CN107146218A - It is a kind of to be rebuild and tracer kinetics method for parameter estimation based on the dynamic PET images that image is split - Google Patents
It is a kind of to be rebuild and tracer kinetics method for parameter estimation based on the dynamic PET images that image is split Download PDFInfo
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Abstract
Rebuild and tracer kinetics method for parameter estimation based on the dynamic PET images that image is split the invention provides a kind of, it can obtain more accurately combining reconstructed results by the way that statistics reconstruction model is combined with the model for having physiological significance.When rebuilding and segmentation is coupled in a joint or solution framework simultaneously, for segmentation task, the information that noise model is modeled to Raw projection data can be obtained, and the result based on segmentation can also strengthen the uniformity in each region, so as to realize the reconstructed results for more meeting truth.Compared with other individually rebuild the algorithm of dynamic PET images or estimated driving force parameter, the present invention can also obtain preferable reconstructed results.With reference to performance of the present invention in analogue data and True Data experiment, compared with other algorithms for individually rebuilding dynamic PET images, estimated driving force parameter and image segmentation, the present invention can also obtain preferable reconstructed results.
Description
Technical field
The invention belongs to PET technical field of imaging, and in particular to it is a kind of based on image split dynamic PET images rebuild and
Tracer kinetics method for parameter estimation.
Background technology
Positron emission tomography (Positron Emission Tomography, abbreviation PET) is nuclear medicine
One kind, its important effect is just gradually being shown in biomedical research and clinic diagnosis.PET imaging techniques pass through to note
The increased radioactivity for entering tracer in organism is imaged, and the metabolic disorder of cell can be found from molecular level, is disease
The early diagnosis and prevention of disease provide effective foundation.Relative to radioactivity in bio-tissue can only be provided in certain time window
For the static PET imaging techniques being evenly distributed of intensity, it is biological that dynamic pet imaging results in description based on kinetic model
The quantitative function parameter of body vital movement, has significant application value in scientific research and clinical practice.
In dynamic PET Problems of Reconstruction, it is common practice to divide the image into, image reconstruction and Chemical kinetic parameter estimation
As three individually the problem of separately solve.Requirement more and more higher with dynamic pet imaging technology to temporal resolution, it is each
Limited photon counting constantly challenges dynamic pet imaging quality in frame measurement data.Now, due to the photon of frame data
Count deficiency can not reflected well statistical property, each frame data are carried out using the algorithm for reconstructing based on statistical property single
The method solely rebuild can not often obtain very accurate reconstructed results.Now, introduced by combining tracer dynamics model
The prior information of radioactive intensity distribution from the time longitudinal axis, can be on the basis of PET reconstructed image qualities be improved simultaneously
Realize the estimation to kinetic parameter.In addition, image segmentation is also a conventional difficulties in PET imaging techniques.Except right
Beyond PET image is split, an also class way is the time-acttivity curve (time-activity to dynamic PET
Curve, TAC) come the operation that is clustered, so as to distinguish functional areas different in biological tissue.But either from PET's
This problem is still treated from the perspective of kinetic parameter on the plane of delineation, the partitioning algorithm degree of accuracy based on reconstructed results is begun
The accuracy with back reconstructed results is relied on eventually, it is impossible to solve partitioning algorithm to measurement noise sensitive issue.
In fact, the relation between image segmentation, image reconstruction and Chemical kinetic parameter estimation these three problems is very tight
Close.By the way that three is coupled into same target equation, by selecting suitable noise model preferably to match PET
Measurement data, now segmentation result the susceptibility of noise will be reduced；And the introducing of segmentation result can make existing figure
As estimated result is more accurate, so as to generally obtain the reconstructed results for more conforming to truth.
The content of the invention
In view of it is above-mentioned, rebuild the invention provides a kind of based on the dynamic PET images that image is split and tracer kinetics ginseng
Number estimation method, the segmentation and dynamic PET joints that functional area can be realized simultaneously is rebuild.
It is a kind of to be rebuild and tracer kinetics method for parameter estimation based on the dynamic PET images that image is split, including following step
Suddenly：
(1) biological tissue for being injected with radiopharmaceutical agent is detected using detector, it is each that dynamic acquisition obtains correspondence
The coincidence counting vector at individual moment, and set up coincidence counting matrix Y；
(2) make dynamic PET image combined sequence into PET concentration distribution matrix X, according to PET image-forming principles, set up PET
Measure equation；
(3) full variation (Total Variation, TV) constraint is introduced by measuring PET equation, obtained based on TV's
PET image reconstruction model L (X)；
(4) using compartment model matching estimation tracer kinetics parameter, set up on X and Ф synchronous reconstruction model S (X,
Ф)；
(5) region segmentation result obtained based on pretreatment, is clustered to tracer kinetics parameter matrix Ф, is gathered
Class parted pattern C (Ф)；
(6) above three model L (X), S (X, Ф) and C (Ф) are combined and obtain the synchronous object function LSC rebuild
(X, Ф) is as follows：
Wherein：γ and ∈ are weight coefficient；
(7) object function LSC (X, Ф) is carried out obtaining PET concentration distribution matrix X after optimization and spike is dynamic
Mechanics parameter matrix Ф.
The coincidence counting matrix Y is chronologically rearranged by each coincidence counting vector, the PET concentration distribution matrix X
Chronologically rearranged by corresponding PET concentration distribution vector of each moment (i.e. a frame PET image).
The expression formula of the PET measurements equation is as follows：
Y=GX+R+S
Wherein：G is sytem matrix, and R and S are respectively the measurement noise matrix for reflecting chance event and scattering events.
The expression formula of the PET image reconstruction model L (X) is as follows：
Wherein：α is weight coefficient, and TV (X) is the full variation regular terms on X, gijArranged for the i-th row jth in sytem matrix G
Element value (its represent be outgoing at j-th of pixel the probability that is received by i-th of detector of photon), yimTo meet meter
I-th row m column element values, x in matrix number YjmFor jth row m column element values, r in PET concentration distribution matrix XimFor reflect with
I-th row m column element values, s in the measurement noise matrix R of machine eventimI-th in measurement noise matrix S to reflect scattering events
Row m column element values, i, j and m are natural number and 1≤i≤N, 1≤j≤K, 1≤m≤M, N are the dimension of coincidence counting vector
Degree, K is the pixel number that PET concentration distribution matrix X line number is PET image, and M is for PET concentration distribution matrix X columns
Sampling time length.
The expression formula of the full variation regular terms TV (X) is as follows：
Wherein：D(xjm) it is on xjmTwo dimensional difference vector, the vectorial the first row element value be xjm-xJ, m+1, the second row
Element value is xjm-xJ+1, m, xJ, m+1For jth row m+1 column element values, x in PET concentration distribution matrix XJ+1, mIt is distributed for PET concentration
The row of jth+1 m column element values in matrix X, | | | |2Represent 2 norms.
The expression formula of the synchronous reconstruction model S (X, Ф) is as follows：
Wherein：μ is weight coefficient, and Ψ is dictionary matrix,TTransposition is represented, | | | |22 norms are represented, | | | |1Represent 1 norm.
The expression formula of the cluster segmentation MODEL C (Ф) is as follows：
Wherein：ChTo belong to the parameter vector set of h classes, φ in tracer kinetics parameter matrix ФhFor parameter vector collection
Close ChIn any parameter vector, nhFor parameter vector set ChIn parameter vector number, h is that natural number and 1≤h≤H, H are
The class number of cluster,TRepresent transposition.
Using ADMM, (Alternating Direction Method of Multipliers are handed in the step (7)
For direction Multiplier Algorithm) object function LSC (X, Ф) is entered with reference to soft-threshold (Soft-Thresholding) iteration optimization algorithms
Row optimization；Wherein, ADMM is iterated Optimization Solution for PET concentration distribution matrix X, and soft-threshold is directed to spike power
Parameter matrix Ф iteration optimizations are learned to solve.
The soft-threshold iteration optimization algorithms are based on below equation and carry out linear process with to tracer kinetics parameter matrix
Ф is iterated renewal：
Nh=Ih-Eh/nh
Wherein：EhFor a n all constituted by 1h×nhTie up matrix, IhFor one and matrix EhDimension identical unit square
Battle array, μ is weight coefficient,TTransposition is represented, Ψ is dictionary matrix, ChTo belong to the ginseng of h classes in tracer kinetics parameter matrix Ф
Number vector set, φhFor parameter vector set ChIn any parameter vector, nhFor parameter vector set ChIn parameter vector
Number, xhFor in PET concentration distribution matrix X with parameter vector φhA corresponding TAC, | | | |22 norms are represented, | | | |1Represent
1 norm, h is natural number and 1≤h≤H, H are the class number of cluster.
The expression formula of the dictionary matrix Ψ is as follows：
Wherein：CIAnd C (t)I(τ) is respectively the concentration value of t and τ moment radiopharmaceutical agents in blood plasma,With
Respectively on m groups coincidence counting vector collection at the beginning of between and the end time, θcCorrespond to c-th of chamber tissue index
When the columns that the coefficient of function, m and c are natural number and 1≤m≤M, 1≤c≤Z, M are PET concentration distribution matrix X is sampling
Between length, Z is natural number more than 1；θ1~θNValue be in interval [θmin, θmax] in by it is exponential interval chosen,
θminAnd θmaxThe respectively bound threshold value of coefficient, t and τ represent the time.
The present invention can obtain more accurate by the way that statistics reconstruction model is combined with the model for having physiological significance
Joint reconstructed results., can for segmentation task when rebuilding and segmentation is coupled in a joint or solution framework simultaneously
To obtain the information that noise model is modeled to Raw projection data, and the result based on segmentation can also strengthen each region
Interior uniformity, so as to realize the reconstructed results for more meeting truth.Dynamic PET images are individually rebuild with other or are estimated
The algorithm of meter kinetic parameter is compared, and the present invention can also obtain preferable reconstructed results.With reference to the present invention in analogue data and
Performance in True Data experiment, the calculation of dynamic PET images, estimated driving force parameter and image segmentation is individually rebuild with other
Method is compared, and the present invention can also obtain preferable reconstructed results.
Brief description of the drawings
Fig. 1 is the template image of Monte Carlo simulation Zubal thoracic cavities data.
Fig. 2 (a) is the true picture of the frame of Zubal thoracic cavities data the 4th.
Fig. 2 (b) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 5*10^4 using ML-EM methods
The 4th two field picture result rebuild.
Fig. 2 (c) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 1*10^5 using ML-EM methods
The 4th two field picture result rebuild.
Fig. 2 (d) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 5*10^4 using the inventive method
The 4th two field picture result rebuild.
Fig. 2 (e) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 1*10^5 using the inventive method
The 4th two field picture result rebuild.
Fig. 3 (a) is the true picture of the frame of Zubal thoracic cavities data the 6th.
Fig. 3 (b) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 5*10^4 using ML-EM methods
The 6th two field picture result rebuild.
Fig. 3 (c) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 1*10^5 using ML-EM methods
The 6th two field picture result rebuild.
Fig. 3 (d) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 5*10^4 using the inventive method
The 6th two field picture result rebuild.
Fig. 3 (e) is that data counts rate is to Monte Carlo simulation Zubal thoracic cavities data under 1*10^5 using the inventive method
The 6th two field picture result rebuild.
Fig. 4 (a) is cluster result schematic diagram of the Monte Carlo simulation Zubal thoracic cavity data under using the inventive method.
Fig. 4 (b) is cluster result signal of the Monte Carlo simulation Zubal thoracic cavity data under using k average sorting techniques
Figure.
Fig. 4 (c) is Monte Carlo simulation Zubal thoracic cavity data using based on poly- under kinetic model profile classification method
Class result schematic diagram.
Embodiment
In order to more specifically describe the present invention, below in conjunction with the accompanying drawings and embodiment is to technical scheme
It is described in detail.
Dynamic PET and kinetic parameter joint method for reconstructing of the present invention based on region segmentation, comprise the following steps：
(1) according to Model Establishment the measurement data matrix Y and sytem matrix G of dynamic PET scan.
Dynamic PET scanning process is marked off into detector in a number of time frame, each time frame as required
Collect coincidence counting vector can go out dynamic PET measurement data matrix Y according to the sequential build of time；And
The probability that the photon of outgoing at each pixel is received by each detector is counted, so as to obtain sytem matrix G.
(2) according to the positron radionuclide species of the mark tracer compound of measurement data and the distribution of time frame period,
Dictionary matrix Ψ based on the theoretical setup time basic function of double compartment models.
If analogue data, then index parameters θ and detector is set to sweep with the half-life period of position nucleic according to the spike of simulation
Retouch time interval and set up corresponding dictionary matrix；If True Data, then according to the spike used in practical operation with position nucleic
Corresponding dictionary matrix is set up with Setup Experiments.
The radioactive intensity that can be solved according to compartment model in tissue changes with time, instant m- radioactivity function
Be input tissue TAC and δ (t) function and a class index function convolution, be all tissue compartments TAC it
With.Therefore, a PET spikes compartment model can represent that each equation represents a difference with one group of order-1 linear equation
Chamber in tracer radioactive intensity, i.e.,：
s.t.ψ0(t)=CI(t)
Wherein：CT(t) radioactive intensity in t tissue is represented.N represents the sum of different chambers, ψc(t) c is represented
Plant the function that the corresponding radioactive intensity of chamber is changed over time, φcIt is ψc(t) corresponding coefficient.θcIt is the finger of correspondence chamber
Parameter in number function.CI(t) radioactive intensity of t input is represented.
The dynamic PET images for each frame rebuild can be regarded as in the time interval of this frame and previous frame to chamber tissue
When m- activity curve integration, i.e.,：
Wherein, xjmIt is the radioactive intensity corresponding to the pixel j of m frames in PET image sequence,WithIt is m respectively
Between at the beginning of frame and the end time,It is corresponding TAC at the pixel j of mode tissue.Based on this relation, we are by one
It is as follows that the corresponding equation groups of group TAC expand to a dictionary matrix：
Wherein：
(3) initialize, set the step-length σ in weight coefficient α, γ and μ, soft-threshold algorithm, iterations k to set to 0, set most
Big iterations kMAX。
Weight coefficient α is [27.5,28.5] left and right, this is that the term of reference provided according to original existing algorithm is adjusted
It is whole to obtain.Weight coefficient γ is general in the range of [1,5] left and right, and this is what the result based on experiment was obtained.Weight system
Number μ can typically be selected suitably value (according to bibliography Positron in the range of [0.01,0.15]
Emission Tomography Compartmental Models&colon；A Basis Pursuit Strategy for
Experimental result in Kinetic Modeling), when noise increase, algorithm can not be determined just from dictionary exactly
True time-acttivity curve, now needs appropriate increase μ value, strengthens sparse constraint.
(4) algorithm iteration renewal process is entered, for kth time iteration, fixed kinetic parameter ΦkObtain PET image
Update result Xk+1。
4.1 extract the following sub- optimization problem of part acquisition only including PET image X in target component：
Wherein：TV (X) is full variation regular terms, and α is weight coefficient, i=1 ..., and N is the numbering of detector, m=1 ...,
M represents time frame, j=1 ..., and K represents the numbering of pixel on imaging plane；Therefore yimIt is the survey of i-th of detector of m frames
Measure data, xjmIt is the concentration value of j-th of pixel of m frames, and gijIt is then an element of sytem matrix, represents j-th of pixel
The probability that the photon of outgoing is received by i-th of detector at point, rimAnd simCorresponding time frame and detector are represented respectively
Chance event and scattering events in measurement data.
4.2 calculation formula based on full variation regular terms define new variables ωjmAnd the target equation in 4.1 is converted into increasing
Wide Lagrange's equation is as follows：
Wherein：Wherein vector υjmIt is Lagrange multiplier, βjmIt is then penalty coefficient, xmIt is m frame PET image pixel groups
Into vector,It is then xmDiscrete partially micro- operator at j-th of pixel.
4.3 fix X, utilize two-dimensional contraction formula more new variables ωjm；
4.4 fix ωjm, by LA(ωjm, X) and to updating PET image X according to equation below after X derivations：
Xk+1=Xk-ρkdk(X)Xk
Wherein：ρkIt is the most fast decline step-length determined by reverse Non-monotone linear search, dk(X) it is augmentation Lagrange
Derivative of the journey to X；
4.5 fix X and ωjm, update Lagrange multiplier；
4.6 judge whether to meet iteration stopping condition：X change ＜ 10-3Or maximum sub- iterations is reached, it is unsatisfactory for then
Return to 4.4；The iteration stopping if meeting, obtains PET image X renewal result Xk+1。
(5) for kth time iteration, fixed PET image Xk+1With kinetic parameter Φk, using Di Li Crays cluster process more
New cluster result
(6) for kth time iteration, fixed PET image Xk+1Obtain the estimated result Φ of kinetic parameterk+1：
6.1 extract the following sub- optimization problem of part acquisition only including kinetic parameter Φ in target component：
Wherein：Represent the subset for the pixel for belonging to h classes in coefficient matrix Φ, nhIn being the set
The number of pixel, ρhThe matrix being made up of the average value of the corresponding pixel of h classes, ∈ is the weight system of control submodel
Number.
6.2 by defining a new matrix Nh=Ih-Eh/nh, it is assumed that EhIt is a n all constituted by 1h×nhDimension
Matrix, IhIt is one and EhDimension identical unit matrix simultaneously defines new matrix Nh=Ih-Eh/nh.IntroduceAbbreviation
Above-mentioned equation：
6.3 pairs of above formulas carry out the kinetic parameter that can be updated using soft-threshold iteration operator after linearization process
Φk+1。
(7) judge whether to meet iteration stopping condition：X and Φ change ＜ 10-3Or reach maximum iteration kMAX, no
Then return to step (4) are met, the iteration stopping if meeting obtains PET image X, tracer kinetics parameter Φ and cluster result.
We carry out experiment to verify system of the present invention by the Zubal thoracic cavities template data to Monte Carlo simulation below
System rebuilds the accuracy with segmentation result, and Fig. 1 is the template schematic diagram of the Zubal thoracic cavities data used in experiment, by different areas
Domain is divided into three regions interested (region of interest, ROI).Testing running environment is：8G internal memories, 3.40GHz,
64 bit manipulation systems, CPU is intel i7-3770；The PET scanner model Hamamatsu SHR-22000 simulated, if
Fixed radionuclide and medicine be18F-FDG, setting sinogram are 128 projection angles, 128 beams under each angle
The data result collected, sytem matrix G size is 16384 × 16384.In this experiment, to 5 × 104、1×105Two
The data for projection planted under different counting rates is tested.
To the result of PET image and traditional ML-EM (maximum likelihood-expectation maximum) weight in reconstruction framework of the present invention
Build result to compare, the two is using identical measurement data matrix Y and sytem matrix G with the comparativity of control result.Fig. 2 (a)
It is distribution true value with Fig. 3 (a), it in ML-EM in counting rate is 5 × 10 that Fig. 2 (b)~Fig. 2 (e), which is respectively,4With 1 × 105Situation
Reconstruction framework lower and of the present invention is 5 × 10 in counting rate4With 1 × 105In the case of dynamic PET images sequence in the 4th frame
Reconstructed results；Fig. 3 (b)~Fig. 3 (e) be respectively ML-EM counting rate be 5 × 104With 1 × 105In the case of and the present invention
Reconstruction framework is 5 × 10 in counting rate4With 1 × 105In the case of dynamic PET images sequence in the 6th frame reconstructed results.With
Will become apparent from joint reclosing acquisition result in region noise be significantly less than ML-EM acquisition image, ensure edge contrast
In the case of it is more smooth in functional area, table 1 is its further quantitative analysis result.
Table 1
Fig. 4 (a)~Fig. 4 (c) is the comparative result of cluster, functional area distribution and have that reconstruction framework of the present invention is obtained
The classification of k averages and the obtained result of the profile classification method based on kinetic model be compared.It can be seen that joint is rebuild
Cluster result in noise it is significantly greater, this mainly due to Di Li Crays process carry out classification pretreatment when be with pixel
What point was handled for unit, thus it is very sensitive to noise.
The above-mentioned description to embodiment is understood that for ease of those skilled in the art and using the present invention.
Person skilled in the art obviously can easily make various modifications to above-described embodiment, and described herein general
Principle is applied in other embodiment without passing through performing creative labour.Therefore, the invention is not restricted to above-described embodiment, ability
Field technique personnel are according to the announcement of the present invention, and the improvement made for the present invention and modification all should be in protection scope of the present invention
Within.
Claims (10)
1. a kind of rebuild and tracer kinetics method for parameter estimation based on the dynamic PET images that image is split, comprise the following steps：
(1) biological tissue for being injected with radiopharmaceutical agent is detected using detector, when dynamic acquisition obtains corresponding to each
The coincidence counting vector at quarter, and set up coincidence counting matrix Y；
(2) make dynamic PET image combined sequence into PET concentration distribution matrix X, according to PET image-forming principles, set up PET measurements
Equation；
(3) full variational methods are introduced by measuring equation to PET, obtains the PET image reconstruction model L (X) based on TV；
(4) using compartment model matching estimation tracer kinetics parameter, the synchronous reconstruction model S (X, Ф) on X and Ф is set up；
(5) region segmentation result obtained based on pretreatment, is clustered to tracer kinetics parameter matrix Ф, obtains cluster point
Cut MODEL C (Ф)；
(6) above three model L (X), S (X, Ф) and C (Ф) are combined and obtain the synchronous object function LSC (X, Ф) rebuild
It is as follows：
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Wherein：γ and ∈ are weight coefficient；
(7) object function LSC (X, Ф) is carried out obtaining PET concentration distribution matrix X and tracer kinetics after optimization
Parameter matrix Ф.
2. dynamic PET images according to claim 1 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
The coincidence counting matrix Y is chronologically rearranged by each coincidence counting vector, and the PET concentration distribution matrix X is by each moment
Corresponding PET concentration distribution vector is chronologically rearranged.
3. dynamic PET images according to claim 1 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
The expression formula of the PET measurements equation is as follows：
Y=GX+R+S
Wherein：G is sytem matrix, and R and S are respectively the measurement noise matrix for reflecting chance event and scattering events.
4. dynamic PET images according to claim 3 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
The expression formula of the PET image reconstruction model L (X) is as follows：
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Wherein：α is weight coefficient, and TV (X) is the full variation regular terms on X, gijFor the i-th row jth column element in sytem matrix G
Value, yimFor the i-th row m column element values, x in coincidence counting matrix YjmFor jth row m column elements in PET concentration distribution matrix X
Value, rimI-th row m column element values, s in measurement noise matrix R to reflect chance eventimTo reflect the measurement of scattering events
I-th row m column element values in noise matrix S, i, j and m are natural number and 1≤i≤N, 1≤j≤K, 1≤m≤M, N are to meet
The dimension of count vector, K is the pixel number that PET concentration distribution matrix X line number is PET image, and M is distributed for PET concentration
Matrix X columns is sampling time length.
5. dynamic PET images according to claim 4 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
The expression formula of the full variation regular terms TV (X) is as follows：
<mrow>
<mi>T</mi>
<mi>V</mi>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<mo>|</mo>
<mo>|</mo>
<mi>D</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>j</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
<msub>
<mo>|</mo>
<mn>2</mn>
</msub>
</mrow>
Wherein：D(xjm) it is on xjmTwo dimensional difference vector, the vectorial the first row element value be xjm-xJ, m+1, the second row element
It is worth for xjm-xJ+1, m, xJ, m+1For jth row m+1 column element values, x in PET concentration distribution matrix XJ+1, mFor PET concentration distribution matrix
The row of jth+1 m column element values in X, | | | |2Represent 2 norms.
6. dynamic PET images according to claim 1 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
The expression formula of the synchronous reconstruction model S (X, Ф) is as follows：
<mrow>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>,</mo>
<mi>&Phi;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>|</mo>
<mo>|</mo>
<mi>X</mi>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>&Psi;</mi>
<mi>&Phi;</mi>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>|</mo>
<msubsup>
<mo>|</mo>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mi>&mu;</mi>
<mo>|</mo>
<mo>|</mo>
<mi>&Phi;</mi>
<mo>|</mo>
<msub>
<mo>|</mo>
<mn>1</mn>
</msub>
</mrow>
Wherein：μ is weight coefficient, and Ψ is dictionary matrix,TTransposition is represented, | | | |22 norms are represented, | | | |1Represent 1 norm.
7. dynamic PET images according to claim 1 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
The expression formula of the cluster segmentation MODEL C (Ф) is as follows：
<mrow>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>&Phi;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>H</mi>
</munderover>
<munder>
<mo>&Sigma;</mo>
<mrow>
<msub>
<mi>&phi;</mi>
<mi>h</mi>
</msub>
<mo>&Element;</mo>
<msub>
<mi>C</mi>
<mi>h</mi>
</msub>
</mrow>
</munder>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&phi;</mi>
<mi>h</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&rho;</mi>
<mi>h</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&phi;</mi>
<mi>h</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&rho;</mi>
<mi>h</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
<msub>
<mi>&rho;</mi>
<mi>h</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>n</mi>
<mi>h</mi>
</msub>
</mfrac>
<munder>
<mo>&Sigma;</mo>
<mrow>
<msub>
<mi>&phi;</mi>
<mi>h</mi>
</msub>
<mo>&Element;</mo>
<msub>
<mi>C</mi>
<mi>h</mi>
</msub>
</mrow>
</munder>
<msub>
<mi>&phi;</mi>
<mi>h</mi>
</msub>
</mrow>
Wherein：ChTo belong to the parameter vector set of h classes, φ in tracer kinetics parameter matrix ФhFor parameter vector set Ch
In any parameter vector, nhFor parameter vector set ChIn parameter vector number, h is natural number and 1≤h≤H, H are cluster
Class number,TRepresent transposition.
8. dynamic PET images according to claim 1 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
Optimization is carried out to object function LSC (X, Ф) using ADMM combination soft-threshold iteration optimization algorithms in the step (7)；
Wherein, ADMM is iterated Optimization Solution for PET concentration distribution matrix X, and soft-threshold is directed to tracer kinetics parameter matrix Ф
Iteration optimization is solved.
9. dynamic PET images according to claim 8 are rebuild and tracer kinetics method for parameter estimation, it is characterised in that：
The soft-threshold iteration optimization algorithms are based on below equation and carry out linear process to change to tracer kinetics parameter matrix Ф
In generation, updates：
Nh=Ih-Eh/nh
Wherein：EhFor a n all constituted by 1h×nhTie up matrix, IhFor one and matrix EhDimension identical unit matrix, μ
For weight coefficient,TTransposition is represented, Ψ is dictionary matrix, ChFor belong in tracer kinetics parameter matrix Ф the parameters of h classes to
Duration set, φhFor parameter vector set ChIn any parameter vector, nhFor parameter vector set ChIn parameter vector number,
xhFor in PET concentration distribution matrix X with parameter vector φhA corresponding TAC, | | | |22 norms are represented, | | | |1Represent 1 model
Number, h is natural number and 1≤h≤H, H are the class number of cluster.
10. the dynamic PET images according to claim 6 or 9 are rebuild and tracer kinetics method for parameter estimation, its feature exists
In：The expression formula of the dictionary matrix Ψ is as follows：
<mrow>
<mi>&Psi;</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>&psi;</mi>
<mn>10</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>&psi;</mi>
<mn>11</mn>
</msub>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<msub>
<mi>&psi;</mi>
<mrow>
<mn>1</mn>
<mi>Z</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mtable>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
</mtable>
</mtd>
<mtd>
<mtable>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
</mtable>
</mtd>
<mtd>
<mtable>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
</mtable>
</mtd>
<mtd>
<mtable>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
</mtable>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&psi;</mi>
<mrow>
<mi>M</mi>
<mn>0</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mi>&psi;</mi>
<mrow>
<mi>M</mi>
<mn>1</mn>
</mrow>
</msub>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<msub>
<mi>&psi;</mi>
<mrow>
<mi>M</mi>
<mi>Z</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
<mrow>
<msub>
<mi>&psi;</mi>
<mrow>
<mi>m</mi>
<mn>0</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>e</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>s</mi>
</msubsup>
</mrow>
</mfrac>
<msubsup>
<mo>&Integral;</mo>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>s</mi>
</msubsup>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>e</mi>
</msubsup>
</msubsup>
<msub>
<mi>C</mi>
<mi>I</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
<mrow>
<msub>
<mi>&psi;</mi>
<mrow>
<mi>m</mi>
<mi>c</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>e</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>s</mi>
</msubsup>
</mrow>
</mfrac>
<msubsup>
<mo>&Integral;</mo>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>s</mi>
</msubsup>
<msubsup>
<mi>t</mi>
<mi>m</mi>
<mi>e</mi>
</msubsup>
</msubsup>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mi>t</mi>
</msubsup>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>c</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>-</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<msub>
<mi>C</mi>
<mi>I</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>&tau;</mi>
</mrow>
Wherein：CIAnd C (t)I(τ) is respectively the concentration value of t and τ moment radiopharmaceutical agents in blood plasma,WithRespectively
For on m groups coincidence counting vector collection at the beginning of between and the end time, θcCorrespond to c-th of chamber tissue exponential function
Coefficient, m and c are that natural number and 1≤m≤M, 1≤c≤Z, M are that the sampling time is long for PET concentration distribution matrix X columns
Degree, Z is the natural number more than 1；θ1~θNValue be in interval [θmin, θmax] in by it is exponential interval chosen, θminWith
θmaxThe respectively bound threshold value of coefficient, t and τ represent the time.
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