CN109993808A - A kind of double tracer PET method for reconstructing of the dynamic based on DSN - Google Patents
A kind of double tracer PET method for reconstructing of the dynamic based on DSN Download PDFInfo
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Abstract
The invention discloses a kind of double tracer PET method for reconstructing of dynamic based on DSN, the concentration profile of two kinds of tracers are reconstructed in the case where capable of injecting two kinds of tracers at the same time, and have preferable robustness to noise.The PET method for reconstructing stacks the reconstruction of network implementations mixing tracer dynamic PET concentration distributed image by deep layer, and main realization process is first to use the concentration distribution image of mixing tracer as input, and Boltzmann machine is combined to carry out pre-training to network；Then recessive stack is carried out to network as label and error function further combined with single tracer true value to finely tune, obtain trained model.This preparatory trained network simultaneously combines the recessive training method for stacking fine tuning, and network can be enabled to possess bigger characteristic window in input dimension, so that more robust feature is arrived in study, finally realize accurate image reconstruction.
Description
Technical field
The invention belongs to PET technical field of imaging, and in particular to dynamic of the one kind based on DSN (deep layer stacking network) is double to be shown
Track PET method for reconstructing.
Background technique
Positron emission tomography (Positron emission tomography, PET) is non-intruding living body molecule
One kind of imaging is widely used in the medical domains such as tumour, nervous system, heart.PET mainly becomes using to various physiological functions
The tracer for changing sensitive labelled with radioisotope is imaged, these tracers relate generally to glucose, protein and
The macromolecular substances such as nucleic acid, common radioactive isotope have18F、11C、13N etc., so that PET can be mentioned in molecular level
For the physiological function information in relation to internal organs, for example glucose metabolism, blood perfusion, weary oxygen and cell Proliferation etc., are disease
Early diagnosis and prevention provide effective information.In view of the complexity of disease, multi-angle, the multi-faceted physiology for portraying internal organs are needed
Or pathological characters, therefore it is very necessary to carry out using a variety of tracers PET scan imaging.In traditional PET scan imaging, respectively
A tracer independent injection scanning imagery, inevitably bring sweep time extend, each tracer concentration distributed image when
The problems such as sky registration and expense increase.Therefore single sweep operation-injects double tracer PET scan imaging techniques simultaneously and needs to develop,
And the gammaphoton that different tracers generation decays generate in PET imaging process is identical to energy, is all 511KeV, it can not be from energy
Two kinds of tracer signals are distinguished on measuring angle.
There are two main classes for double tracer PET image reconstructions at present: one kind is to utilize tracer prior information and interval injection
To distinguish the signal of different tracers；It is another kind of, using deep learning with data-driven version come to the different tracer figures of separation
Picture.Preceding one kind method usually has the following problems: (1) tracer being required to have different half-life period or the same position of different radioactivity
Element；(2) kinetic model for needing to have constructed in advance, may be not suitable for new tracer；(3) simple linear model is used only
To be fitted tracer signal；(4) specific tracer pair is needed.Problem above reduces the practical feasibility of such methods, and
Such methods usually require the injection of collocation interval to assist separating, and sweep time are further extended, after separation
Two kinds of tracer images need additional time-space relation.Latter class method mainly has the separation of double tracers based on self-encoding encoder at present
Algorithm, however the model has only used common gradient descent algorithm to update model parameter, so that the feature representation learnt
It is inadequate to the robustness of noise, to limit the raising of separation accuracy.
Summary of the invention
In view of above-mentioned, the present invention provides a kind of double tracer PET method for reconstructing of dynamic based on DSN, can infuse at the same time
The concentration profile of two kinds of tracers is reconstructed in the case where penetrating two kinds of tracers, and has preferable robustness to noise.
A kind of double tracer PET method for reconstructing of the dynamic based on DSN, include the following steps:
(1) it injects tracer I and tracer II simultaneously to biological tissue to go forward side by side Mobile state PET detection, obtains corresponding difference
The coincidence counting vector at moment, and then form the dynamic coincidence counting sequence to reflect dual tracer mixed distribution situation
Ydual；
(2) successively injected to biological tissue tracer I and tracer II go forward side by side Mobile state PET detection, respectively obtain two kinds
Single tracer corresponds to the coincidence counting vector of different moments, and then forms and reflect tracer I and tracer II distribution situation respectively
Dynamic coincidence counting sequence YIAnd YII；
(3) dynamic coincidence counting sequence Y is calculated using PET image reconstruction algorithmdual、YIAnd YIICorresponding dynamic
PET image sequence Xdual、XIAnd XII；
(4) make Xdual、XIAnd XIIComposition is used as a sample, is repeated repeatedly according to step (1)~(3) big to obtain
Sample is measured, and then all samples are divided into training set and test set；
(5) X in training set sample is extracteddual、XIAnd XIIBased on the TAC of each pixel, make X in training set sampledual's
TAC stacks the input of network, X in training set sample as deep layerIAnd XIITAC as deep layer stack network output true value mark
Label are trained to obtain dynamic dual tracer PET reconstruction model by stacking network to the deep layer；
(6) X in test set sample is extracteddualTAC based on each pixel is input to the dynamic dual tracer PET and rebuilds
In model, model exports to obtain the TAC of each pixels of corresponding two kinds of single tracer dynamic PET images sequences, and then by these TAC
It is combined into the corresponding dynamic PET images sequence X of tracer I and tracer IIIAnd XII。
Further, all samples are divided into training set and test set in the step (4), two set do not repeat mutually and
The sample proportion of training set and test set is greater than half.
Further, X in training set sample is extracted according to following formula in the step (5)dual、XIAnd XIIBased on each
The TAC of pixel:
Wherein:For the X of training set sampledualThe TAC of middle the 1~n pixel of correspondence,For the X of training set sampleIThe TAC of middle the 1~n pixel of correspondence,For training set sample
XIIThe TAC of middle the 1~n pixel of correspondence, n are the sum of all pixels of PET image,TIndicate transposition.
Further, network is stacked to deep layer in the step (5) and is trained that detailed process is as follows:
5.1 buildings one are sequentially connected the deep neural network formed by input layer, hidden layer and output layer, and initialize
The parameter of the neural network includes learning rate, the number of iterations and bias vector and weight matrix between layers；
5.2 take X in training set sampledualThe corresponding TAC of j-th of pixel is input in deep neural network, defeated by calculating
The TAC of corresponding two kinds single tracers of the pixel exports result outIt calculatesWith
True value labelBetween error function, and then according to error function by gradient descent method to neural network
In bias vector between layers and weight matrix be modified update；Wherein,For X in training set sampleIJ-th
The corresponding TAC of pixel,For X in training set sampleIJ-th of pixel corresponding TAC, j are natural number and 1≤j≤n,
N is the sum of all pixels of PET image；
5.3 execute repeatedly according to step 5.2 iteration, and the input layer of deep neural network consists of two parts: a part is
X in training set sampledualTAC, another part is the TAC of corresponding two kinds of an iteration single tracers before the result of output layer is
Output is as a result, the feed back input of initialization is 0, so that the deep neural network between adjacent iteration twice forms recessive heap
Folded, stacking number is determined by the number of iterations；
5.4 in current iteration, according to step 5.2~5.3 batches by X in training set sampledualTAC be input to depth
It is trained in neural network to update network parameter, until having traversed TAC all in training set sample；It changes by certain
After generation number i.e. it is recessive stack certain number of plies after, corresponding deep neural network recessiveness heap when taking average error function L minimum
It builds up deep layer and stacks network as dynamic dual tracer PET reconstruction model.
Further, deep neural network bias vector between layers and weight matrix are initial in the step 5.1
Change and is completed by limited Boltzmann machine (Restricted Boltzmann Machine, RBM) pre-training.
Further, the expression formula of the mean error function L is as follows:
Wherein: b is the TAC quantity that each batch is input in deep layer stacking network,WithIt is respectively each
In batch i-th of TAC be input to deep layer stack the TAC output that corresponding two kinds single tracers are calculated in network as a result,
WithThe TAC true value label of corresponding two kinds single tracers of i-th of TAC in respectively each batch, | | | |2Indicate 2 norms.
The present invention stacks the reconstruction of network implementations mixing tracer dynamic PET concentration distributed image, master by deep layer
The realization process wanted is first to use the concentration distribution image of mixing tracer as input, and Boltzmann machine is combined to carry out network
Pre-training；Then network recessiveness is stacked as label and error function further combined with single tracer true value and is finely tuned, obtained
Trained model.This preparatory trained network simultaneously combines the recessive training method for stacking fine tuning, and network can be enabled to tie up in input
Possess bigger characteristic window on degree, so that more robust feature is arrived in study, finally realizes accurate image reconstruction.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of DSN of the present invention.
Fig. 2 is complicated brain template image.
Fig. 3 (a) is11The actual concentration distributed image of the 10th frame of C-DTBZ.
Fig. 3 (b) is11The forecast image that the 10th frame of C-DTBZ and algorithm for reconstructing are ML-EM.
Fig. 3 (c) is11The forecast image that the 10th frame of C-DTBZ and algorithm for reconstructing are ADMM.
Fig. 4 (a) is11The actual concentration distributed image of the 10th frame of C-FMZ.
Fig. 4 (b) is11The forecast image that the 10th frame of C-FMZ and algorithm for reconstructing are ML-EM.
Fig. 4 (c) is11The forecast image that the 10th frame of C-FMZ and algorithm for reconstructing are ADMM.
Fig. 5 (a) is11C-DTBZ algorithm for reconstructing is the bias-variance relational graph of prediction result under all frame numbers of ADMM.
Fig. 5 (b) is11C-DTBZ algorithm for reconstructing is the bias-variance relational graph of prediction result under all frame numbers of MLEM.
Fig. 5 (c) is11C-FMZ algorithm for reconstructing is the bias-variance relational graph of prediction result under all frame numbers of ADMM.
Fig. 5 (d) is11C-FMZ algorithm for reconstructing is the bias-variance relational graph of prediction result under all frame numbers of MLEM.
Specific embodiment
In order to more specifically describe the present invention, with reference to the accompanying drawing and specific embodiment is to technical solution of the present invention
It is described in detail.
The present invention is based on the double tracer PET method for reconstructing of the dynamic of DSN, include the following steps:
(1) preparing experiment data.
1.1 inject the mixing pair composed by two different tracers (tracer I and tracer II) to biological tissue
Tracer is gone forward side by side Mobile state PET detection, acquires the coincidence counting vector of different moments sequentially in time, and then it is mixed to form reflection
Close the dynamic coincidence counting sequence Y of dual tracer distribution situationdual；
1.2 successively injected to biological tissue tracer I and tracer II go forward side by side Mobile state PET detection, obtain two groups of lists and show
Track agent corresponds to the coincidence counting vector of different moments, and then forms and reflect the three of tracer I and tracer II distribution situation respectively
Tie up dynamic coincidence counting sequence YIAnd YII；
1.3 calculate Three-Dimensional Dynamic coincidence counting sequence Y using PET image reconstruction algorithmdual、YIAnd YIICorresponding three
Tie up dynamic PET images sequence Xdual、XIAnd XII；
1.4 repeat repeatedly according to step 1.1~1.3, obtain a large amount of dynamic PET images sequence Xsdual、XIAnd XII。
(2) data set divides.
By Xdual、XIAnd XIIIn the ratio of about 2:1,2/3 data are extracted as training setAnd labelResidue 1/3 is used as test setAnd its true valueEffect is rebuild as assessment later
Fruit；Dynamic PET images sequenceWithTo embody mode as follows:
In above-mentioned expression formulaAndRespectively indicate mixing tracer, independent tracer I and tracer II
The curve i.e. TAC that j-th of pixel concentration value of dynamic PET concentration distribution map changes over time, N are the total pixel number of PET image；
TAC can be further embodied as:
Wherein:Indicate the concentration value of j-th of pixel kth frame of dynamic PET concentration distribution map, subscript * expression is injected
Tracer (mixing tracer, independent tracer I and tracer II), S is then total frame of dynamic PET images sequence acquisition
Number；In addition label and the data mode of true value are answered are as follows:
(3) DSN is built.
A DNN as shown in Figure 1 is built, is made of input layer, hidden layer and output layer, input layer size is
It is originally inputtedWith labelColumn vector direction series connection after it is in the same size, output layer node size with
LabelColumn vector direction dimension is in the same size.
(4) network parameter setting and initialization.
Pre-training is carried out to network using limited Boltzmann machine first, is initialized between the bias vector of each layer and each layer
Weight coefficient.Learning rate is set in present embodiment as 0.01, the hidden layer number of plies is set as 3, each hidden layer number of nodes difference
60,40 and 30 are set as, activation primitive is set as sigmoid function and batch-size is set as 32.
(5) network training.
Recessive stack training is carried out to the DNN of building under the guidance of true value label: by dynamic PET images sequenceIn based on j-th of pixel extract TAC beAbove-mentioned network is inputted in the form of batch, and calculates batch data pair
Result should be exportedWith true value labelIn extracted based on j-th pixel
Between conjunction error L, wherein j is natural number and 1≤j≤N, N are the sum of all pixels of PET concentration image.Pass through according to error L is closed
Gradient descent algorithm is modified the weight parameter between each layer of input layer, hidden layer and output layer of whole network, into
And from dynamic PET images sequenceThe middle DNN proposed after TAC Introduced Malaria corresponding to next group pixel.
Training set is inputted into network, and using recessive stack training after iteration each time to weight parameter between each layer
It is constantly modified with bias vector, the error function L of backpropagation is as follows:
Wherein:WithRespectively DSN to the predicted value of tracer I and tracer II,WithRespectively tracer I
With the true value of tracer II, batch_size is batch size, n=1,2 ..., N/batch_size.
DNN recessiveness when last time iteration is taken to be stacked into DSN, as double tracer PET image reconstruction models.
(6) outcome evaluation.
In order to which effect is rebuild in quantitative evaluation, we have mainly used two indexs of deviation bias and variance variance,
Its expression formula are as follows:
Wherein:xiAndThe respectively predicted value, true value of concentration profile ith pixel point and this is interested
The mean predicted value in region, R are the total pixel number of the area-of-interest.
We verify accuracy of the invention by simulated experiment below, and complicated brain template is selected to be covered in experiment
The simulation of special Carlow generates data set, the tracer of setting to for11C-FMZ and11C-DTBZ, template is by corresponding to different tissues portion
The area-of-interest (Region ofinterest, ROI) of position is constituted.Fig. 2 as includes that the complexity of 4 region of interest ROI is big
Brain template, the PET scanner simulated are Siemens Company, U.S. biography 16HR, which shares 3 crystal rings,
It amounts in 48 detector modules that 24336 LSO crystals are uniformly distributed on each ring in the form of an array, crystal array size
It is 13 × 13, wherein the diameter of crystal rings is 824mm.To the data set of generation with the ratio of 2:1,2/3 is extracted as training number
According to residue 1/3 is used as test data；In order to observe influence of the different algorithm for reconstructing to DSN, we are concentrated use in ADMM in training
Sinogram is reconstructed into radioactive concentration distribution map by algorithm for reconstructing, and classical ML-EM algorithm is also used in test set part
To complete the reconstruction of mixing dual tracer radioactive concentration distribution map.
Fig. 3 (a)~Fig. 3 (c) is respectively11The 10th frame radioactive concentration of C-DTBZ is distributed true value, test set algorithm for reconstructing
The DSN neural network forecast concentration profile that DSN neural network forecast concentration profile and algorithm for reconstructing for ML-EM are ADMM, Fig. 4
(a)~Fig. 4 (c) is respectively11The 10th frame radioactive concentration distribution true value of C-FMZ, the DSN that test set algorithm for reconstructing is ML-EM
The DSN neural network forecast concentration profile that neural network forecast concentration profile and algorithm for reconstructing are ADMM.Table 1 presents test set weight
In the case where algorithm is built as ADMM, the reconstruction effect of each area-of-interest, Fig. 5 (a)~Fig. 5 under two kinds of tracer difference frame numbers
It (d) is respectively to use two kinds of models of SAE and DSN, using identical training set and test set, two kinds of tracers are not
With the reconstruction effect of area-of-interest total under frame number, and displaying is compared by bias-variance relational graph.
Table 1
The concentration profile comparison of concentration profile true value and DSN neural network forecast shown in the attached drawing and table 1 are shown
Each area-of-interest in deviation and variance between true value and predicted value, it may be said that the bright present invention can be good at completing double show
Track PET image reconstruction, and demonstrate its accuracy；Simultaneously by utilizing bias-variance relational graph and existing algorithm SAE's
Comparison, demonstrates DSN to the robustness of noise.
The above-mentioned description to embodiment is for that can understand and apply the invention convenient for those skilled in the art.
Person skilled in the art obviously easily can make various modifications to above-described embodiment, and described herein general
Principle is applied in other embodiments without having to go through creative labor.Therefore, the present invention is not limited to the above embodiments, ability
Field technique personnel announcement according to the present invention, the improvement made for the present invention and modification all should be in protection scope of the present invention
Within.
Claims (6)
1. a kind of double tracer PET method for reconstructing of dynamic based on DSN, include the following steps:
(1) it injects tracer I and tracer II simultaneously to biological tissue to go forward side by side Mobile state PET detection, obtains corresponding different moments
Coincidence counting vector, and then form the dynamic coincidence counting sequence Y to reflect dual tracer mixed distribution situationdual；
(2) successively injected to biological tissue tracer I and tracer II go forward side by side Mobile state PET detection, respectively obtain two kinds and singly show
Track agent corresponds to the coincidence counting vector of different moments, and then forms and reflect the dynamic of tracer I and tracer II distribution situation respectively
State coincidence counting sequence YIAnd YII；
(3) dynamic coincidence counting sequence Y is calculated using PET image reconstruction algorithmdual、YIAnd YIICorresponding dynamic PET images
Sequence Xdual、XIAnd XII；
(4) make Xdual、XIAnd XIIComposition is used as a sample, is repeated repeatedly according to step (1)~(3) to obtain a large amount of samples
This, and then all samples are divided into training set and test set；
(5) X in training set sample is extracteddual、XIAnd XIIBased on the TAC of each pixel, make X in training set sampledualTAC make
The input of network, X in training set sample are stacked for deep layerIAnd XIITAC as deep layer stack network output true value label, lead to
It crosses and deep layer stacking network is trained to obtain dynamic dual tracer PET reconstruction model；
(6) X in test set sample is extracteddualTAC based on each pixel is input to the dynamic dual tracer PET reconstruction model
In, model exports to obtain the TAC of each pixel of corresponding two kinds of single tracer dynamic PET images sequences, and then combines these TAC
At the corresponding dynamic PET images sequence X of tracer I and tracer IIIAnd XII。
2. the double tracer PET method for reconstructing of dynamic according to claim 1, it is characterised in that: will own in the step (4)
Sample is divided into training set and test set, two set do not repeat mutually and the sample proportion of training set and test set be greater than two/
One.
3. the double tracer PET method for reconstructing of dynamic according to claim 1, it is characterised in that: in the step (5) according to
Lower expression formula extracts X in training set sampledual、XIAnd XIITAC based on each pixel:
Wherein:For the X of training set sampledualThe TAC of middle the 1~n pixel of correspondence,
For the X of training set sampleIThe TAC of middle the 1~n pixel of correspondence,For the X of training set sampleIIMiddle correspondence
The TAC of the 1~n pixel, n are the sum of all pixels of PET image,TIndicate transposition.
4. the double tracer PET method for reconstructing of dynamic according to claim 1, it is characterised in that: to deep layer in the step (5)
It stacks network and is trained that detailed process is as follows:
5.1 buildings one are sequentially connected the deep neural network formed by input layer, hidden layer and output layer, and initialize the mind
Parameter through network includes learning rate, the number of iterations and bias vector and weight matrix between layers；
5.2 take X in training set sampledualThe corresponding TAC of j-th of pixel is input in deep neural network, is exported by calculating
The TAC of corresponding two kinds single tracers of the pixel exports resultIt calculatesWith
True value labelBetween error function, and then according to error function by gradient descent method to neural network
In bias vector between layers and weight matrix be modified update；Wherein,For X in training set sampleIJ-th
The corresponding TAC of pixel,For X in training set sampleIJ-th of pixel corresponding TAC, j are natural number and 1≤j≤n,
N is the sum of all pixels of PET image；
5.3 execute repeatedly according to step 5.2 iteration, and the input layer of deep neural network consists of two parts: a part is training
Collect X in sampledualTAC, another part is the TAC output of corresponding two kinds of an iteration single tracers before the result of output layer is
As a result, the feed back input of initialization is 0, so that the deep neural network between adjacent iteration twice forms recessive stacking,
Stacking number is determined by the number of iterations；
5.4 in current iteration, according to step 5.2~5.3 batches by X in training set sampledualTAC be input to depth nerve
It is trained in network to update network parameter, until having traversed TAC all in training set sample；By certain iteration time
After number after the i.e. recessive certain number of plies of stacking, deep neural network recessiveness corresponding when average error function L minimum is taken to be stacked into
Deep layer stacks network as dynamic dual tracer PET reconstruction model.
5. the double tracer PET method for reconstructing of dynamic according to claim 4, it is characterised in that: depth mind in the step 5.1
It is completed through network bias vector between layers and weight matrix initialization by limited Boltzmann machine pre-training.
6. the double tracer PET method for reconstructing of dynamic according to claim 4, it is characterised in that: the mean error function L's
Expression formula is as follows:
Wherein: b is the TAC quantity that each batch is input in deep layer stacking network,WithRespectively each batch
In i-th of TAC be input to deep layer stack the TAC output that corresponding two kinds single tracers are calculated in network as a result,WithThe TAC true value label of corresponding two kinds single tracers of i-th of TAC in respectively each batch, | | | |2Indicate 2 norms.
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