CN105279777A - Static PET image reconstruction method based on improved sequential filtering - Google Patents

Abstract

A static PET image reconstruction method based on improved sequential filtering comprises the following steps: 1) a state spatial model of a PET system is built; 2) a concentration reconstruction process based on improved sequential filtering is as follows: 2.1) an initial value and an initial estimate covariance of radioactive concentration distribution are set firstly, so that xhat<0>(0) = xhat(0) and P<0>(0) = P(0); 2.2) sonogram data y(t) are obtained; 2.3) the sonogram data y(t) are divided into r blocks; 2.4) an equation (3) is used to calculate a gain matrix K<i>(t); 2.5) a measurement value y<i>(t) and the gain matrix K<i>(t) are used to calculate a spatial concentration estimate xhat<i>(t) according to a status updating equation (2); 2.6) if i < r, then i = i + 1, and the method jumps to the step 2.4), otherwise, xhat(t) = xhat<r>(t) and P(t) = P<r>(t); and 2.7) if t < N, then t = t + 1, and the method jumps to the step 2.2), otherwise, the algorithm ends and final reconstruction results are obtained. The method ensures the reconstruction effects, reduces the calculation cost, and improves the reconstruction speed.

Description

Based on the static PET image reconstruction method improving Sequential filter

Technical field

The present invention relates to positron emission tomography field, being specifically related to a kind of static PET image reconstruction method based on improving Sequential filter.

Background technology

Positron emission tomography (PositronEmissionTomography, PET) technology is a kind of by following the trail of metabolic alterations on a molecular scale, monitoring, thus reaches early detection to disease, prevents the medical imaging technology of object.PET technology, as functional imaging technology, can reflect the situation of patient body's intracellular metabolic, thus earlier can detect focus.Therefore, PET technology is widely used in diagnosis and bioorganism imaging, drug screening and the exploitation of tumour, heart disease, nerve and psychosis, has demonstrated huge application prospect.

First accelerator is used to produce positron nuclide when carrying out PET scanning, then will by the isotopically labeled infusion of medicine human body of radioactivity coordination, by blood circulation, these materials will form certain distribution in each histoorgan in human body.Because the half life period of radioactivity coordination nucleic is shorter, and extremely unstable, will decay very soon.In decay process, radioactivity coordination nucleic can produce positron and with neighbouring free electron generation annihilation reaction, produce the gamma photons that a pair direction is contrary, energy is equal.At this moment, technology can be met by the utilization of external detector and photon is detected, then correct via noise, obtain data for projection.Utilize data for projection to carry out inverting by some reconstructing methods to solve, the spatial concentration distribution of the radiomaterial of human body can be reconstructed.

At present, PET image reconstruction method is broadly divided into two classes: analytical method and Iterative statistical method.Last class mainly filtered back-projection, computing velocity is fast, and cost is little, but can not restraint speckle very well, so that reconstructed image quality is not high.Therefore, there is the Iterative statistical method taking maximum-likelihood method as representative.Due to process of iteration Corpus--based Method model, good to fragmentary data adaptability, become the focus of PET reconstruction algorithm research gradually.Compared to analytical method, the reconstruction image that process of iteration obtains is more clear.But be the key affecting process of iteration reconstructed results on the accurate modeling of PET system imaging process.The introducing of state space, has effectively promoted the development of process of iteration.State-space method can by the process modelling of PET imaging (providing the mathematical expression of PET imaging process), carry out corresponding portraying to the physiology of the statistical property of PET scanning process and biosome, architectural characteristic, thus some existing algorithm for estimating combined by this model often can provide and better rebuild effect.Current existing state space method for solving is mainly based on H ₂filtering (i.e. Kalman filtering), H _∞filtering etc.But due to the number needing the sharpness of rebuilding image often to depend on voxel, and the latter is directly connected to the calculated amount of filtering restructing algorithm.Therefore, in most cases, the PET image reconstructing method based on filtering algorithm all faces very high-dimensional matrix inversion operation, and this brings great computational burden can to the PET image reconstruct based on general filtering algorithm.

Summary of the invention

In order to overcome the deficiency that computing cost is comparatively large, reconstructed velocity is slower of existing PET image reconstruction method, the invention provides a kind of static PET image reconstruction method based on improving Sequential filter, this invention proposes observable higher-dimension sinusoidal data to be divided into multiple low-dimensional observation data.When system carries out filtering based on the observation of these low-dimensionals, originally require that inverse higher dimensional matrix be instead of by the low-dimensional matrix that some and low-dimensional observe dimension consistent, this can greatly assess the cost in reduction, improves reconstructed velocity, provides the reconstruction effect the same with the PET method for reconstructing based on Kalman filtering.

Following technical scheme is provided in order to solve the problems of the technologies described above:

Based on the static PET image reconstruction method improving Sequential filter, comprise the steps:

1) state-space model of PET system is set up:

$\left\{\begin{array}{c}x\left(t+1\right)=x\left(t\right)+v\left(t\right)\\ y\left(t\right)=Dx\left(t\right)+e\left(t\right)\end{array}\right.---\left(1\right)$

Wherein, t represents the time; Y (t) is observed reading, is just through the sinogram data obtained after noise is corrected; D represent human body inside radiation concentration and PET scan between the projection matrix of projection relation, determined by the inherent characteristic of PET device; X (t) is radioactive concentration distribution, namely needs the object rebuild; V (t) is process noise; The measurement noise that e (t) is residual for data acquisition and after meeting rectification;

2) the reconstruction image based on improving Sequential filter is obtained according to following equations:

${\hat{x}}_i\left(t\right)={\hat{x}}_{i-1}\left(t\right)+K_i\left(t\right)\left(y_i\right(t)-D{\hat{x}}_{i-1}(t\left)\right),{\hat{x}}_0\left(t\right)=\hat{x}\left(0\right)---\left(2\right)$

$K_i\left(t\right)=P_i\left(t\right)D_i^T{(D_i{P}_i\left(t\right)D_i^T+R_i)}^{-1}---\left(3\right)$

$P_i\left(t\right)=P_{i-1}\left(t\right)+Q_i-K_i\left(t\right)\left(D_i{P}_i\left(t\right)D_i^T+R_i\right)K_i^T\left(t\right),P_0\left(t\right)=P\left(t\right)---\left(4\right)$

$\hat{x}\left(t\right)={\hat{x}}_r\left(t\right)---\left(5\right)$

P(t)＝P _r(t)(6)

Wherein, for the filtering reconstructed value of spatial concentration, for the filtering initial value of spatial concentration, y (t) is the sinogram data after detectable correction, the predictor error covariance matrix that P (t) is spatial concentration, and P (0) is initial space concentration predictor error covariance, y (t) is divided into r block, y _it () is i-th piecemeal of y (t), D _i, R _i, Q _icorresponding to y _ithe matrix D of (t), the piecemeal of R, Q, K _it () is corresponding to y _ithe filter gain matrix of (t), for based on y (0) ..., y (t-1), y ₁(t) ..., y _i(t) } spatial concentration filtering reconstructed value, P _i(t) be corresponding to y (0) ..., y (t-1), y ₁(t) ..., y _i(t) } filtering error covariance matrix.Iteration is from initial value p (0) sets out, throughput measured value y (t), through N iteration, finally obtains radioactive concentration distribution process of reconstruction is as follows:

2.1) initial value and the initial estimation covariance of radioactive concentration distribution is first set p ₀(0)=P (0);

2.2) sinogram data y (t) is obtained;

2.3) sinogram data y (t) is divided into r block;

2.4) equation (3) calculated gains matrix K is utilized _i(t);

2.5) utilization measured value y _i(t) and gain K _it (), calculates spatial concentration estimated value according to state updating equation (2) and release corresponding predictor error covariance matrix P according to (4) _i(t);

2.6) if i < is r, i=i+1, jumps to step 2.4), otherwise, p (t)=P _r(t);

2.7) if t < is N, t=t+1, jumps to step 2.2), otherwise algorithm terminates.

Technical conceive of the present invention is: based on analysis PET system being used to kalman filter method image-forming principle, find this reconstructing method reconstructed velocity slowly problem be higher-dimension observation cause higher dimensional matrix to be inverted, by higher-dimension observation being blocked into the observation of relative low-dimensional, final demand solution low-dimensional inverse of a matrix, thus efficiently solve the problems referred to above.

As can be seen from technique scheme, beneficial effect of the present invention is mainly manifested in: under ensure that (reconstructing with the direct PET image based on Kalman filtering) has the prerequisite of identical quality reconstruction, effectively prevent higher dimensional matrix to invert, and then improve reconstructed velocity.

Accompanying drawing explanation

Fig. 1 is the steps flow chart schematic diagram of PET image reconstruction method of the present invention.

Embodiment

In order to more specifically describe the present invention, below in conjunction with the drawings and the specific embodiments, static PET concentration method for reconstructing of the present invention is described in detail.

As shown in Figure 1, a kind of static PET image reconstruction method based on improving Sequential filter, comprises the steps:

1) according to PET image-forming principle, state space system is set up:

$\left\{\begin{array}{c}x\left(t+1\right)=x\left(t\right)+v\left(t\right)\\ y\left(t\right)=Dx\left(t\right)+e\left(t\right)\end{array}\right.---\left(7\right)$

Wherein, t represents the time; Y (t) is observed reading, is just through the sinogram data obtained after noise is corrected; D represent human body inside radiation concentration and PET scan between the projection matrix of projection relation, determined by the inherent characteristic of PET device, adopt the approximate treatment of single line of response model to obtain in an experiment; X (t) is radioactive concentration distribution, namely needs the object rebuild; V (t) is process noise; E (t) is for data acquisition and measurement noise residual after noise is corrected; V (t), e (t) obey covariance matrix and are respectively diagonal matrix Q, the normal Gaussian distribution of R;

2) the reconstruction image based on improving Sequential filter is obtained according to following equations:

${\hat{x}}_i\left(t\right)={\hat{x}}_{i-1}\left(t\right)+K_i\left(t\right)\left(y_i\right(t)-D{\hat{x}}_{i-1}\left(t\right)),{\hat{x}}_0\left(t\right)=\hat{x}\left(0\right)---\left(8\right)$

$K_i\left(t\right)=P_i\left(t\right)D_i^T{(D_i{P}_i\left(t\right)D_i^T+R_i)}^{-1}---\left(9\right)$

$P_i\left(t\right)=P_{i-1}\left(t\right)+Q_i-K_i\left(t\right)\left(D_i{P}_i\left(t\right)D_i^T+R_i\right)K_i^T\left(t\right),P_0\left(t\right)=P\left(t\right)---\left(10\right)$

P(t)＝P _r(t)(12)

Wherein, for the filtering reconstructed value of spatial concentration, for the filtering initial value of spatial concentration, y (t) is the sinogram data after detectable correction, the predictor error covariance matrix that P (t) is spatial concentration, P (0) is initial space concentration predictor error covariance, subscript i=1 ..., r, y (t) is divided into r block, y _it () is i-th piecemeal of y (t), D _i, R _i, Q _ibe and y _it matrix D that () is compatible, the piecemeal of R, Q, K _it () is corresponding to y _ithe filter gain matrix of (t), for based on until observation y _ithe spatial concentration filtering reconstructed value of (t), P _it () is corresponding to observation until observation y _ithe filtering error covariance matrix of (t).Iteration is from initial value p (0) sets out, throughput measured value y (t), through successive ignition, finally obtains radioactive concentration distribution as shown in Figure 1, as follows based on the image reconstruction iterative process improving Sequential filter:

2.1) initial value and the initial variance of radioactive concentration distribution is first set p ₀(0), these two values are provided by empirical value, but when not having priori, can be by p ₀(0) null matrix and unit matrix is taken as respectively;

2.2) sinogram data y (t) is obtained;

2.3) sinogram data y (t) is divided into r block;

2.4) equation (9) calculated gains matrix K is utilized _i(t);

2.5) utilization measured value y _i(t) and gain K _it (), calculates spatial concentration estimated value according to state updating equation (8) and release corresponding predictor error covariance matrix P according to (10) _i(t);

2.6) if i < is r, i=i+1, jumps to step 2.4), otherwise, p (t)=P _r(t);

2.7) if t < is N, t=t+1, jumps to step 2.2), otherwise algorithm terminates, and obtains final concentration reconstruction result.

Claims (1)

1., based on the static PET image reconstruction method improving Sequential filter, it is characterized in that: described image rebuilding method comprises the steps:

1) state-space model of PET system is set up:

$\left\{\begin{array}{c}x(t+1)=x\left(t\right)+v\left(t\right)\\ y\left(t\right)=Dx\left(t\right)+e\left(t\right)\end{array}\right.---\left(1\right)$

Wherein, t represents the time; Y (t) is observed reading, is just through the sinogram data obtained after noise is corrected; D represent human body inside radiation concentration and PET scan between the projection matrix of projection relation, determined by the inherent characteristic of PET device; X (t) is radioactive concentration distribution, namely needs the object rebuild; V (t) is process noise; The measurement noise that e (t) is residual for data acquisition and after meeting rectification;

2) the reconstruction image based on improving Sequential filter is obtained according to following equations:

${\hat{x}}_i\left(t\right)={\hat{x}}_{i-1}\left(t\right)+K_i\left(t\right)\left(y_i\right(t)-D{\hat{x}}_{i-1}(t\left)\right),{\hat{x}}_0\left(t\right)=\hat{x}\left(0\right)---\left(2\right)$

$K_i\left(t\right)=P_i\left(t\right)D_i^T{\left(D_i{P}_i\right(t)D_i^T+R_i)}^{-1}---\left(3\right)$

$P_i\left(t\right)=P_{i-1}\left(t\right)+Q_i-K_i\left(t\right)\left(D_i{P}_i\right(t)D_i^T+R_i)K_i^T\left(t\right),P_0\left(t\right)=P\left(t\right)---\left(4\right)$

$\hat{x}\left(t\right)={\hat{x}}_r\left(t\right)---\left(5\right)$

P(t)＝P _r(t)(6)

Wherein, for the filtering reconstructed value of spatial concentration, for the filtering initial value of spatial concentration, y (t) is the sinogram data after detectable correction, the predictor error covariance matrix that P (t) is spatial concentration, and P (0) is initial space concentration predictor error covariance, y (t) is divided into r block, y _it () is i-th piecemeal of y (t), D _i, R _i, Q _icorresponding to y _ithe matrix D of (t), the piecemeal of R, Q, K _it () is corresponding to y _ithe filter gain matrix of (t), for based on y (0) ..., y (t-1), y ₁(t) ..., y _i(t) } spatial concentration filtering reconstructed value, P _i(t) be corresponding to y (0) ..., y (t-1), y ₁(t) ..., y _i(t) } filtering error covariance matrix.Iteration is from initial value p (0) sets out, throughput measured value y (t), through N iteration, finally obtains radioactive concentration distribution process of reconstruction is as follows:

2.1) initial value and the initial estimation covariance of radioactive concentration distribution is first set p ₀(0)=P (0);

2.2) sinogram data y (t) is obtained;

2.3) sinogram data y (t) is divided into r block;

2.4) equation (3) calculated gains matrix K is utilized _i(t);

2.5) utilization measured value y _i(t) and gain K _it (), calculates spatial concentration estimated value according to state updating equation (2) and release corresponding predictor error covariance matrix P according to (4) _i(t);

2.6) if i < is r, i=i+1, jumps to step 2.4), otherwise, p (t)=P _r(t);

2.7) if t < is N, t=t+1, jumps to step 2.2), otherwise algorithm terminates, and obtains final reconstructed results.