CN103164863B - For rebuilding the method for positron emission computerized tomography image - Google Patents

Abstract

The invention provides a kind of method for rebuilding positron emission computerized tomography image, it comprises: according to the scattered photon example projection principle of work of Compton scattering, creates the scattered photon example projection probability model described by designated model parameter; According to described scattered photon example projection probability model, create scattered photon example point spread function; According to scattered photon example projection model and scattered photon example point spread function, create non-scatter photon example point spread function; Utilize statistics iterative reconstruction algorithm, according to scattered photon example point spread function and non-scatter photon example point spread function, by scattered photon example and non-scatter photon event reconstruction PET image.The present invention can improve detection efficiency, significantly reduces the radiation dose suffered by detected object and operator, shortens the supervision time, improves service efficiency, complete data is sampled, simplifies panel detector structure, reduces detector cost in clinical practice.

Description

For rebuilding the method for positron emission computerized tomography image

Technical field

The present invention relates to a kind of method of imaging, particularly relating to a kind of method for rebuilding positron emission computerized tomography image.

Background technology

Positron emission computerized tomography (PositronEmissionComputedTomography, PET) as a kind of medicine imaging technique, for the diagnosis of major disease, the more afterwards research and development etc. of observation and novel drugs provide important information, in clinical practice and biomedical research, there is important value.Its cardinal principle is: inject in detected object body by the medicine (tracer agent) that marked positron radionuclide, positron is launched when decay occurs positron radionuclide on tracer agent, positron and the electronics generation annihilation reaction in body generate that both direction is contrary, gamma-ray photon that energy is 511keV (back-to-back gamma-ray photon to), and the detector that these two gamma-ray photons are placed on around detected object detects.One time annihilation reaction is called as an example, and as shown in Figure 1, Figure 2 shown in a and Fig. 2 b, the line between the crystal bar detecting two gamma-ray photons of an example is called line of response (LineofResponse, LOR).Wherein, Fig. 1 shows positron annihilation and produces two gamma-ray photons, is detected respectively by two crystal bars as detector 1.Fig. 2 a and Fig. 2 b then shows gamma-ray photon back-to-back, in detected object, scattering process occurs, solid line is photon spread path, dotted line is actual LOR line, and to specifically comprising the positron radionuclide generation decay emission be injected in the detected object body internal labeling medicine of positron radionuclide (tracer agent), gamma-ray photon goes out that positron is contrary with the both direction that the electronics generation annihilation reaction in detected object body generates, energy is the gamma-ray photon of 511keV back-to-back.In addition, Fig. 2 a shows single photon single scattering, single photon single scattering example specifically comprises gamma-ray photon centering back-to-back to be had and is detected the scattered photon example that device detects after only having a gamma-ray photon and a detected object interaction generation Compton scattering, and namely the gamma-ray photon pair back-to-back of single photon single scattering occurs.In single photon single scattering example, there is not interactional gamma-ray photon and will be detected device direct detection in gamma-ray photon centering back-to-back with detected object.Fig. 2 b shows two-photon single scattering, two gamma-ray photons that two-photon single scattering example specifically comprises gamma-ray photon centering are back-to-back detected the scattered photon example that device detects respectively with after a detected object interaction generation Compton scattering, and namely the gamma-ray photon pair back-to-back of two-photon single scattering occurs.After detecting a large amount of this gamma-ray photons, the distribution of tracer drug in detected object body can be obtained through image reconstruction.Because tracer drug participates in certain physiology in biosome or biochemical process, therefore, PET image is utilized can to obtain physiology in biosome or Biochemical Information.

Above-mentioned PET imaging process is only limited to a kind of ideal situation, i.e. two gamma-ray photons interaction (such as Compton scattering of not making gamma-ray photon energy or the direction of propagation change with detected object after producing, but be not limited thereto), arrive pet detector in the mode of rectilinear propagation to be detected device and to detect, this example is called as non-scatter photon example (i.e. good example).Because the position of example generation in good example is on LOR, therefore, the image reconstructed by good example truly can reflect the distribution of nucleic (tracer drug).But, in actual conditions, only some has been example to the example that PET detects, when two gamma-ray photons of an example are propagated in detected object, one of them or two gamma-ray photons likely collide with the extranulear electron of wherein certain atom, produce Compton scattering, photon energy and the direction of propagation change, these examples that scattering occurred are called scattered photon example, as above describe in detail, scattered photon example specifically comprises two-photon single scattering example and single photon single scattering example.LOR line due to scattered photon example deviate from the position (as Fig. 2 a, Fig. 2 b) at positron annihilation place, if do not rejected and used it for image reconstruction, PET image will certainly be caused truly can not to reflect the distribution of tracer agent, bring comparatively big error to follow-up quantitative calculating and clinical diagnosis work.Therefore, be all utilize scatter correction algorithm to be rejected by scattered photon example in conventional P ET.

In fact, when setting up rational scattered photon example projection model, scattered photon example also may be used for image reconstruction and obtains Radio-nuclide distribution image.Account for significant proportion due in the example that scattered photon example all detects in pet detector, utilize scattered photon example and non-scatter photon example to carry out image reconstruction simultaneously, will the detection efficiency of PET be improved.In clinical practice, this radiation dose that will significantly reduce suffered by detected object and operator; Under same medicine dosage, this will shorten patient's supervision time, improve the service efficiency of PET.

In addition, pet detector 1 has ring texture as shown in Figure 3 a (or closed polygonized structure) and two slab constructions two kinds as shown in Figure 3 b.Compared with the ring-shaped P ET detector 1 shown in Fig. 3 a, two dull and stereotyped pet detector 1 cost shown in Fig. 3 b is lower, installation and maintenance simple, and can possess the larger detection visual field, has application and universal prospect preferably.But, for static two dull and stereotyped pet detector, launching track and two flat boards do not have intersection point or only have the LOR of an intersection point to be detected, as shown in Figure 4, in static two dull and stereotyped pet detector 1, utilize scattered photon example to solve data sampling incomplete problem, dotted line is non-scatter photon example travel path (detector 1 cannot obtain the example launched in the direction), and solid line is the possible travel path (detector can obtain the example launched in the direction) of scattered photon example.Owing to there is the incomplete problem of data sampling, image reconstruction of low quality, which has limited the widespread use of static two dull and stereotyped pet detector 1.

Given this, industry develops the dull and stereotyped pet detector with rotating mechanism, although it can solve the incomplete problem of above-mentioned sampling.But comparing with the two dull and stereotyped PET of static state with ring-shaped P ET, there is obvious shortcoming in it.First, adding of rotating mechanism allows system become more complicated, and the skew of detector center and rotation center, can cause the deviation of geometry location during reconstruction, thus have a strong impact on picture quality; Secondly, the mode of rotating acquisition needs in different position acquisition measured object information, and sweep time increases greatly, reduces the service efficiency of pet detector.

In fact, as there is scattering in communication process in the example not having intersection point along above-mentioned launching track and two flat boards or only have the LOR of an intersection point to launch, become scattered photon example, be can (as Fig. 4) of detecting by the detector of static two dull and stereotyped PET, therefore, when utilizing these scattered photon examples to rebuild, the incomplete problem of data sampling in static two dull and stereotyped PET image reconstruction will be solved.

To sum up, if scattered photon example is used for PET imaging in conjunction with non-scatter photon example, the detection efficiency of pet detector will be improved, thus in clinical practice, significantly reduce detected object and the radiation dose suffered by operator; Under same medicine dosage, shorten patient's supervision time, improve the service efficiency of PET.Be conducive to solving the incomplete problem of slab construction pet detector data sampling simultaneously, simplify pet detector structure, reduce pet detector manufacture and maintenance cost.

Application number is the Chinese patent application of CN201080030171.9 open a kind of " utilize and rebuild based on the flight-time information timc-of-fiight positron emission tomography of picture material that event generates one by one " technical scheme, but the prior art is only limited to and has flight time (timeofflight, the pet detector of TOF) measuring technique uses, it needs to utilize TOF commercial measurement to obtain gamma-ray photon centering two gamma-ray photons to be back-to-back detected the mistiming that device detects, and be only applicable to gamma-ray photon centering back-to-back and have and the scattered photon example (single photon single scattering example) only having a gamma-ray photon generation Compton scattering, therefore there is larger limitation.

Summary of the invention

The object of the present invention is to provide a kind of method for rebuilding positron emission computerized tomography image, with solve prior art exist there is larger circumscribed problem.

In order to solve the problem, the invention provides a kind of method for rebuilding positron emission computerized tomography image, it comprises the following steps: step one: according to the scattered photon example projection principle of work of Compton scattering, create the scattered photon example projection probability model described by designated model parameter, wherein, described scattered photon example comprises two-photon single scattering example and single photon single scattering example, described two-photon single scattering example is that two gamma-ray photons of gamma-ray photon centering are back-to-back detected the scattered photon example that device detects respectively with after a detected object interaction generation Compton scattering, described single photon single scattering example is that gamma-ray photon centering has and is detected the scattered photon example that device detects after only having a gamma-ray photon and a detected object interaction generation Compton scattering back-to-back, in described single photon single scattering example, there is not interactional gamma-ray photon and will be detected device direct detection in gamma-ray photon centering back-to-back with detected object, described gamma-ray photon is back-to-back contrary with the both direction that the electronics generation annihilation reaction in detected object body generates to going out positron for the positron radionuclide generation decay emission be injected in the detected object body internal labeling tracer agent of positron radionuclide, energy is the gamma-ray photon of 511keV, described designated model parameter forms relevant physical quantity establishment by the material of fundamental physical quantity and detected object, the material of detected object forms the fundamental physical quantity that can refer to the establishment of existing fundamental physical quantity obtain manner after the relevant physical quantity material comprised by creating detected object forms, step 2: according to described scattered photon example projection probability model, create scattered photon example point spread function, described scattered photon example point spread function comprises two-photon single scattering example point spread function and single photon single scattering example point spread function, described two-photon single scattering example point spread function is the probability of specifying described gamma-ray photon back-to-back of some transmitting pair and detected object generation two-photon single scattering to be finally detected device in the detector detection visual field to detect, described single photon single scattering example point spread function is the probability of specifying gamma-ray photon back-to-back of some transmitting pair and detected object generation single photon single scattering to be finally detected device in the detector detection visual field to detect, step 3: according to scattered photon example projection model and scattered photon example point spread function, create non-scatter photon example point spread function, wherein, described non-scatter example for described in two gamma-ray photons of gamma-ray photon centering back-to-back interaction of not making gamma-ray photon energy or the direction of propagation change with detected object after producing and arrive detector in the mode of rectilinear propagation and be finally detected the photon example that device detects, described non-scatter photon example point spread function is the interaction of specifying two gamma-ray photons of the centering of gamma-ray photon back-to-back of a bit launching not make with detected object gamma-ray photon energy or the direction of propagation change after generation in the detector detection visual field and arrives detector in the mode of rectilinear propagation and be finally detected the probability that device detects, step 4: utilize statistics iterative reconstruction algorithm, according to scattered photon example point spread function and non-scatter photon example point spread function, by scattered photon example and non-scatter photon event reconstruction positron emission computerized tomography image.

As from the foregoing, instant invention overcomes the limitation defect that prior art exists, do not need to measure as TOF technology and obtain gamma-ray photon centering two gamma-ray photons back-to-back and be detected the mistiming that device detects, two-photon single scattering example and single photon single scattering example are used for PET image reconstruction in conjunction with non-scatter photon example, the detection efficiency of PET can be improved.In clinical practice, significantly reduce detected object and the radiation dose suffered by operator; Under same medicine dosage, shorten patient's supervision time, improve the service efficiency of PET.Be conducive to solving the incomplete problem of slab construction pet detector data sampling simultaneously, simplify pet detector structure, reduce pet detector manufacture and maintenance cost.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the line of response of two gamma-ray photons between crystal bar of an example;

Fig. 2 a is the schematic diagram of single photon single scattering;

Fig. 2 b is the schematic diagram of two-photon single scattering;

Fig. 3 a is ring-shaped P ET panel detector structure schematic diagram;

Fig. 3 b is dull and stereotyped pet detector structural representation;

Fig. 4 is that static two dull and stereotyped pet detector utilizes scattered photon example to solve the schematic diagram of the incomplete problem of data sampling;

Fig. 5 is the schematic flow sheet according to the method for rebuilding positron emission computerized tomography image of the present invention;

Fig. 6 is the schematic diagram of computing module of the present invention;

Fig. 7 is scattered photon example perspective view;

Fig. 8 is scattered photon example point spread function schematic diagram;

Fig. 9 is the schematic diagram of embodiment device.

Wherein, description of reference numerals is as follows:

1 detector

S1, S2, S3, S4 step

21 scattered photon example projection model creation modules

22 scattered photon example point spread function creation modules

23 non-scatter photon example point spread function creation modules

24 rebuild PET image module

31 detectors

32 electronics modules

33 computing modules

34 imitative bodies

35 radioactive sources

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further details.

Fig. 5 shows the process flow diagram according to the method for rebuilding positron emission computerized tomography image of the present invention, and as shown in the figure, it comprises four step S1-S4 and is sequentially described as follows.

Step S1: according to the scattered photon example projection principle of work of Compton scattering, creates the scattered photon example projection probability model described by designated model parameter.

In this step S1, scattered photon example comprises two-photon single scattering example and single photon single scattering example.Two-photon single scattering example is that two gamma-ray photons of gamma-ray photon centering are back-to-back detected the scattered photon example that device detects respectively with after a detected object interaction generation Compton scattering, and namely the gamma-ray photon pair back-to-back of two-photon single scattering occurs.Single photon single scattering example is that gamma-ray photon centering has and is detected the scattered photon example that device detects after only having a gamma-ray photon and a detected object interaction generation Compton scattering back-to-back, and namely the gamma-ray photon pair back-to-back of single photon single scattering occurs; In single photon single scattering example, there is not interactional gamma-ray photon and will be detected device direct detection in gamma-ray photon centering back-to-back with detected object.Positron is contrary with the both direction that the electronics generation annihilation reaction in detected object body generates, energy is the gamma-ray photon of 511keV to going out for the positron radionuclide generation decay emission be injected in the detected object body internal labeling tracer agent of positron radionuclide for described gamma-ray photon back-to-back.

Designated model parameter forms relevant physical quantity establishment by the material of fundamental physical quantity and detected object.Fundamental physical quantity can refer to existing fundamental physical quantity (such as formula 1) below obtain manner and creates, and specifically creates by disclosed research data and the existing fundamental physical quantity obtain manner of fundamental physical quantity database.The material of detected object forms the physical quantity that can refer to the establishment of existing fundamental physical quantity obtain manner after the relevant physical quantity material comprised by creating detected object forms.

The material composition creating detected object specifically comprises: use measuring method to create the material composition of detected object, especially by use computer tomography (ComputerTomography, CT), magnetic resonance imaging (MagneticResonanceImaging, MRI) etc. existing have the mode creating detected object three-dimensional structure image function and create detected object three-dimensional structure image, thus create the material composition of detected object; Or use non-measured method to create the material composition of detected object, the priori that the material especially by detected object forms calculates the material composition creating detected object.

This step S1 by the scattered photon example projection principle of work of computing machine according to Compton scattering, can create the scattered photon example projection probability model described by designated model parameter, as follows:

For outstanding key physical rule avoids miscellaneous calculating simultaneously, scattered photon example projection probability model to carry out abstract to three dimensions, the two dimensional surface that arbitrary tangent is formed in space sets up mathematical description, is certainly not limited thereto, also directly can set up 3-d mathematics in three dimensions and describe.

It is E that formula 1 describes zero energy ₀photon and detected object generation Compton scattering after, its dump energy E _ωwith scattering angle ω relation.

$E_{\mathrm{\ω}}=\frac{E_0}{1+\frac{E_0}{m{c}^2}(1-\cos \mathrm{\ω})},$ Formula 1

Wherein, m is electron rest mass, and c is the light velocity, m and c is fundamental physical quantity.

With reference to figure 7 and Fig. 8, formula 2 describes the Compton scattering projection process of two-photon single scattering example, and the gamma-ray photon back-to-back namely launched by the some S in the model space is to respectively at a M ₁, some M ₂interact with detected object (i.e. scattering medium) and Compton scattering occurs, scattering angle is respectively ω ₁, ω ₂(namely scattering angle is to (ω ₁, ω ₂)), two gamma-ray photons are scattered rear moment track and change and be finally detected device cells D respectively ₁, D ₂(namely detector cells is to (D ₁, D ₂)) probability that detects, i.e. flux differential.

$\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)|S,(M_1,M_2))=\frac{f\left(S\right)d{S}_S}{2\mathrm{\π}}\mathrm{\δ}(\∠M_{1}S{M}_2-\mathrm{\π})\mathrm{\φ}(S\→M_1)\frac{1}{\mathrm{\σ}}\mathrm{\φ}(S\→M_2)\frac{1}{\mathrm{\σ}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_1\right)n_e\left(M_1\right)d{S}_{M_1}$

$\mathrm{\φ}(M_1\→D_1)\frac{1}{{\mathrm{\σ}}^{\′}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_2\right)n_e\left(M_2\right)d{S}_{M_2}\mathrm{\φ}(M_2\→D_2)\frac{1}{{\mathrm{\σ}}^{\′}},$ Formula 2

Wherein, S=(x _s, y _s) represent that radioactivity density is certain point of f (S); represent certain point in scattering medium; represent certain detector cells, its detected to interact with detected object there is Compton scattering after energy be gamma-ray photon; ∠ M ₁sM ₂represent the angle M being summit with a S ₁sM ₂; δ represents discrete system Unit sample response function, as ∠ M ₁sM ₂when equaling other angle values, its value is 0, as ∠ M ₁sM ₂when equaling π, its value is 1(point M ₁, some S and some M ₂conllinear, ∠ M ₁sM ₂for the straight angle); DS _srepresent the face infinitesimal of some S; represent some M _iface infinitesimal; σ represents the line infinitesimal of scattering medium; σ ' represents the line infinitesimal of detector; n _e(M _i) be a M _ielectron density, by a M _idetected object material composition create; φ (S → M _i) represent that the gamma-ray photon that sends of some S is at a M _iflux, describe with formula 3; φ (M _i→ D _j) represent at a M _iwith detected object interact there is Compton scattering gamma-ray photon at detector cells D _iflux, describe with formula 4; σ _c(ω) represent differential cross-section when gamma-ray photon generation scattering angle is the Compton scattering of ω, describe with formula 5.

$\mathrm{\φ}(S\→M_i)=2\arctan \left(\frac{\mathrm{\σ}}{2\left|S{M}_i\right|}\right),$ Formula 3

Wherein, SM _irepresent that some S is to some M _idistance.

$\mathrm{\φ}(M_i\→D_j)\text{=2arctan}\left(\frac{{\mathrm{\σ}}^{\′}}{2\left|M_i{D}_j\right|}\right),$ Formula 4

Wherein, M _id _jrepresent some M _ito detector cells D _jdistance.

${\mathrm{\σ}}_C\left(\mathrm{\ω}\right)=\frac{1}{2}\mathrm{\π}{r}_e^{2}P\left(\mathrm{\ω}\right),$ Formula 5

Wherein, r _ebeing classical electron radius, is fundamental physical quantity; P (ω) is Klein Gordon equation-benevolence section (Klein – Nishina) scattering probability density, describes with formula 6;

$P\left(\mathrm{\ω}\right)=\frac{1+{\cos }^2\mathrm{\ω}}{{(2-\cos \mathrm{\ω})}^2}[1+\frac{{(1-\cos \mathrm{\ω})}^2}{(2-\cos \mathrm{\ω})(1+{\cos }^2\mathrm{\ω})}],$ Formula 6

Formula 7 describes interacting with detected object of set point S transmitting and scattering angle occurs to (ω ₁, ω ₂) Compton scattering and be detected device unit to (D ₁, D ₂) the right flux of the gamma-ray photon back-to-back that detects, gamma-ray photon back-to-back that the set point S namely in the model space launches pair and detected object interact and scattering angle occur to (ω ₁, ω ₂) Compton scattering be finally detected unit to (D ₁, D ₂) probability that detects.

$\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)|S)=\∫\∫\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)|S,(M_1,M_2))\mathrm{\δ}(\∠S{M}_1{D}_1-(\mathrm{\π}-{\mathrm{\ω}}_1))\mathrm{\δ}(\∠S{M}_2{D}_2-(\mathrm{\π}-{\mathrm{\ω}}_2)),$ Formula 7

Wherein, ∠ SM _id _ithink a M _ithe angle SM on summit _id _i.

Formula 7 can be called two-photon single scattering Klein Gordon equation-benevolence section (Klein – Nishina) flux differential formulas.

Refer again to Fig. 7 and Fig. 8, when scattering angle is to (ω ₁, ω ₂) meet ω ₁=0 or ω ₂=0 but | ω ₁|+| ω ₂| during >0, scattered photon example is single photon single scattering example (in other words, single photon single scattering example becomes the special case of scattered photon example), and formula 2 can be reduced to formula 8-1 or 8-2, and formula 7 can be reduced to formula 9-1 or 9-2.

$\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1=0,{\mathrm{\ω}}_2\≠0)|S,M_2)=\frac{f\left(S\right)d{S}_S}{2\mathrm{\π}}\mathrm{\δ}(\∠D_{1}S{M}_2-\mathrm{\π})\mathrm{\φ}(S\→D_1)\frac{1}{{\mathrm{\σ}}^{\′}},$ Formula 8-1

$\mathrm{\φ}(S\→M_2)\frac{1}{\mathrm{\σ}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_2\right)n_e\left(M_2\right)d{S}_{M_2}\mathrm{\φ}(M_2\→D_2)\frac{1}{{\mathrm{\σ}}^{\′}}$

$\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1\≠0,{\mathrm{\ω}}_2=0)|S,M_1)=\frac{f\left(S\right)d{S}_S}{2\mathrm{\π}}\mathrm{\δ}(\∠D_{2}S{M}_1-\mathrm{\π})\mathrm{\φ}(S\→D_2)\frac{1}{{\mathrm{\σ}}^{\′}},$ Formula 8-2

$\mathrm{\φ}(S\→M_1)\frac{1}{\mathrm{\σ}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_1\right)n_e\left(M_1\right)d{S}_{M_1}\mathrm{\φ}(M_1\→D_1)\frac{1}{{\mathrm{\σ}}^{\′}}$

Wherein, ∠ D ₁sM ₂represent the angle D being summit with a S ₁sM ₂; ∠ D ₂sM ₁represent the angle D being summit with a S ₂sM ₁.

8-1 is example with the formula, formula 2 is formula 8-1 by following process simplification: in single photon single scattering example, gamma-ray photon centering interactional gamma-ray photon does not occur with detected object will be detected device direct detection back-to-back, and can not with detected object generation Compton scattering, the described gamma-ray photon namely launched by some S will directly arrive probe unit D ₁, formula 8-1 mid point S, some M ₁with a D ₁conllinear, ∠ M in formula 2 ₁sM ₂be reduced to ∠ D in formula 8-1 ₁sM ₂.Therefore, gamma-ray photon described in formula 2 is at a M ₁cells D is detected after there is Compton scattering ₁the probability of detection $\mathrm{\φ}(S\→M_1)\frac{1}{\mathrm{\σ}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_1\right)n_e\left(M_1\right)d{S}_{M_1}\mathrm{\φ}(M_1\→D_1)\frac{1}{{\mathrm{\σ}}^{\′}}$ Be reduced to the described gamma-ray photon launched by a S in formula 8-1 and directly arrive probe unit D ₁probability particularly, at a M ₁there is not Compton scattering in place, represents the probability of described physical process in formula 2 there is not physical significance, be therefore simplified at formula 8-1; The described gamma-ray photon launched by a S is linearly propagated and is arrived probe unit D ₁, in formula 2, represent that the described gamma-ray photon that some S launches passes through a some M ₁arrive detector cells D again ₁probability be reduced to the described gamma-ray photon launched by a S in formula 8-1 and linearly propagate arrival probe unit D ₁probability wherein, the described gamma-ray photon launched by a S in formula 2 is by some M ₁arrive detector cells D again ₁probability the described gamma-ray photon launched by a S is at a M ₁per unit throughputs with described gamma-ray photon by a M ₁arrive detector cells D again ₁per unit throughputs product representation.Formula 2 can refer to said process to the simplification of formula 8-2 and obtains.

$\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1=0,{\mathrm{\ω}}_2\≠0)|S)=\∫\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1=0,{\mathrm{\ω}}_2\≠0)|S,M_2)\mathrm{\δ}(\∠S{M}_2{D}_2-(\mathrm{\π}-{\mathrm{\ω}}_2)),$ Formula 9-1

$\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1\≠0,{\mathrm{\ω}}_2=0)|S)=\∫\mathrm{d\Φ}((D_1,D_2),({\mathrm{\ω}}_1\≠0,{\mathrm{\ω}}_2=0)|S,M_1)\mathrm{\δ}(\∠S{M}_1{D}_1-(\mathrm{\π}-{\mathrm{\ω}}_1)),$ Formula 9-2

Formula 9-1 and 9-2 can be called single photon single scattering Klein Gordon equation-benevolence section (Klein – Nishina) flux differential formulas.9-1 is example with the formula, and formula 7 is formula 9-1 by following process simplification: work as ω ₁when=0, δ (∠ SM in formula 7 ₁d ₁-(π-ω ₁)) be reduced to δ (∠ SM ₁d ₁-π), in single photon single scattering example, there is not interactional gamma-ray photon and will be detected device direct detection in gamma-ray photon centering back-to-back with detected object, therefore formula 9-1 mid point S, some M ₁with a D ₁conllinear, ∠ SM ₁d ₁for the straight angle, δ (∠ SM ₁d ₁-π)=1.D Φ ((D in formula 7 ₁, D ₂), (ω ₁, ω ₂) | S, (M ₁, M ₂)) be reduced to d Φ ((D in formula 9-1 ₁, D ₂), (ω ₁=0, ω ₂≠ 0) | S, M ₂), the process that simplifies is with reference to the simplification process of formula 2 to formula 8-1.Contrast equation 7, only at a M in formula 9-1 ₂there is a Compton scattering, therefore only to a M ₂integration.Formula 7 can refer to said process to the simplification of formula 9-2 and obtains.

Formula 1 describes the establishment of scattered photon example projection probability model to formula 9-2, and the fundamental physical quantity that wherein designated model parameter is related to formula 9-2 by formula 1 forms relevant physical quantity establishment with the material of detected object.Wherein, two-photon single scattering Klein Gordon equation-benevolence section (Klein – Nishina) flux differential formulas and single photon single scattering Klein Gordon equation-benevolence section (Klein – Nishina) flux differential formulas can be referred to as Klein Gordon equation-benevolence section (Klein – Nishina) flux differential formulas.

Step S2: according to scattered photon example projection probability model, create scattered photon example point spread function.

In this step, scattered photon example point spread function is the probability of specifying gamma-ray photon back-to-back of some transmitting pair and detected object generation two-photon single scattering and single photon single scattering to be finally detected device in the detector detection visual field to detect, and described scattered photon example point spread function comprises two-photon single scattering example point spread function and single photon single scattering example point spread function.Two-photon single scattering example point spread function is the probability of specifying gamma-ray photon back-to-back of some transmitting pair and detected object generation two-photon single scattering to be finally detected device in the detector detection visual field to detect.Single photon single scattering example point spread function is the probability of specifying gamma-ray photon back-to-back of some transmitting pair and detected object generation single photon single scattering to be finally detected device in the detector detection visual field to detect.

In this step, can perform by computing machine the operation creating scattered photon example point spread function, specifically comprise: the probability of specifying gamma-ray photon back-to-back of some transmitting pair and detected object generation two-photon single scattering and single photon single scattering to be finally detected device in the calculating detector detection visual field to detect; In other words, two-photon single scattering example point spread function and single photon single scattering example point spread function is calculated.Principle is as follows:

With reference to figure 8, for two-photon single scattering example, i.e. ω ₁≠ 0 and ω ₂≠ 0, set point S, detector cells are to (D ₁, D ₂) and scattering angle to (ω ₁, ω ₂), the integration of formula 7 is to a M ₁, some M ₂the point of composition is to (M ₁, M ₂) track integration (be certainly not limited thereto, also can adopt other be suitable for two-dimensional integration pattern), above-mentioned integral process specifically comprises:

On two dimensional surface, some M _ipath of integration is some S, puts M _iwith a D _istring SD in determined circle _iright angle of circumference be the arc of π-ω.For gamma-ray photon 1, at arc SM ₁d ₁determine 1 M ₁, the feature contrary according to gamma-ray photon transmit direction back-to-back, some M ₁unique straight line M is determined with a S ₁s, straight line M ₁s and arc SM ₂d ₂intersection point uniquely determine a M ₂, afterwards at arc SM ₁d ₁upper transfer point M ₁, become the point of " S " type to (M ₁, M ₂) line integral.On two dimensional surface, string SD _iright angle of circumference be that the arc of π-ω co-exists in two, therefore put (M on two dimensional surface ₁, M ₂) integration be two " S " type curvilinear integrals.Or, in three dimensions, string SD _iright angle of circumference be that the arc of π-ω becomes with string SD _ifor fixed axis, arc SM _id _ifor the surface of revolution that bus turns round and formed, therefore put (M in three dimensions ₁, M ₂) integration be the surface of revolution integration of two " S " type buses.

Refer again to Fig. 8, for single photon single scattering example, i.e. ω ₁=0 or ω ₂=0 but | ω ₁|+| ω ₂| >0, set point S, detector cells are to (D ₁, D ₂) and scattering angle to (ω ₁, ω ₂), the integration of formula 9-1 or 9-2 is to a M ₁or some M ₂the integration of track, above-mentioned integration specifically comprises: work as ω _iwhen=0, some S, some M _iwith a D _iconllinear.9-1 is example with the formula, and the gamma-ray photon 1 of gamma-ray photon centering is directly detected device cells D by there is not Compton scattering after a S transmitting back-to-back ₁detection, scattering angle occurs the gamma-ray photon 2 of gamma-ray photon centering is back-to-back ω ₂compton scattering after be detected device cells D ₂detection, by line segment D ₁s is along putting D ₁extend to some S direction, its extended line and arc SM ₂d ₂intersection point will uniquely determine a M ₂.Therefore set point S, detector cells are to (D ₁, D ₂) and scattering angle to (ω ₁≠ 0, ω ₂=0) or (ω ₁=0, ω ₂≠ 0), to a M ₁or some M ₂the integration of track is well-determined some M ₁or some M ₂.

Set point S, detector cells are to (D ₁, D ₂) and scattering angle to (ω ₁, ω ₂), for two-photon single scattering example and single photon single scattering example, determine the integration concrete form of formula 7 and formula 9-1,9-2 respectively, calculate the generation of the gamma-ray photon back-to-back scattering angle launched by set point S to (ω ₁, ω ₂) Compton scattering be finally detected device to (D ₁, D ₂) probability that detects, namely create two-photon single scattering example point spread function and single photon single scattering example point spread function respectively, thus create scattered photon example point spread function.

Step S3: according to scattered photon example projection model and scattered photon example point spread function, creates non-scatter photon example point spread function.

In this step, non-scatter photon example point spread function can be created by computing machine, specifically comprise: interaction (the such as Compton scattering of specifying two gamma-ray photons of the centering of gamma-ray photon back-to-back of a bit launching not make gamma-ray photon energy or the direction of propagation change with detected object after producing in the calculating detector detection visual field, certainly be not limited thereto) and arrive in the mode of rectilinear propagation the probability that pet detector is detected device detection, in other words, the two-photon single scattering example a bit launched can be specified in the calculating detector detection visual field, scattering angle all occurs two gamma-ray photon is the probability that 0 Compton scattering is finally detected device unit and detects.Principle is as follows:

With reference to figure 7 and Fig. 8, for non-scatter photon example, when scattering angle is to (ω ₁, ω ₂) meet ω ₁=0 and ω ₂when=0, formula 2 or formula 8-1,8-2 can be reduced to formula 10, and formula 7 or formula 9-1,9-2 can be reduced to and formula 10 equivalence (in other words, non-scatter photon example is the special case of scattered photon example).

$\mathrm{d\Φ}\left((D_1,D_2)\right|S)=\frac{f\left(S\right)d{S}_S}{2\mathrm{\π}}\mathrm{\δ}(\∠D_{1}S{D}_2-\mathrm{\π})\mathrm{\φ}(S\→D_1)\frac{1}{{\mathrm{\σ}}^{\′}}\mathrm{\φ}(S\→D_2)\frac{1}{{\mathrm{\σ}}^{\′}},$ Formula 10

Wherein, φ (S → D ₁) represent that the gamma-ray photon that sends of some S is at a D _iflux, describe with formula 11; ∠ D ₁sD ₂represent the angle D being summit with a S ₁sD ₂.

$\mathrm{\φ}(S\→D_i)=2\arctan \left(\frac{{\mathrm{\σ}}^{\′}}{2\left|S{D}_i\right|}\right),$ Formula 11

Wherein, SD _irepresent that some S is to detector cells D _idistance.

Set point S, detector cells are to (D ₁, D ₂) and scattering angle to (ω ₁, ω ₂), for non-scatter photon example, the gamma-ray photon back-to-back that formula 10 is launched for set point S is not directly detected device unit to (D with detected object generation Compton scattering ₁, D ₂) probability that detects, in other words the generation of the gamma-ray photon back-to-back scattering angle launched for set point S of formula 10 is to (ω ₁=0, ω ₂=0) Compton scattering is detected device unit to (D ₁, D ₂) probability that detects.Computing formula 10, creates the point spread function of non-scatter example thus.

8-2 is example with the formula, and formula 10 is obtained by formula 8-2 by following process simplification: the gamma-ray photon back-to-back that some S launches directly is not detected device unit to (D with detected object generation Compton scattering ₁, D ₂) probability that detects, and can not with detected object generation Compton scattering, there is a Compton scattering and be detected device cells D in the described gamma-ray photon centering of namely being launched by a S in formula 8-2 and detected object ₁the gamma-ray photon of detection will directly arrive probe unit D in formula 10 ₁, some S, some M ₁with a D ₁conllinear, ∠ M ₁sM ₂be reduced to ∠ D ₁sM ₂.Therefore, gamma-ray photon described in formula 8-2 is at a M ₁cells D is detected after there is Compton scattering ₁the probability of detection $\mathrm{\φ}(S\→M_1)\frac{1}{\mathrm{\σ}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_1\right)n_e\left(M_1\right)d{S}_{M_1}\mathrm{\φ}(M_1\→D_1)\frac{1}{{\mathrm{\σ}}^{\′}}$ Be reduced to the probability that the described gamma-ray photon launched by a S in formula 10 directly arrives probe unit D1 particularly, at a M ₁there is not Compton scattering in place, represents the probability of described physical process in formula 8-2 there is not physical significance, be therefore simplified at formula 10; The described gamma-ray photon launched by a S is linearly propagated and is arrived probe unit D ₁, in formula 8-2, represent that the described gamma-ray photon that some S launches passes through a some M ₁arrive detector cells D again ₁probability be reduced to the described gamma-ray photon launched by a S in formula 10 and linearly propagate arrival probe unit D ₁probability wherein, the described gamma-ray photon launched by a S in formula 8-2 is by some M ₁arrive detector cells D again ₁probability the described gamma-ray photon launched by a S is at a M ₁per unit throughputs with described gamma-ray photon by a M ₁arrive detector cells D again ₁per unit throughputs product representation.Formula 8-1 can refer to said process to the simplification of formula 10 and obtains.

In addition, formula 10 also by first formula 2 being reduced to formula 8-1 or 8-2, then is obtained by formula 8-1 or 8-2 simplification.

9-2 is example with the formula, and formula 10 is obtained by formula 9-2 by following process simplification: work as ω ₁when=0, δ (∠ SM in formula 9-2 ₁d ₁-(π-ω ₁)) be reduced to δ (∠ SM ₁d ₁-π), represent that gamma-ray photon will be detected device direct detection, therefore formula 9-2 mid point S, some M ₁with a D ₁conllinear, ∠ SM ₁d ₁for the straight angle, δ (∠ SM ₁d ₁-π)=1.D Φ ((D in formula 9-2 ₁, D ₂), (ω ₁=0, ω ₂≠ 0) | S, M ₂) be reduced to d Φ ((D in formula 10 ₁, D ₂) | S), the process that simplifies is with reference to the simplification process of formula 8-2 to formula 10.Formula 9-1 can refer to said process to the simplification of formula 10 and obtains.

In addition, formula 10 also by first formula 7 being reduced to formula 9-1 or 9-2, then is obtained by formula 9-1 or 9-2 simplification.

Step S4: utilize statistics iterative reconstruction algorithm, according to scattered photon example point spread function and non-scatter photon example point spread function, by scattered photon example and non-scatter photon event reconstruction PET image.

In this step, statistics iterative reconstruction algorithm can be utilized by computer function module, according to scattered photon example point spread function and non-scatter photon example point spread function, by scattered photon example and non-scatter photon event reconstruction PET image, as follows:

Statistics iterative reconstruction algorithm is a kind of conventional images reconstruction algorithm based on data for projection statistical law, and statistics iterative reconstruction algorithm realizes flexibly, multiple physical factor being comprised to come in by gamma-ray photon example point spread function.In PET image reconstruction, its gordian technique obtains gamma-ray photon back-to-back that in the detection visual field, specified point is launched to the probability detected by a pair detector cells, namely obtains gamma-ray photon example point spread function.

According to scattered photon example point spread function and non-scatter photon example point spread function, citing and non-limiting, the embodiment of the present invention adopts maximum likelihood to expect, and maximum (MaximumLikelihoodExpectationMaximization, MLEM) adds up iterative reconstruction algorithm by scattered photon example and non-scatter photon event reconstruction PET image.

Formula 12 is rebuild PET image for adopting existing MLEM to add up iterative approximation.

$f^{\left(k\right)}\left(s_i\right)=\frac{f^{(k-1)}\left(s_i\right)}{\underset{(j_1,j_2)}{\mathrm{\Σ}}\hat{p}(s_i,(D_{j_1},D_{j_2}))}\underset{(j_1,j_2)}{\mathrm{\Σ}}\hat{p}(s_i,(D_{j_1},D_{j_2}))\frac{P(D_{j_1},D_{j_2})}{\underset{i}{\mathrm{\Σ}}\hat{p}(s_i,(D_{j_1},D_{j_2}))f^{(k-1)}\left(s_i\right)},$ Formula 12

Formula 13 is adopt the MLEM of scattered photon example and non-scatter photon example to add up iterative approximation to rebuild PET image.

$f^{\left(k\right)}\left(s_i\right)=\frac{f^{(k-1)}\left(s_i\right)}{\underset{(k_1,k_2)}{\mathrm{\Σ}}\underset{(j_1,j_2)}{\mathrm{\Σ}}\hat{p}(s_i,(D_{j_1},D_{j_2}),({\mathrm{\ω}}_{k_1},{\mathrm{\ω}}_{k_2}))}\underset{(k_1,k_2)}{\mathrm{\Σ}}\underset{(j_1,j_2)}{\mathrm{\Σ}}\hat{p}(s_i,(D_{j_1},D_{j_2}),({\mathrm{\ω}}_{k_1},{\mathrm{\ω}}_{k_2}))\frac{P((D_{j_1},D_{j_2}),({\mathrm{\ω}}_{k_1},{\mathrm{\ω}}_{k_2}))}{\underset{i}{\mathrm{\Σ}}\hat{p}(s_i,(D_{j_1},D_{j_2}),({\mathrm{\ω}}_{k_1},{\mathrm{\ω}}_{k_2}))f^{(k-1)}\left(s_i\right)},$ Formula 13

Wherein, f (s _i) represent pixel s _iradioactivity density, k represents statistics iterative reconstruction algorithm iterations; represent gamma-ray photon example point spread function, represent some s _ithe gamma-ray photon back-to-back launched arrives pet detector to the interaction not making with detected object gamma-ray photon energy or the direction of propagation change (such as Compton scattering, but be not limited thereto) etc. in the mode of rectilinear propagation and is detected device unit pair the probability of detection; In formula 12 be specially in formula 13 represent some s _ithe gamma-ray photon back-to-back launched is to generation scattering angle pair compton scattering be detected device unit pair the probability of detection; represent the interaction (such as Compton scattering, but be not limited thereto) not making with detected object gamma-ray photon energy or the direction of propagation change etc. and arrive pet detector in the mode of rectilinear propagation and be detected device unit pair the gamma-ray photon quantity detected, is obtained by the electronics module of detector and is transferred to computer module; In formula 12 be specially in formula 13 represent and scattering angle pair occurs compton scattering be detected device unit pair the gamma-ray photon quantity detected, is obtained by the electronics module of detector and is transferred to computer module.

Particularly, when by a s _iduring the generation of the gamma-ray photon back-to-back scattered photon example launched, for scattered photon example point spread function, formula 13 is adopt the MLEM of scattered photon example to add up iterative approximation to rebuild PET image.When by a s _iduring the generation of the gamma-ray photon back-to-back non-scatter photon example launched, for non-scatter photon example point spread function; Now, formula 13 is of equal value with formula 12, adds up iterative approximation rebuild PET image for adopting the MLEM of non-scatter photon example.

In addition, Fig. 6 shows the structure for the computing module by scattering and non-scatter photon transportation positron emission computerized tomography image of the present invention, and these computing modules can run in a computer equipment, and it comprises:

The scattered photon example projection model creation module 21 that designated model parameter describes, for the scattered photon example projection theory according to Compton scattering, creates the scattered photon example projection probability model described by designated model parameter, for performing above-mentioned steps S1.

Scattered photon example point spread function creation module 22, for according to scattered photon example projection probability model, creates scattered photon example point spread function, for performing above-mentioned steps S2.

Non-scatter photon example point spread function creation module 23, for according to scattered photon example projection model and scattered photon example point spread function, creates non-scatter photon example point spread function, for performing above-mentioned steps S3.

By scattered photon example and non-scatter photon event reconstruction PET image module 24, for utilizing statistics iterative reconstruction algorithm, according to scattered photon example point spread function and non-scatter photon example point spread function, by scattered photon example and non-scatter photon event reconstruction PET image, for performing above-mentioned steps S4.

To sum up, the present invention is by the scattered photon example projection theory of Compton scattering, create the scattered photon example projection probability model described by designated model parameter, and by scattered photon example projection probability model, create scattered photon example point spread function, again by scattered photon example projection model and scattered photon example point spread function, create non-scatter photon example point spread function, thus by scattered photon example and non-scatter photon event reconstruction PET image, improve the detection efficiency of PET, so that in clinical practice, significantly reduce detected object and the radiation dose suffered by operator, under same medicine dosage, shorten patient's supervision time, improve the service efficiency of PET.Be conducive to solving the incomplete problem of slab construction PET data sampling simultaneously, simplify PET structure, reduce PET manufacture and maintenance cost.

Method of the present invention goes for annular detector, static two flat panel detector or dynamic two flat panel detector, is certainly not limited thereto, as long as can detect the detector obtaining above-mentioned scattering example.

Finally, with reference to the two dull and stereotyped PET system of the static state shown in Fig. 9, the actual mechanical process of the method for rebuilding positron emission computerized tomography image of the present invention is described: in the detection visual field (FieldofView, FOV) of the detector 31 of the two dull and stereotyped PET system of a static state, place an organic glass thin plate imitate body (phantom) 34.Imitative body 34 is positioned at detector 31 center, and length and width are identical with FOV length and width, and it is identical that thickness and detector 31 detect minimum unit height.There is a F at Fang Ti 34 center ¹⁸spherical radioactive source 35, the diameter of radioactive source 35 is identical with imitative body 34 thickness, utilizes the two increased radioactivity of dull and stereotyped PET system to imitative body 34 of this static state to carry out imaging.

The detector 31 of static two dull and stereotyped PET system is made up of two flat panel detectors.The wide high end face side of each flat panel detector receives the gamma-ray photon example arrived, opposite side connects an electronics module 32 to obtain the information such as energy, position of gamma example, information will be transferred to computing module 33, for by scattering and non-scatter photon transportation PET image, these computing modules run in a computer equipment.

The minimum component units of detector is tellurium zinc cadmium (cadmiumzinctelluride, CdZnTe are abbreviated as CZT) crystal bar, and crystal bar is of a size of 10mm length × 1mm, and wide × 1mm is high.Two flat panel detectors are relatively parallel for the wide high end face detecting gamma-ray photon example, and distance be 64mm, therefore the desired detection bulk of static pair of dull and stereotyped PET system be 64mm length × 44mm wide × 13mm is high.The detection visual field of static two dull and stereotyped PET system is determined by the design of desired detection space and electronic device, here design detection visual field sizes be 64mm length × 32mm wide × 1mm is high, be positioned at desired detection space center, detect that gamma-ray photon example be energy to ensure as far as possible, positional information is by the gamma-ray photon example obtained nondestructively, exactly.Image space with detection visual field sizes identical, be made up of 64 × 32 voxels, voxel size be 1mm length × 1mm wide × 1mm is high.

Body 34 imitated by thin plate and spherical radioactive source 35 is positioned at the center detecting the visual field, and detection visual field height is only 1mm, and the three dimensions of the detection visual field and image space is approximately two dimensional surface, sets up scattered photon example projection probability model mathematical description.Now, image space is made up of 64 × 32 pixels, and Pixel Dimensions is that 1mm length × 1mm is wide.

Described fundamental physical quantity is obtained by American National Standard and Technical Board (NIST) database; The known scattering medium of priori is organic glass, and electron density is obtained by NIST database; Thus, form relevant physical quantity establishment designated model parameter by the material of described fundamental physical quantity and described detected object.Given described PET system and detected material parameter, determine the geometric sense in Fig. 7 and Fig. 8, according to formula 1 to formula 9-2, create the scattered photon example that in the vision detector that described by designated model parameter, each image slices vegetarian refreshments is launched and project to each detector cells to projection probability model.

Wherein, carry out discretize to the contingent scattering angle of scattered photon example, scattering angle scope is 1 ° ~ 55 °, angle intervals 1 °, and the scattering angle of two-photon single scattering is to being likely combining of two described discrete scattering angle.

Utilize the integration concrete form of formula 7 and formula 9-1,9-2 on two dimensional surface, calculate by detector effective field of view each image slices vegetarian refreshments launch gamma-ray photon back-to-back occur each scattering angle to, finally by each detector to detection probability, create two-photon single scattering example point spread function and single photon single scattering example point spread function respectively, thus create scattered photon example point spread function.

Similarly, according to described scattered photon example projection model and described scattered photon example point spread function, two dimensional surface calculates gamma-ray photon back-to-back respectively that launched by each image slices vegetarian refreshments in detector effective field of view and Compton scattering does not occur directly by the probability of each detector cells to detection, create non-scatter photon example point spread function.

According to described scattered photon example point spread function and non-scatter photon example point spread function, the MLEM described in formula 13 is adopted to add up iterative reconstruction algorithm by scattered photon example and non-scatter photon event reconstruction PET image.Occur each scattering angle to, finally by each detector to detection gamma-ray photon quantity, be transferred to computing module 33 by the electronics module 32 of detector.

As known by the technical knowledge, the present invention can be realized by other the embodiment not departing from its Spirit Essence or essential feature.Therefore, above-mentioned disclosed embodiment, with regard to each side, all just illustrates, is not only.Within the scope of the present invention all or be all included in the invention being equal to the change in scope of the present invention.

Claims (6)

1. for rebuilding a method for positron emission computerized tomography image, it is characterized in that, comprising the following steps:

Step one (S1): according to the scattered photon example projection principle of work of Compton scattering, creates the scattered photon example projection probability model described by designated model parameter;

Wherein:

Described scattered photon example comprises two-photon single scattering example and single photon single scattering example;

Described two-photon single scattering example is that two gamma-ray photons of gamma-ray photon centering are back-to-back detected the scattered photon example that device detects respectively with after a detected object interaction generation Compton scattering;

Described single photon single scattering example is that gamma-ray photon centering has and is detected the scattered photon example that device detects after only having a gamma-ray photon and a detected object interaction generation Compton scattering back-to-back, in described single photon single scattering example, there is not interactional gamma-ray photon and will be detected device direct detection in gamma-ray photon centering back-to-back with detected object;

Positron is contrary with the both direction that the electronics generation annihilation reaction in detected object body generates, energy is the gamma-ray photon of 511keV to going out for the positron radionuclide generation decay emission be injected in the detected object body internal labeling tracer agent of positron radionuclide for described gamma-ray photon back-to-back;

Described designated model parameter forms the physical quantity establishment of being correlated with by the material of fundamental physical quantity and detected object, and the material of detected object forms the physical quantity that can refer to the establishment of existing fundamental physical quantity obtain manner after the relevant physical quantity material comprised by creating detected object forms;

Step 2 (S2): according to described scattered photon example projection probability model, create scattered photon example point spread function;

Wherein:

Described scattered photon example point spread function comprises two-photon single scattering example point spread function and single photon single scattering example point spread function;

Described two-photon single scattering example point spread function is the probability of specifying described gamma-ray photon back-to-back of some transmitting pair and detected object generation two-photon single scattering to be finally detected device in the detector detection visual field to detect;

Described single photon single scattering example point spread function is the probability of specifying gamma-ray photon back-to-back of some transmitting pair and detected object generation single photon single scattering to be finally detected device in the detector detection visual field to detect;

Step 3 (S3): according to scattered photon example projection probability model and scattered photon example point spread function, creates non-scatter photon example point spread function;

Wherein:

Described non-scatter photon example for described in two gamma-ray photons of gamma-ray photon centering back-to-back interaction of not making gamma-ray photon energy or the direction of propagation change with detected object after producing and arrive detector in the mode of rectilinear propagation and be finally detected the photon example that device detects;

Described non-scatter photon example point spread function is the interaction of specifying two gamma-ray photons of the centering of gamma-ray photon back-to-back of a bit launching not make with detected object gamma-ray photon energy or the direction of propagation change after generation in the detector detection visual field and arrives detector in the mode of rectilinear propagation and be finally detected the probability that device detects;

Step 4 (S4): utilize statistics iterative reconstruction algorithm, according to scattered photon example point spread function and non-scatter photon example point spread function, by scattered photon example and non-scatter photon event reconstruction positron emission computerized tomography image;

Wherein:

In step one, scattered photon example projection probability model is Klein Gordon equation-benevolence section flux differential;

Klein Gordon equation-benevolence section flux differential comprises two-photon single scattering Klein Gordon equation-benevolence section flux differential and single photon single scattering Klein Gordon equation-benevolence section flux differential, and single photon single scattering Klein Gordon equation-benevolence section flux differential is the special case of two-photon single scattering Klein Gordon equation-benevolence section flux differential;

Two-photon single scattering Klein Gordon equation-benevolence section flux differential and single photon single scattering Klein Gordon equation-benevolence section flux differential are two dimensional surface differential;

The procurement process of the two dimensional surface differential of two-photon single scattering Klein Gordon equation-benevolence section flux is:

Following formula 1 is utilized to describe zero energy for E ₀photon and detected object generation Compton scattering after, its dump energy E _ωwith the relation of scattering angle ω;

$E_{\mathrm{\ω}}=\frac{E_0}{1+\frac{E_0}{{\mathrm{mc}}^2}(1-cos\mathrm{\ω})},$ Formula 1

Wherein, m is electron rest mass, and c is the light velocity;

Utilize following formula 2 to describe the Compton scattering projection process of two-photon single scattering example, the gamma-ray photon back-to-back namely launched by the some S in the model space is to respectively at a M ₁, some M ₂interact with detected object and Compton scattering occurs, scattering angle is respectively ω ₁, ω ₂, two gamma-ray photons are scattered rear moment track and change last respectively by pet detector cells D ₁, D ₂the probability detected;

$\begin{array}{c}d\mathrm{\Φ}\left(\right(D_1,D_2),({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)|S,(M_1,M_2\left)\right)=\frac{f\left(S\right){\mathrm{dS}}_S}{2\mathrm{\π}}\mathrm{\δ}(\∠M_1{\mathrm{SM}}_2-\mathrm{\π})\mathrm{\φ}(S\→M_1)\frac{1}{\mathrm{\σ}}\mathrm{\φ}(S\→M_2)\frac{1}{\mathrm{\σ}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_1\right)n_e\left(M_1\right){\mathrm{dS}}_{M_1}\\ \mathrm{\φ}(M_1\→D_1)\frac{1}{{\mathrm{\σ}}^{\′}}{\mathrm{\σ}}_C\left({\mathrm{\ω}}_2\right)n_e\left(M_2\right){\mathrm{dS}}_{M_2}\mathrm{\φ}(M_2\→D_2)\frac{1}{{\mathrm{\σ}}^{\′}}\end{array},$ Formula 2

Wherein, S=(x _s, y _s) represent that radioactivity density is certain point of f (S);

represent certain point in scattering medium;

represent certain detector cells, its detected to interact with detected object there is Compton scattering after energy be gamma-ray photon;

∠ M ₁sM ₂represent the angle M being summit with a S ₁sM ₂;

δ represents discrete system Unit sample response function, as ∠ M ₁sM ₂when equaling π, its value is 1, namely puts M ₁, some S and some M ₂conllinear, ∠ M ₁sM ₂for the straight angle, as ∠ M ₁sM ₂when equaling other angle values, its value is 0;

DS _srepresent the face infinitesimal of some S;

represent some M _iface infinitesimal;

σ represents the line infinitesimal of scattering medium;

σ ' represents the line infinitesimal of detector;

N _e(M _i) be a M _ielectron density, by a M _idetected object material composition create;

φ (S → M _i) represent that the gamma-ray photon that sends of some S is at a M _iflux, described by following formula 3;

φ (M _i→ D _j) represent at a M _iwith detected object interact there is Compton scattering gamma-ray photon at detector cells D _jflux, described by following formula 4;

σ _c(ω) represent differential cross-section when gamma-ray photon generation scattering angle is the Compton scattering of ω, described by formula 5;

$\mathrm{\φ}(S\→M_i)=2arctan\left(\frac{\mathrm{\σ}}{2\left|{\mathrm{SM}}_i\right|}\right),$ Formula 3

Wherein, SM _irepresent that some S is to some M _idistance;

$\mathrm{\φ}(M_i\→D_j)=2arctan\left(\frac{{\mathrm{\σ}}^{\′}}{2\left|M_i{D}_j\right|}\right),$ Formula 4

Wherein, M _id _jrepresent some M _ito detector cells D _jdistance;

${\mathrm{\σ}}_C\left(\mathrm{\ω}\right)=\frac{1}{2}{\mathrm{\πr}}_e^{2}P\left(\mathrm{\ω}\right),$ Formula 5

Wherein, r _ebe classical electron radius, P (ω) is Klein Gordon equation-benevolence section scattering probability density, is described by following formula 6;

$P\left(\mathrm{\ω}\right)=\frac{1+{\cos }^2\mathrm{\ω}}{{(2-cos\mathrm{\ω})}^2}\[1+\frac{{(1-cos\mathrm{\ω})}^2}{(2-\cos \mathrm{\ω})(1+{\cos }^2\mathrm{\ω})}\],$ Formula 6

Utilize following formula 7 to describe interacting with detected object of set point S transmitting and scattering angle occurs to (ω ₁, ω ₂) Compton scattering and be detected device unit to (D ₁, D ₂) the right flux differential of the gamma-ray photon back-to-back that detects, thus obtain gamma-ray photon back-to-back that the set point S in the model space launches pair and detected object and interact and scattering angle occurs to (ω ₁, ω ₂) Compton scattering be finally detected unit to (D ₁, D ₂) probability that detects;

D Φ ((D ₁, D ₂), (ω ₁, ω ₂) | S)=∫ ∫ d Φ ((D ₁, D ₂), (ω ₁, ω ₂) | S, (M ₁, M ₂)) δ (∠ SM ₁d ₁-(π-ω ₁)) δ (∠ SM ₂d ₂-(π-ω ₂)), formula 7

Wherein, ∠ SM _id _iwith a M _ifor the angle SM on summit _id _i.

2. the method for rebuilding positron emission computerized tomography image according to claim 1, is characterized in that, the integration of formula 7 is trajectory quadratures.

3. the method for rebuilding positron emission computerized tomography image according to claim 1, is characterized in that, in step 3, non-scatter photon example is the special case of scattered photon example.

4. the method for rebuilding positron emission computerized tomography image according to claim 1, is characterized in that, in described step 4, described statistics iterative reconstruction algorithm is that maximum likelihood expects maximum statistics iterative reconstruction algorithm.

5. the method for rebuilding positron emission computerized tomography image according to claim 1, is characterized in that, described detector is annular detector, static two flat panel detector or dynamic two flat panel detector.

6. the method for rebuilding positron emission computerized tomography image according to any one of claim 1-5, it is characterized in that, detector receives the gamma-ray photon example arrived, and obtain gamma example by the electronics module be connected with detector comprise energy, position, scattering angle, quantity is in interior information, these information by electronics module transfer in a computing module, computing module is according to described scattered photon example point spread function and non-scatter photon example point spread function, carry out statistics iterative reconstruction algorithm, rebuild positron emission computerized tomography image.