CN108765318A - A kind of dynamic PET images factor treatment based on dynamics cluster - Google Patents
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Abstract
The dynamic PET images factor treatment based on dynamics cluster of the present invention, includes the following steps, (1) carries out dynamic scan using PET imaging devices and carries out image reconstruction and denoising, obtains dynamic PET images；(2) Factor Analysis Model is established, the model established is linear model；(3) the α divergences of dynamic PET images and Factor Analysis Model are defined：(4) α divergences are minimized and obtains primary factors image and corresponding primary factors；(5) dynamics pixel-based classifies to image；(6) factor is minimized at a distance from cluster, obtains final factor graph picture and the corresponding final factor.The present invention clusters priori since the factor graph picture obtained to decomposition introduces dynamics, can effectively improve the accuracy of factor graph picture so as to accurately obtain each tissue factor graph picture and the corresponding factor.
Description
Technical field
The present invention relates to a kind of image analysis method of medical image, more particularly to a kind of dynamic based on dynamics cluster
PET image factor treatment.
Background technology
Positron emission tomography (Positron Emission Tomography, PET) is the most advanced skill of nuclear medicine
The representative of art, it images function of organization using radioisotope labeling thing, can measure specific objective knot non-interventionly
The bio distribution of structure or area-of-interest radiopharmaceutical quantifies to change at any time.By applied dynamics model, can obtain
The functional parameters such as local blood flow, substance transportation rate, accretion rate and the receptor Percentage bound of each histoorgan, to be disease
Diagnosis, treatment and drug development provide guidance.In the application of kinetic model, the estimation of blood input function is very crucial.
Conventional method estimates blood input function by continuous blood sampling, however prolonged blood sampling would generally cause patient's
It is uncomfortable.The method of efficiently and accurately urgently non-invasive obtains blood input function in dynamic pet imaging.
Estimation blood input function method widely used at present is based on region of interest domain method, and the method is by there is experience people
Scholar sketches out area-of-interest (such as left ventricle) on dynamic PET images, to obtain corresponding time activity curve as blood
Input function.It is simple and practicable based on region of interest domain method, but it is very dependent on the area-of-interest that doctor delineates by hand, and feel emerging
The accuracy in interesting region is influenced by doctor personal experience and partial volume effect again.
Nineteen eighty-two, Di Paola etc. be put forward for the first time in dynamic sequence image using Factor Analysis Model extraction tissue when
Between activity curve.This method assumes that the time activity curve of each tissue is the factor, and principal component point is being carried out to dynamic sequence image
Nonnegativity restrictions backspin moves on to the axis of shadow after analysis, and then obtains factor graph picture and the factor.Nineteen ninety-five, Hsiao-MingWu etc. is by this method
It is applied in human body dynamic PET myocardial datas, the factor and the blood input function extracted is consistent substantially.1999,
Attias etc. proposes the time activity curve of the method extraction tissue based on independent component analysis.2000, Sitek etc. was in the factor
Prior information is introduced on the basis of analysis model, and is applied to dynamic SPECT images.The experimental results showed that this method obtains
Tissue time activity curve and actual value it is more consistent.Then, the propositions least square method such as Sitek and Fakhri is to the factor
Analysis model is solved, and proposes that unique constraints minimizes the overlapping degree between each factor graph picture.This method solves well
In Factor Analysis Model of having determined the problem of nonuniqueness solution.2007, Yi Su etc. proposed maximum likelihood factor analysis
(MLFA), overlapping degree solves the problems, such as not exclusive between blood sampling is used in combination and minimizes the factor, can more be accurately obtained tissue
Time activity curve, however, this method needs to sample blood compartment of terrain.
For nonuniqueness in Factor Analysis Model, traditionally using the overlapping degree minimized between factor graph picture this about
Beam solves the problems, such as this, but due to being influenced by PET image resolution ratio and partial volume effect, myocardial signal is often adulterated
The blood signal of 10%-15%, the fact that constraint of the overlapping degree between factor graph picture fails to consider is minimized.Cause
The accuracy that blood input function is estimated in dynamic pet imaging is limited.
Therefore, in view of the shortcomings of the prior art, providing a kind of dynamic PET images factor treatment based on dynamics cluster
It is very necessary to overcome the deficiencies of the prior art.
Invention content
A kind of dynamic clustered based on dynamics is provided it is an object of the invention to avoid the deficiencies in the prior art place
PET image factor treatment can accurately obtain each tissue factor graph picture and the corresponding factor, be that blood is defeated in dynamic pet imaging
Enter Function Estimation and technical support is provided.
The above-mentioned purpose of the present invention is realized by following technological means.
A kind of dynamic PET images factor treatment clustered based on dynamics is provided, is as follows：
(1) dynamic scan is carried out to target object using PET imaging devices and carries out image reconstruction and denoising, obtained
Dynamic PET images；
(2) Factor Analysis Model is established, specifically：
Dynamic PET sequence images are decomposed into limited time series vector and voxel corresponding with time series vector
Spatial distribution, decomposition model formula are：
I=CF+ ε ... formulas I；
Wherein, I indicates PET image, and the size of dynamic PET images is X, and X=N × T, N indicate the picture of each frame PET image
Vegetarian refreshments number, T indicate the frame number of dynamic PET images；ε indicates residual signal, i.e., the noise of image and is ignored by model small
Part signal；F indicates factor matrix, is equal to K × T；C is the size of factor graph picture, is equal to N × K, and wherein K is required extraction
Factor number, K<<N and K<<T；ε indicates residual signal, the i.e. noise of image and the fraction signal ignored by model；
(3) the α divergences of dynamic PET images and Factor Analysis Model are defined：
WhereinI=1 ..., N, f=1 ..., T indicate the institute at current factor graph picture C and factor F
Obtained estimated value；
(4) α divergences are minimized and obtains primary factors image and corresponding primary factors；
(5) dynamics pixel-based classifies to image；
(6) factor is minimized at a distance from cluster, obtains final factor graph picture and the corresponding final factor.
Preferably, step (4) is specifically：
Based on the object function estimation factor F and factor graph picture C for minimizing α Divergence Measures:
Model is expressed as convex optimization problem：
Preferably, the convex optimization problem of model is calculated by iterative manner and is solved, and specific algorithm is as follows：
Iv. C, F are initialized：Random number of the element between 0-1 in C is set, estimates initial F further according to C；
V. iteration：
a)C-step:Estimate C according to current dynamic image I and F；
B) the minus element in C is set to 0：
c)F-step:Estimate F according to current dynamic image I and C；
D) the minus element in F is set to 0：
E) whether inspection formula IV restrains, if not restraining, return to step a；
Vi. normalization factor image C, further according to the proportional zoom F of scaling
Wherein, it in C-step, enablesIt obtains
In F-step, enableIt obtainsWherein m indicates iteration step
Number.
Preferably, dynamics pixel-based classifies to image in the step (5), specifically：
Setting dynamic image I, there is the class of K different characteristic, Fuzzy C-Means Cluster Algorithm to be based on minimizing object function：
Wherein | | | | represent Euclidean distance, IjIndicate j-th of pixel in image I, vk is the center of k-th of cluster, ukj
Indicate that j-th of pixel belongs to the degree of membership of kth and subset, q is fuzzy parameter, q>1.
Preferably, in step (6), the factor is minimized under nonnegativity restrictions at a distance from cluster, factor R-1F is to cluster centre
vkDistance be：
Penalty term fn (CR, R-1F) ensures that the value of the factor and factor graph picture is non-negative, is indicated by following formula：
Wherein
Object function f is minimized by simulated annealingTAC+b1fnIt is not exclusive in factorial analysis to solve the problems, such as, it asks
The optimal solution for obtaining R, obtains final factor graph picture CR and corresponding factor R-1F。
Preferably, it is to carry out image reconstruction by using filtered back-projection method in the step (1), obtains dynamic PET
Image.
Preferably, the step (1) is specifically：
For dynamic sequence PET image I, tracer activity xs of the pixel j in m framesjmIt is calculated by following integral formula
It arrives：
Wherein, c (j, t) indicates pixel, in the tracer activity of time point t, tm,sAnd tm,eRising for m frames is indicated respectively
Begin time and termination time；Then：
WhereinA row of I indicate that a frame image, a line of I indicate the time activity curve of single pixel point.
The dynamic PET images factor treatment based on dynamics cluster of the present invention includes the following steps, (1) utilizes
PET imaging devices carry out dynamic scan and carry out image reconstruction and denoising, obtain dynamic PET images；(2) Factor minute is established
Model is analysed, the model established is linear model；(3) the α divergences of dynamic PET images and Factor Analysis Model are defined：(4) minimum
Change α divergences and obtains primary factors image and corresponding primary factors；(5) dynamics pixel-based classifies to image；(6)
The factor is minimized at a distance from cluster, obtains final factor graph picture and the corresponding final factor, (7) are examined using anthropomorphic phantom
It tests.
The present invention minimizes the α Divergence Measures of dynamic PET images and Factor Analysis Model, Ke Yixuan with new alternative manner
Different α values are taken, factorial analysis is carried out to different noise images, obtains corresponding factor graph picture and the factor.Due to decomposing
To factor graph picture introduce dynamics cluster priori, can effectively improve the accuracy of factor graph picture so as to accurately obtain
Each tissue factor graph picture and the corresponding factor.
Description of the drawings
Using attached drawing, the present invention is further illustrated, but the content in attached drawing does not constitute any limit to the present invention
System.
Fig. 1 is a kind of flow chart of the dynamic PET images factor treatment clustered based on dynamics of the present invention.
Fig. 2 is that the reverse S-line of Golden of 4D XCAT number body films is (left：Male, it is right：Women) and women heart area dropping cut slice.
The phantom image for the emulation that Fig. 3 embodiment of the present invention 2 uses and corresponding time activity curve.
Fig. 4 be based on minimize the obtained final factor graph picture of overlapping degree Factor Analysis Model between the factor and it is final because
Son.
Fig. 5 indicates the final factor graph picture obtained based on dynamics cluster-factor analysis model and the final factor.
Fig. 6 indicates when α takes different value two kinds of myocardium (myocardium) factors of models estimation under (α=1,2 ..., 20)
With the RMSE of blood pool (blood) factor.Wherein MSO is indicated based on overlapping degree Factor Analysis Model, KB tables between the minimum factor
Show and is based on dynamics cluster-factor analysis model.
Specific implementation mode
The invention will be further described with the following Examples.
Embodiment 1.
A kind of dynamic PET images factor treatment based on dynamics cluster, as shown in Figure 1, include the following steps,
(1) dynamic scan is carried out to target object using PET imaging devices and carries out image reconstruction and denoising, obtained
Dynamic PET images；
Step is specially：
For dynamic sequence PET image I, tracer activity xs of the pixel j in m framesjmIt can be calculated by following integral formula
It obtains：
Wherein, c (j, t) indicates pixel, in the tracer activity of time point t, tm,sAnd tm,eRising for m frames is indicated respectively
Begin time and termination time, then：
WhereinA row of I indicate that a frame image, a line of I indicate the time activity curve of single pixel point.
(2) Factor Analysis Model is established, the specific steps are：
Dynamic PET sequence images are decomposed into limited time series vector and voxel corresponding with time series vector
Spatial distribution, decomposition model formula are：
I=CF+ ε ... formulas I；
Wherein, I indicates PET image, and the size of dynamic PET images is X, and X=N × T, N indicate the picture of each frame PET image
Vegetarian refreshments number, T indicate the frame number of dynamic PET images；ε indicates residual signal, i.e., the noise of image and is ignored by model small
Part signal；F indicates factor matrix, is equal to K × T；C is the size of factor graph picture, is equal to N × K, and wherein K is required extraction
Factor number, K<<N and K<<T；ε indicates residual signal, the i.e. noise of image and the fraction signal ignored by model；
(3) the α divergences of dynamic PET images and Factor Analysis Model are defined：
WhereinI=1 ..., N, f=1 ..., T indicate the institute at current factor graph picture C and factor F
Obtained estimated value；
(4) α divergences are minimized and obtains primary factors image and corresponding primary factors, publicity is as follows：
Based on the object function estimation factor F and factor graph picture C for minimizing α Divergence Measures:
Model is expressed as convex optimization problem：
(5) dynamics pixel-based classifies to image；
(6) factor is minimized at a distance from cluster, obtains final factor graph picture and the corresponding final factor.
Specifically, step (4), model can be expressed as convex optimization problem：
We solve above formula by way of iteration, and specific algorithm is as follows：
Specific algorithm is as follows：
I initializes C, F：Random number of the element between 0-1 in C is set, estimates initial F further according to C；
II iteration：
a)C-step:Estimate C according to current dynamic image I and F；
B) the minus element in C is set to 0：
c)F-step:Estimate F according to current dynamic image I and C；
D) the minus element in F is set to 0：
E) whether inspection formula IV restrains, if not restraining, return to step a；
III normalization factor image C, further according to the proportional zoom F of scaling
Wherein, it in C-step, enablesIt obtains
In F-step, enableIt obtainsWherein m indicates iteration step
Number.
Specifically, dynamics pixel-based classifies to image in the step (5), specifically：
Assuming that there is dynamic image I the class of K different characteristic, Fuzzy C-Means Cluster Algorithm to be based on minimizing object function:
Wherein | | | | represent Euclidean distance, IjIndicate j-th of pixel in image I, vk is the center of k-th of cluster, ukj
Indicate that j-th of pixel belongs to the degree of membership of kth and subset, q (q>1) it is fuzzy parameter.
Further, in step (6), the factor is minimized under nonnegativity restrictions at a distance from cluster, factor R-1In F to cluster
Heart vkDistance be：
Penalty term fn (CR, R-1F) ensures that the value of the factor and factor graph picture is non-negative, can be represented by the formula：
Wherein
Object function (f is minimized by simulated annealingTAC+b1fn) not exclusive in factorial analysis to solve the problems, such as,
The optimal solution for acquiring R obtains final factor graph picture (CR) and the corresponding factor (R-1F)。
Specifically, being to carry out image reconstruction by using filtered back-projection method in the step (1), dynamic PET is obtained
Image.
The dynamic PET images factor treatment based on dynamics cluster of the present invention includes the following steps, (1) utilizes
PET imaging devices carry out dynamic scan and carry out image reconstruction and denoising, obtain dynamic PET images；(2) Factor minute is established
Model is analysed, the model established is linear model；(3) the α divergences of dynamic PET images and Factor Analysis Model are defined：(4) minimum
Change α divergences and obtains primary factors image and corresponding primary factors；(5) dynamics pixel-based classifies to image；(6)
The factor is minimized at a distance from cluster, obtains final factor graph picture and the corresponding final factor.
The present invention minimizes the α Divergence Measures of dynamic PET images and Factor Analysis Model, Ke Yixuan with new alternative manner
Different α values are taken, factorial analysis is carried out to different noise images, obtains corresponding factor graph picture and the factor.Due to decomposing
To factor graph picture introduce dynamics cluster priori, can effectively improve the accuracy of factor graph picture so as to accurately obtain
Each tissue factor graph picture and the corresponding factor.
Embodiment 2.
A kind of dynamic PET images factor treatment based on dynamics cluster, other feature is same as Example 1, no
It is with place：The present embodiment is tested by increasing using anthropomorphic phantom, specially：
In computer simulation experiment, used herein based on XCAT number body films as shown in Figure 1, heart area is by blood
Pond, two parts of cardiac muscular tissue constitute, are separately separated out by heart area herein.The tissue points number of model is 64 × 64
× 30, tissue points size is 3.27 × 3.27 × 3.27mm3.We are based on single compartment model[19]Simulate heart area physiology
The functional imaging process of metabolism, the radionuclide used are82Rb, half-life period 1.27min.In simulation process, blood inputs letter
It counts and the measured value of corresponding kinetic parameter is respectively organized to be all from the 5 of Johns Hopkins University of the U.S. medical centers PET
Position volunteer.Based on single compartment model, blood input function and corresponding kinetic parameter (setting kinetic parameter K1=
1.4822ml/min/g k2=0.3159/min and blood volume fraction are Vp=0.3829) the time activity for generating cardiac muscular tissue is bent
Line, it is each to organize time activity curve and spatial distribution as shown in Figure 2.Entire dynamic PET scan agreement is set as：12 × 5s, 6 ×
10s amounts to 18 time frames.By the spatial distribution of each frame blood pool and the time activity assignment of cardiac muscular tissue to its corresponding tissue
On position, the dynamic PET images of simulation heart area are generated.The phantom image for the emulation that Fig. 3 embodiment of the present invention 2 uses and
Corresponding time activity curve.
The nothing that is changed over time of dynamic image progress forward projection is made an uproar data for projection.In data for projection simulation process
The total photon counting generated is set as 5 × 106.Poisson noise can be emulated plus projection number of making an uproar is added in data for projection
According to.FBP algorithm for reconstructing pair plus the data for projection made an uproar is used to rebuild herein.After obtaining reconstruction image, with FWHM=4mm's
Gaussian filter carries out denoising to the dynamic image reconstructed.
The excellent performance in factorial analysis is clustered in order to illustrate based on dynamics, we are by it with traditional based on minimum
Change the factor between overlapping degree Factor Analysis Model make comparisons, Fig. 4, Fig. 5 indicate respectively to SNR (signal noise ratio)=
10 dynamic sequence is with overlapping degree factorial analysis between traditional factor based on minimum and is based on dynamics cluster-factor analysis
(α=5) obtained final factor graph picture and the corresponding final factor.Fig. 6 is indicated when α takes different value (α=1,2 ..., 20)
The RMSE of the lower estimation of two kinds of models myocardium (myocardium) factor and blood pool (blood) factor, wherein MSO are indicated based on minimum
Overlapping degree Factor Analysis Model between the change factor, KB indicate to be based on dynamics cluster-factor analysis model.To avoid result random
Property influence, we run for each method and average for 30 times.It can be seen that the side of the present invention from the result of fig. 4 to fig. 6
The obtained final factor graph picture accuracy of method is high, and the acquired corresponding final factor also has the characteristics that accuracy is high.
Finally it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention rather than is protected to the present invention
The limitation of range, although being explained in detail to the present invention with reference to preferred embodiment, those skilled in the art should manage
Solution, technical scheme of the present invention can be modified or replaced equivalently, without departing from technical solution of the present invention essence and
Range.
Claims (7)
1. a kind of dynamic PET images factor treatment based on dynamics cluster, it is characterised in that：Include the following steps,
(1) dynamic scan is carried out to target object using PET imaging devices and carries out image reconstruction and denoising, obtain dynamic
PET image；
(2) Factor Analysis Model is established, specifically：
Dynamic PET sequence images are decomposed into the space of limited time series vector and voxel corresponding with time series vector
Distribution, decomposition model formula are：
I=CF+ ε ... formulas I；
Wherein, I indicates PET image, and the size of dynamic PET images is X, and X=N × T, N indicate the pixel of each frame PET image
Number, T indicate the frame number of dynamic PET images；ε indicates residual signal, the i.e. noise of image and the fraction ignored by model
Signal；F indicates factor matrix, is equal to K × T；C be factor graph picture size, be equal to N × K, wherein K be required extraction because
Subnumber mesh, K<<N and K<<T；ε indicates residual signal, the i.e. noise of image and the fraction signal ignored by model；
(3) the α divergences of dynamic PET images and Factor Analysis Model are defined：
WhereinObtained by indicating at current factor graph picture C and factor F
Estimated value；
(4) α divergences are minimized and obtains primary factors image and corresponding primary factors；
(5) dynamics pixel-based classifies to image；
(6) factor is minimized at a distance from cluster, obtains final factor graph picture and the corresponding final factor.
2. the dynamic PET images factor treatment according to claim 1 based on dynamics cluster, it is characterised in that：
Step (4) is specifically：
Based on the object function estimation factor F and factor graph picture C for minimizing α Divergence Measures:
Model is expressed as convex optimization problem：
3. the dynamic PET images factor treatment according to claim 2 based on dynamics cluster, it is characterised in that：
The convex optimization problem of model is calculated by iterative manner and is solved, and specific algorithm is as follows：
I. C, F are initialized：Random number of the element between 0-1 in C is set, estimates initial F further according to C；
Ii. iteration：
a)C-step:Estimate C according to current dynamic image I and F；
B) the minus element in C is set to 0：
c)F-step:Estimate F according to current dynamic image I and C；
D) the minus element in F is set to 0：
E) whether inspection formula IV restrains, if not restraining, return to step a；
Iii. normalization factor image C, further according to the proportional zoom F of scaling
Wherein, it in C-step, enablesIt obtains
In F-step, enableIt obtainsWherein
M indicates iterative steps.
4. the dynamic PET images factor treatment according to claim 3 based on dynamics cluster, it is characterised in that：
Dynamics pixel-based classifies to image in the step (5), specifically：
Setting dynamic image I, there is the class of K different characteristic, Fuzzy C-Means Cluster Algorithm to be based on minimizing object function：
Wherein | | | | represent Euclidean distance, IjIndicate j-th of pixel in image I, vkIt is the center of k-th of cluster, ukjIndicate the
J pixel belongs to the degree of membership of kth and subset, and q is fuzzy parameter, q>1.
5. the dynamic PET images factor treatment according to claim 4 based on dynamics cluster, it is characterised in that：
In step (6), the factor is minimized under nonnegativity restrictions at a distance from cluster, factor R-1F to cluster centre vkDistance be：
Penalty term fn (CR, R-1F) ensures that the value of the factor and factor graph picture is non-negative, is indicated by following formula：
Wherein
Object function f is minimized by simulated annealingTAC+b1fnIt is not exclusive in factorial analysis to solve the problems, such as, acquire R's
Optimal solution obtains final factor graph picture CR and corresponding factor R-1F。
6. the dynamic PET images factor treatment according to claim 5 based on dynamics cluster, it is characterised in that：
It is to carry out image reconstruction by using filtered back-projection method in the step (1), obtains dynamic PET images.
7. the dynamic PET images factor treatment according to claim 6 based on dynamics cluster, it is characterised in that：
The step (1) is specifically：
For dynamic sequence PET image I, tracer activity xs of the pixel j in m framesjmIt is calculated by following integral formula：
Wherein, c (j, t) indicates pixel, in the tracer activity of time point t, tm,sAnd tm,eWhen indicating the starting of m frames respectively
Between and terminate the time；Then：
WhereinA row of I indicate that a frame image, a line of I indicate the time activity curve of single pixel point.
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