety of sequences.
(4) present invention is after input layer, the followed by one channel composite operator based on coil sensitivity, to ensure the more of network
Channel processing capacity.
(5) all hyper parameters in convolutional neural networks proposed by the present invention are not manually set instead of, pass through mass data
What training obtained, therefore for clinical complicated structure, including scanned position, signal noise ratio (snr) of image etc., can provide more steady
Fixed image reconstruction quality.
(6) with bibliography Schlemper, Jo, Caballero, Jose, Hajnal, Joseph V., the Price of this paper,
Anthony,Rueckert,Daniel.A Deep Cascade of Convolutional Neural Networks for
MR Image Reconstruction.arXiv:1703.00555v1 preprint 2017 is compared, the present invention is in the convolution Holy Bible
Convex set projection layer is added in network, uses convex set projection layer (POCS Layer) that the network structure is handled from more
The MR data in channel, and this bibliography can only handle single pass data；Convex set projection layer (the POCS of the present invention
Layer the band-wise processing ability) brought can more effectively utilize the redundancy properties of MR data itself, help to be based on
The convolutional neural networks of deep learning establish more stable, accurately end-to-end mapping relations, fundamentally improve magnetic resonance reconstruction
Quality, more obviously shorten the magnetic resonance imaging time；Relative to single convex set projection layer (POCS Layer), by convex set projection
The convolutional neural networks structure that layer (POCS Layer) incorporates sequence model in the form of concatenated can improve the general of network structure
Change ability, the stability for promoting network training and test.The convex set projection layer that this method proposes is incorporated entire by sequential fashion
In network structure, but they are shared the identical coil sensitivity calculated based on magnetic resonance priori and have acquired K skies
Between data.The coil sensitivity has broad applicability by being accurately calculated.
(7) in the present invention, increase convergence/anti-convergence-level in convolutional neural networks module, convolutional neural networks can be increased
Receptive field promotes the learning ability of network structure, brings better reconstruction performance, and anti-convergence-level is for ensuring output output number
According to the consistency of size.
Description of the drawings
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to required in embodiment
The attached drawing used is briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, right
For those of ordinary skill in the art, without creative efforts, it can also be obtained according to these attached drawings
His attached drawing.Shown in attached drawing, above and other purpose of the invention, feature and advantage will be more clear.In whole attached drawings
In identical reference numeral indicate identical part.Actual size equal proportion scaling is not pressed deliberately draws attached drawing, it is preferred that emphasis is
The purport of the present invention is shown.
Fig. 1 is the process schematic of the spaces K self calibration data structure correction matrix A；
Fig. 2 is to construct the corresponding matrix G of each pixel according to matrix VqProcess schematic；
Fig. 3 is by matrix GqCarry out the calculated coil sensitivity profiles hum pattern of Eigenvalues Decomposition；
Fig. 4 is the convolutional neural networks structure connected with residual error based on functional expression model for incorporating magnetic resonance priori.
Specific implementation mode
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction in the embodiment of the present invention
Attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is this hair
Bright a part of the embodiment, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art are not having
There is the every other embodiment obtained under the premise of making creative work, shall fall within the protection scope of the present invention.
The magnetic resonance reconstruction technology based on deep learning to solve current can only support single channel MR data, can not locate
The problem of managing multi-channel magnetic resonance data, the present invention provides a kind of magnetic resonance reconstruction side based on deep learning and convex set projection
Method.The convolutional neural networks of the deep learning proposed in this method use training sample data by back-propagation process first
It is trained and verifies, determine all parameters in network structure；Then by propagated forward process to test data (lack sampling
MR data) it is rebuild.As all convolutional neural networks based on deep learning, in training and checking stage, need
The input data and flag data that pairing is provided to network are instructed with the mapping relations of training network foundation " end-to-end "
Flag data can be accurately mapped as automatically by input data by practicing network.In this magnetic resonance reconstruction field, flag data generation
Table is the known fully sampled image in the spaces K (target of e-learning), and training data is then the corresponding spaces K manually owes to adopt
Sampled images (input of e-learning).In test phase, it is only necessary to provide test data as input to network, then pass through
The convolutional neural networks of training study can complete next data mapping process.From the point of view of image area, which can
Input volume pleat image is mapped as to the complete image of output；From the point of view of the spaces K, which is equivalent to the lack sampling that will be inputted
K space reflections are complete K space data；In real data processing, convolutional network meeting interleaved operation is empty in image area and K
Between, therefore it is referred to as reconstruction process.
When Jo Schlemper in 2017 et al. propose a kind of sparse for the magnetic resonance reconstruction of concatenated deep learning network mode,
There are no being proposed or disclosed in the scheme for effectively handling multi-channel data in neural network, therefore most start him using list
The method in channel.Why single channel can only be handled, be due to the relationship between multiple channel datas need appropriate processing and
Using.
Convex set projection is a kind of algorithm being considered to effectively to handle relationship between multiple channel datas.The main points of the present invention exist
In transforming traditional convex set projection algorithm as a convex set projection layer in convolutional neural networks, and in the form of sequential
It is dissolved into the convolutional neural networks of depth, and then creative puts forward a kind of temporarily new convolutional neural networks structure.The knot
Structure can effectively utilize the redundancy between multiple channels, and convex set projection algorithm and depth are inherited again in network structure
The advantage of convolutional neural networks, therefore can bring and preferably rebuild effect and wider clinical application (because clinically connecing
It is typically all multichannel to receive channel at present).
A kind of magnetic resonance reconstruction method based on deep learning and convex set projection in this specific implementation, includes the following steps：
S1：According to channel composite operator, multiple convolutional neural networks modules and multiple convex set projection layers overlay structure and altogether
It enjoys data structure and rebuilds network, the shared data includes the K space data acquired and Coil sensitivity information, the channel
Composite operator is obtained based on Coil sensitivity information, and the projection layer that highlights is obtained based on shared data.S1 be the present invention the most
Crucial step, specifically, S1 includes the following steps：
S1.1：As shown in Figure 1, lack sampling multi-channel data and self calibration data in the spaces acquisition K, with K spatial multichannel data
In central area be self calibration data, be used for self calibration data K space center region, be to belong to well known in the art.One
As for, may be used the data of the 24X24 sizes of entire K space center, the part removed other than self calibration data is to owe to adopt
Sample multi-channel data Su.The size of K spatial multichannel data can be expressed as：Nx*Ny*Nc, wherein NxRepresent the row of gathered data
Number, NyIndicate the columns of data, NcRepresent the number of receiving channel.
S1.2:Lack sampling multi-channel data S is generated by inverse fourier transformuCorresponding multichannel rolls up pleat image, the image
Size is：Nx*Ny*NcUsing multichannel volume pleat image as the input for rebuilding network.Due to the lack sampling of K space data, lead
It causes image that volume pleat occurs in lack sampling direction, generates artifact.The effect for rebuilding network is to eliminate and be led due to data lack sampling
The image volume pleat artifact of cause is also equivalent to restore the data of lack sampling in the spaces K.
S1.3：Multi-channel coil sensitivity profile information is obtained from self calibration data.
S1.3 is comprised the following specific steps that：
S1.3.1：As shown in 103 in Fig. 1 correction matrix A is generated according to the self calibration data in K spatial multichannel data；It is first
The blocky data in a part, such as Fig. 1, shown in the black box in " 103 " are first chosen in calibration data；Then, by the part
Data are positioned over the row of correction matrix A；Then, local data's block in " 103 " is moved according to direction shown in arrow, obtained entire
Correct the data of matrix A.
S1.3.2：A is put to the proof to correction and carries out singular value decomposition, obtains right singular matrix V, decomposition formula is：
A=U Σ VH, (1)
Wherein, U is left singular matrix, and V is right singular matrix, and singular value is according to the descending master for being arranged sequentially matrix Σ
On diagonal line.Column vector in matrix V is the base of all row vectors in matrix A, therefore also represents in self calibration data " 103 "
The base of local data's block.That is, arbitrary row vector (of equal value, the identical bulk of arbitrary size in the spaces K in matrix A
Data) it can be indicated by the subspace representated by matrix V.
S1.3.3：The sensitivity matrix on each spatial position of image area is constructed according to all column vectors of right singular matrix V
Gq.As shown in Figure 2.Basic process is：The column vector " 302 " in right singular matrix " 301 " is taken out first, is divided into NcPort number
According to, and convert data to blocky data " the 303 " (size of the bulk data, with structural correction matrix in Fig. 1 from column vector
A's is in the same size)；Then, above-mentioned blocky data are transformed into image area " 304 " by inverse Fourier transform；Finally, respectively from
Corresponding multi-channel data is taken out in the same spatial position of data " 304 ", constructs the corresponding sensitivity square in the spatial position
Battle array Gq“305”。
S1.3.4：To each sensitivity matrix GqEigenvalues Decomposition is carried out, the corresponding multi-channel coil spirit in the spatial position is obtained
Sensitivity distributed intelligence：
GqK=λ k (2)
Wherein, λ is scalar, represents matrix GqSome characteristic value, and k then be corresponding to eigenvalue λ feature vector.Such as Fig. 3
It is shown, characteristic value from top to bottom according to from small to large be arranged sequentially left side " 401 "；And characteristic value is " 1 ", i.e. " 402 " institute
Corresponding feature vector, i.e. feature vector amplitude " 403 " and feature vector phase " 404 " just represent the more of the spatial position point
Channel coil sensitivity；
S1.4：As shown in figure 4, S1.4：Based on multi-channel coil sensitivity profile information, by channel composite operator multichannel
Volume pleat image synthesizes image Icomb.The formula that the synthesis of the S1.3 uses for：
Wherein, NcFor number of active lanes, CiFor the coil sensitivity in i-th of channel,For CiConjugate matrices,Indicate normalization
I-th of channel coil sensitivity,ForConjugate matrices,For the figure in i-th of channel with volume pleat of input
Picture, IcombFor the image after synthesis.
S1.5：By convolutional neural networks module CNN1, by image IcombIt is mapped as not rolling up pleat artifact or volume pleat artifact subtracts
Weak output image Icnn1.It can be seen that the concrete structure of convolutional neural networks, convolutional neural networks (CNN) module in Fig. 4
" 505 " include multiple CBR units, and each unit includes at least convolutional layer (convolution layer), a specification
Change layer (BN, Batch Normalization) and a nonlinear activation layer (RELU, Rectifier Linear Units)；
Further, in order to enable network structure obtains the receptive field of bigger and ensures that input and output picture size is consistent, module
It also needs to that convergence-level (Pooling Layer) or anti-convergence-level (Unpooling are added in CBR units in " 505 "
Layer), and convergence-level and anti-convergence-level will occur in pairs, i.e., if there are one convergence-level is applied in CBR units, answer
This is corresponding in some unit in face behind to use anti-convergence-level.In order to ensure the output of convolutional neural networks (CNN) module
With next POCS layers of compatible, CBRndIn convolution number should be equal to 1.Meanwhile convolutional neural networks (CNN) module exists
Residual error connection is introduced in network, i.e., by the input data I of CNN modulescombOr IpocsIt is linked by residual error, with CBRndUnit
Output superposition, constitute CNN modules final output Icnn.The residual error link can not only effectively avoid due to depth increase and
Caused network is degenerated, and learning ability can be significantly improved in the case where depth is constant.
S1.6：It will output image Icnn1Incoming convex set projection layer POCS, according to coil sensitivity point in convex set projection layer POCS
Cloth information and the K spatial multichannel data acquired complete convex set projection process and obtain image Ipocs1；
The convex set projection process of the S1.6 is specially：
fcsm(i)=CiIcnn|1≤i≤Nc (5-1)
Scsm(i)=Ffcsm(i)|1≤i≤Nc (5-2)
Idp=F-1fdp(Scsm,Sacq,k) (5-4)
Wherein, NcFor number of active lanes, i is the serial number in channel,ForConjugate matrices, I in equation (5-1)cnnFor CNN modules
The composograph of input, CiFor coil sensitivity, which is to be based on composograph and coil sensitivity, generates multiple single channels
Image fcsm(i)；F is Fourier transform in equation (5-2), and multiple single pass images are converted to K spacing waves Scsm
(i)；Equation (5-3) is data projection process, and Ω represents the data acquisition system acquired, i.e., if number on some spatial position K
According to being collected, then gathered data S is filled withacq, otherwise fill according to the calculated data S of the above processcsm, in turn
Construct new complete K space data fdp；F in equation [5-4]-1For inverse Fourier transform, by new K space data fdpConversion
For the multichannel image I of image areadp；Equation [5-5] executes the multichannel synthesis based on coil sensitivity, by the figure in multiple channels
As merging to obtain Ipocs。
S1.7：As shown in figure 4, by image Ipocs1Convolutional neural networks module CNN2 is inputted, by image Ipocs1It is mapped as not rolling up
The output image I that pleat artifact or volume pleat artifact weakencnn2；Again by image Icnn2Incoming convex set projection layer POCS, in convex set projection
Convex set projection process is completed according to coil sensitivity profiles information and the K spatial multichannel data acquired obtain figure in layer POCS
As Ipocs2.Specifically, one group of convolutional neural networks to be trained of each neural network module, all parameters therein are all not
Know, therefore, even if the structure of multiple CNN modules is much like, but their effects in the entire network are different, by training
Parameter afterwards just differs, it is possible to say that they are different.And the data manipulation of POCS and parameter be all in convex set projection layer
It is identical.
S1.7 is repeated, profound network structure is constructed, it includes N to amount tocA CNN layers and NcIt is POCS layers a, so far, network struction
It completes, it, can be to this parameter N in specific implementationcIt optimizes and revises.
S2：After the completion of network struction, all-network parameter is trained by back-propagation process, and school is carried out to network parameter
It tests；
The loss function uses the L2 norms of image area：
Wherein, input data is known volume pleat image X, and flag data is the complete image Y synthesized based on coil sensitivity.
S3：The structure and operating characteristic of network are determined according to the network parameter after inspection, are inputted known test set data, are carried out
The propagated forward of network obtains unknown mappings data, completes the reconstruction of magnetic resonance.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any to belong to
In the technical scope disclosed by the present invention, the change or replacement that can be readily occurred in should all be covered those skilled in the art
Within protection scope of the present invention.
Claims (9)
1. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection, which is characterized in that include the following steps：
S1：Net is built according to the overlay structure and shared data of multiple convolutional neural networks modules and multiple convex set projection layers
Network, the shared data include the K space data acquired and Coil sensitivity information, and the convex set projection layer is based on shared number
According to obtaining；
S2：After the completion of network struction, all-network parameter is trained by back-propagation process, and school is carried out to network parameter
It tests；
S3：The structure and operating characteristic of network are determined according to the network parameter after inspection, are inputted known test set data, are carried out
The propagated forward of network obtains unknown mappings data, completes the reconstruction of magnetic resonance.
2. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection according to claim 2, feature exist
In the S1 includes the following steps：
S1.1：Lack sampling multi-channel data and self calibration data in the spaces K are acquired, with the center in K spatial multichannel data
Domain is self calibration data, and the part removed other than self calibration data is lack sampling multi-channel data；
S1.2:The corresponding multichannel of lack sampling multi-channel data is generated by inverse fourier transform and rolls up pleat image, by the multichannel
Pleat image is rolled up as the input for rebuilding network；
S1.3：Multi-channel coil sensitivity profile information is obtained from self calibration data；
S1.4：Based on multi-channel coil sensitivity profile information, multichannel is rolled up by channel composite operator by pleat image and is synthesized
Image Icomb；
S1.5：By convolutional neural networks module CNN1, by image IcombIt is mapped as not rolling up pleat artifact or volume pleat artifact weakens
Output image Icnn1；
S1.6：It will output image Icnn1Incoming convex set projection layer POCS, according to coil sensitivity profiles in convex set projection layer POCS
Information and the K spatial multichannel data acquired complete convex set projection process and obtain image Ipocs1；
S1.7：By image Ipocs1Convolutional neural networks module CNN2 is inputted, by image Ipocs1Be mapped as not rolling up pleat artifact or
Roll up the output image I that pleat artifact weakenscnn2；Again by image Icnn2Incoming convex set projection layer POCS, the root in convex set projection layer POCS
Convex set projection process, which is completed, according to coil sensitivity profiles information and the K spatial multichannel data acquired obtains image Ipocs2；
S1.8：S1.7 is repeated, profound network structure is constructed, it includes N to amount tocA CNN layers and NcIt is POCS layers a, so far, network
Structure is completed.
3. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection according to claim 2, feature exist
In in the S1.1, the S 1.3 includes the following steps：
S1.3.1：Correction matrix A is generated according to the self calibration data in K spatial multichannel data；
S1.3.2：A is put to the proof to correction and carries out singular value decomposition, obtains right singular matrix V, decomposition formula is：
A=U Σ VH, (1)
Wherein, U is left singular matrix, and V is right singular matrix, and singular value is according to the descending master for being arranged sequentially matrix Σ
On diagonal line；
S1.3.3：The sensitivity matrix on each spatial position of image area is constructed according to all column vectors of right singular matrix V；
S1.3.4：Eigenvalues Decomposition is carried out to each sensitivity matrix, it is sensitive to obtain the corresponding multi-channel coil in the spatial position
Spend distributed intelligence.
4. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection according to claim 2, feature exist
In the formula that the synthesis of, the S1.4 uses for：
Wherein, NcFor number of active lanes, CiFor the coil sensitivity in i-th of channel,For CiConjugate matrices,Indicate normalization
I-th of channel coil sensitivity,ForConjugate matrices,For the figure in i-th of channel with volume pleat of input
Picture, IcombFor the image after synthesis.
5. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection according to claim 2, feature exist
In, the convolutional neural networks module in the S1.5 include multiple CBR units, each unit include at least 1 convolutional layer, 1
Standardize layer and 1 nonlinear activation layer.
6. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection according to claim 5, feature exist
In further including convergence-level and anti-convergence-level in the convolutional neural networks.
7. a kind of magnetic resonance reconstruction method of convex set projection based on deep learning according to claim 5 or 6, feature
It is, residual error connection is also introduced in the convolutional neural networks module, by the input data I of convolutional neural networkscombOr Ipocs
It is connected by residual error, residual error connection is Chong Die with the output of CBR units again, constitutes the final output I of convolutional neural networks modulecnn。
8. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection according to right 2, which is characterized in that institute
The convex set projection process for stating S1.6 is specially：
fcsm(i)=CiIcnn|1≤i≤Nc (5-1)
Scsm(i)=Ffcsm(i)|1≤i≤Nc (5-2)
Idp=F-1fdp(Scsm,Sacq,k) (5-4)
Wherein, NcFor number of active lanes, i is the serial number in channel,ForConjugate matrices, I in equation (5-1)cnnFor CNN modules
The composograph of input, CiFor coil sensitivity, which is to be based on composograph and coil sensitivity, generates multiple single channels
Image fcsm(i)；F is Fourier transform in equation (5-2), and multiple single pass images are converted to K spacing waves Scsm
(i)；Equation (5-3) is data projection process, and Ω represents the data acquisition system acquired, i.e., if number on some spatial position K
According to being collected, then gathered data S is filled withacq, otherwise fill according to the calculated data S of the above processcsm, in turn
Construct new complete K space data fdp；F in equation (5-4)-1For inverse Fourier transform, by new K space data fdpConversion
For the multichannel image I of image areadp；Equation (5-5) executes the multichannel synthesis based on coil sensitivity, by the figure in multiple channels
As merging to obtain Ipocs。
9. a kind of magnetic resonance reconstruction method based on deep learning and convex set projection according to claim 1 or 2, feature
It is, the S2 is more specifically：After the completion of network struction, trained by back-propagation process as target using minimizing loss function
Go out all-network parameter；
The loss function uses the L2 norms of image area：
Wherein, input data is known volume pleat image X, and flag data is the complete image Y synthesized based on coil sensitivity.
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| CN113143243B (en) * | 2021-02-25 | 2023-08-22 | 厦门大学 | Deep learning magnetic resonance spectrum reconstruction method based on spectrum decomposition |
| CN113077527A (en) * | 2021-03-16 | 2021-07-06 | 天津大学 | Rapid magnetic resonance image reconstruction method based on undersampling |
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