CN101499173A - Kalman filtering image reconstruction method in PET imaging - Google Patents

Abstract

The invention provides a method for rebuilding Kallman filtering image in PET imaging. The method includes steps as follows: obtaining a sinusoidal chart of an original projective line through PET positron emission faultage scanner, establishing a state space system, getting radioactivity activity distribution through the Kallman filtering method based on the state space and rebuilding image. The method rebuild PET image by using the Kallman filtering method based on the state space system which can increase the rebuild image quality efficiently; compared with the prior rebuild method, declination and dispersion of the rebuild result are increased greatly.

Description

Kalman filtering image reconstruction method in a kind of PET imaging

Technical field

The present invention relates to a kind of medical science fault image method for reconstructing, especially relate to a kind of Kalman filtering image reconstruction method in the PET imaging.

Background technology

(positron emission tomography is one of of paramount importance application in the nuclear medical imaging apparatus as a kind of biomedical research technology and clinical diagnosis means PET) to positron emission tomography.The basic thought of PET: to the isotope-labeled compound of biosome inner injection positron, in external space and time distribution of measuring them by image reconstruction technique.Nowadays many clinical medicine domains have begun to be extensive use of the diagnosis that the PET image carries out tumour, heart disease (before and after the detection of cardiac muscle survival, heart transplant, the interventional therapy monitoring etc.), nerve and psychosis (as the determining of epilepsy focus, Parkinson's, senile dementia and mental disease etc.), and part developed country checks the medical insurance scope of listing in to the PET of part disease.

PET surveys the radiated signal that sends in the human body, handles through meeting with acquisition system, forms projection line, and deposits in the hard disc of computer in sinogram (Sinogram figure) mode.Computing machine is input with Sinogram figure, call image reconstruction module, calculate human body cross-cutting fault image, the metabolic situation of certain histoorgan in the antimer, this class reconstruction inverse problem can be represented with equation Y (t)=DX (t)+v (t) in fact, Y is the measurement data of PET, and X is an image of wanting reconstruct, and D is a system model.Method based on the data Y estimation X that contains noise can be divided into two classes: analytical method and statistics process of iteration.For analytical method, the statistics iterative algorithm comprises maximum likelihood method based on Poisson model, maximum a posteriori probability method and based on the least square method of Gauss model, be based on statistical law, adaptability to fragmentary data is good, can access more accurate result, also therefore be subjected to researchist's extensive concern.

Process of iteration is the initial pictures from width of cloth hypothesis, adopts the method for progressively approaching, and theoretical projection value is compared with the actual measurement projection value, seeks optimum solution under certain optimization criterion instructs.In PET process of iteration commonly used comprise maximum likelihood method (Maximum LikelihoodExpectation-Maximization, MLEM) and OSEM (order subset maximum likelihood method, Ordered Subset Expectation Maximization) algorithm.One of process of iteration advantage be can according to concrete image-forming condition introduce relevant with space geometry or with the big or small relevant constraint condition of measured value, as carrying out the correction of spatial discrimination unevenness, the geometry of objects constraint, the operation of control such as flatness constraint iteration, under some occasion, such as owing relatively to sample, can bringing into play its high-resolution advantage in the nuclear medicine of low counting.The shortcoming of process of iteration maximum is that calculated amount is big, and computing velocity is slow.

The solution by iterative method process is:

A. suppose an initial pictures;

B. calculate this image projection;

C. with measuring the projection value contrast;

D. calculation correction coefficient and upgrade the initial pictures value;

E. satisfy when stopping rule, iteration termination, otherwise go on foot from b as initial pictures with new reconstructed image.

OSEM is the perfect iteratively faster reconstruction algorithm of development in recent years, only uses a sub-set pair data for projection to proofread and correct when rebuilding at every turn, and reconstructed image upgrades once, and all like this subclass are all proofreaied and correct once data for projection, are called iteration one time.Compare with traditional iterative algorithm MLEM, accelerated image reconstruction speed greatly, shortened reconstruction time.

Summary of the invention

The invention provides the Kalman filtering image reconstruction method in a kind of position emissron tomography, increase substantially the PET quality of reconstructed images based on state space theory.

Kalman filtering image reconstruction method of the present invention may further comprise the steps:

(1) sinogram of input original projection line;

Y(t)=DX(t)+v(t)

(2) set up the state space system

X(t+1)=AX(t)+w(t)，

Wherein, t express time; Y is exactly the sinogram data; D is a system matrix, and the photon of expression emission is detected the probability that device receives; A is a state-transition matrix, is a unit matrix under instantaneous steady state (SS); X is the radioactive concentration state variable, is the object of needs reconstruction; W is a process noise, obeys normal state Gaussian distribution ω (t)～N (0, Q (t)); V is the set of various noises for measuring noise, obeys normal state Gaussian distribution v (t)～N (0, R (t));

(3) utilize Kalman filtering, according under establish an equation and draw radioactivity and distribute reconstructed image;

X(t+1，t)＝AX(t) ①

P(t+1，t)＝AP(t)A ^T+Q(t) ②

K(t+1)＝P(t+1，t)D ^T[DP(t+1，t)D ^T+R(t)] ^-1 ③

$\tilde{Z}(t+1)=Z(t+1)-\mathrm{DX}(t+1,t)$ ④

$X(t+1)=X(t+1,t)+K(t+1)\tilde{Z}(t+1)$ ⑤

P(t+1)＝[I-K(t+1)D]P(t+1，t) ⑥

Wherein, Z (t) is a measured value, X ₀Be concentration initial value, P ₀Be the initial concentration error covariance, iteration is from initial X ₀, P ₀, Q ₀, R ₀Set out,, constantly revise the concentration value X that estimates, finally provide radioactivity and distribute reconstructed image by measured value Z (t).

Above-mentioned sinogram (being Sinogram figure) obtains by the PET PET (positron emission tomography) scanner.

The PET PET (positron emission tomography) scanner is carried out transmission scan and emission scan, and transmission scan obtains the attenuation correction coefficient of image, and emission scan is chosen radially unit of 48 sampling angles and 34 in 180 degree.

In above-mentioned steps (3), iterative approximation may further comprise the steps particularly:

1) the at first initial value of set condition and initially covariance X ₀, P ₀

1. and 2. 2) utilize time renewal equation equation in time to extrapolate the priori estimates of current state and error covariance forward;

3) 5., 6. the observed reading Z (t) that utilizes the discrete acquisitions time point to record upgrades priori value according to the state renewal equation, obtains this optimal estimation constantly;

4) repeat alternate steps 2) and step 3) until the optimum reconstructed results of acquisition.

Advantage of the present invention is:

Rebuild the PET image by Kalman filtering method, improved quality of reconstructed images effectively based on the state space system; By comparing with the experiment of existing method for reconstructing, the deviation and the variance of reconstructed results all are greatly improved.

Description of drawings

Accompanying drawing 1 is a scan image data;

Accompanying drawing 2a is the reconstructed results synoptic diagram of MLEM method to accompanying drawing 1;

Accompanying drawing 2b is the reconstructed results synoptic diagram of the present invention to accompanying drawing 1;

Accompanying drawing 3 is radioactive concentration distribution value synoptic diagram of the corresponding true value of a row pixel in the middle of the model;

Accompanying drawing 4 is phantom synoptic diagram;

Accompanying drawing 5 is MLEM method reconstructed results synoptic diagram to accompanying drawing 4;

Accompanying drawing 6 is the present invention's reconstructed results synoptic diagram to accompanying drawing 4.

Embodiment

PET (positron emission tomography) scanner is surveyed the radiated signal that sends in the human body, handles through meeting with acquisition system, forms projection line, and deposits in the hard disc of computer in Sinogram figure (sinogram) mode.Computing machine is input with Sinogram figure, calls image reconstruction module, calculates human body cross-cutting fault image.

When using the PET PET (positron emission tomography) scanner, carry out transmission scan and emission scan.Transmission scan obtains the attenuation correction coefficient of image.Emission scan is chosen radially unit of 48 sampling angles and 34 in 180 degree, system matrix is generated by the software package that Fessler professor research group provides.

To acquired original to the Sinogram diagram data carry out all kinds of corrections, thereby set up a discrete measurement equation:

Y(t)＝DX(t)+v(t)

Wherein, Y is the Sinogram diagram data, and D is a system matrix, and v represents observation noise.

Set up evolution equation: the isotopic distribution in the human body have when in imaging process, temporarily stablizing X (t)= ⁰, by discretize to evolution equation, and the adition process noise, can more generally be expressed:

X(t+1)＝AX(t)+w(t)

Wherein, A is a state-transition matrix, is a unit matrix when isotopic distribution is temporarily stablized.

Make up the state space system: discrete measurement equation and evolution equation are joined together, set up a state space system:

Y(t)＝DX(t)+v(t)

X(t+1)＝AX(t)+w(t)

Wherein, v obeys normal state Gaussian distribution v (t)～N (0, R (t)), and w obeys normal state Gaussian distribution ω (t)～N (0, Q (t)).

Utilize Kalman filtering, according under the reconstructed image that establishes an equation:

X(t+1，t)＝AX(t)①

P(t+1，t)＝AP(t)A ^T+Q(t)②

K(t+1)＝P(t+1，t)D ^T[DP(t+1，t)D ^T+R(t)] ^-1

$\tilde{Z}(t+1)=Z(t+1)-\mathrm{DX}(t+1,t)$ ④

$X(t+1)=X(t+1,t)+K(t+1)\tilde{Z}(t+1)$ ⑤

P(t+1)＝[I-K(t+1)D]P(t+1，t)⑥

Wherein, Z (t) is a measured value, X ₀Be concentration initial value, P ₀Be the initial concentration error covariance, iteration is from initial X ₀, P ₀, Q ₀, R ₀Set out,, constantly revise the concentration value X that estimates, finally draw radioactivity and distribute reconstructed image by measured value Z (t).

When adopting Kalman filtering to carry out image reconstruction, mainly be divided into four steps:

1) the at first initial value of set condition and initially covariance X ₀, P ₀

1. and 2. 2) utilize the time renewal equation in time to extrapolate the priori estimates of current state and error covariance forward;

3) 5., 6. the observed reading Z (t) that utilizes the discrete acquisitions time point to record upgrades priori value according to the state renewal equation, obtains this optimal estimation constantly;

4) repeat alternate steps 2) and step 3) until the optimum reconstructed results of acquisition.

The experimental result of the technology of the present invention is as follows:

Use the technology of the present invention and carry out computer simulation experiment, and make comparisons with the reconstructed results of MLEM method.Adopt the synthetic emission scan data of Zubal thoracic cavity phantom, as shown in Figure 1.The original resolution of image is 32 * 32 pixels, adopts 180 degree following 48 sampling angles of the anglec of rotation and 34 data for projection of radially sampling in the sinogram simulation generative process.For acquisition condition that is virtually reality like reality, added 10% random noise in the S inogram data, with these data that detect as PET.Use MLEM method and method of the present invention to carry out image reconstruction.The MATLAB tool box generation system matrix that experiment utilizes J.A.Fessler professor research group to provide.

Fig. 2 a and Fig. 2 b are respectively the reconstructed results that obtains with MLEM method and method of the present invention, and the radioactive concentration distribution value that the true value of a row pixel correspondence and distinct methods are rebuild in the middle of the model as shown in Figure 3.Further we have calculated the deviation and the variance of the reconstructed results of two kinds of algorithms.The deviation of MLEM method reaches 0.1320, and deviation of the present invention is 0.1054; The variance of MLEM method reaches 0.0468, and variance of the present invention is 0.0254.Two kinds of algorithms can both restore original image basically well as can be seen, and each regional profile is all very clear, and the reconstructed value of middle column pixel meets substantially with true curve.But two pores in the middle of still clearly offering an explanation out from the image 2b that the present invention rebuilds are to such an extent as to and the result of MLEM too smoothly can not tell this two stains.The deviation of reconstructed results and error show that also the present invention is better than traditional MLEM method.

Be the validity of Kalman filtering image reconstruction method in the PET imaging that further specifies that the present invention proposes, we provide and use the result that data that different algorithms obtains in clinical PET system acquisition true phantom are rebuild research.Fig. 4 is used phantom synoptic diagram, pays close attention to F18 solution in six spherulas, is full of water on every side, gathers 25 frames altogether, is respectively 5 * 10s, 5 * 30s, 5 * 60s, 5 * 120s and 5 * 180s.Fig. 5 a, 5b, 5c, 5d utilize the MLEM method to 22,23, the reconstructed results of 24,25 frame data; Fig. 6 a, 6b, 6c, 6d be the present invention to 22,23, the reconstructed results of 24,25 frame data.As can be seen, the reconstruction effect of the present invention under true experiment condition is also better.

Claims (4)

1, the method for reconstructing of Kalman filtering image in a kind of PET imaging is characterized in that: may further comprise the steps:

(1) sinogram of input original projection line;

(2) set up the state space system:

Y(t)＝DX(t)+v(t)

X(t+1)＝AX(t)+w(t)

Wherein, t express time; Y is exactly the sinogram data; D is a system matrix, and the photon of expression emission is detected the probability that device receives; A is a state-transition matrix, is a unit matrix under instantaneous steady state (SS); X is the radioactive concentration state variable, is the object of needs reconstruction; W is a process noise, obeys normal state Gaussian distribution ω (t)～N (0, Q (t)); V is the set of various noises for measuring noise, obeys normal state Gaussian distribution v (t)～N (0, R (t));

(3) utilize Kalman filtering, according under establish an equation and draw radioactivity and distribute reconstructed image:

X(t+1，t)＝AX(t) ①

P(t+1，t)＝AP(t)A ^T+Q(t) ②

K(t+1)＝P(t+1，t)D ^T[DP(t+1，t)D ^T+R(t)] ^-1 ③

$\tilde{Z}(t+1)=Z(t+1)-\mathrm{DX}(t+1,t)$ ④

$X(t+1)=X(t+1,t)+K(t+1)\tilde{Z}(t+1)$ ⑤

P(t+1)＝[I-K(t+1)D]P(t+1，t) ⑥

Wherein, Z (t) is a measured value, X ₀Be concentration initial value, P ₀Be the initial concentration error covariance, iteration is from initial X ₀, P ₀, Q ₀, R ₀Set out,, constantly revise the concentration value X that estimates, finally draw radioactivity and distribute reconstructed image by measured value Z (t).

2, method according to claim 1 is characterized in that: described sinogram obtains by the PET PET (positron emission tomography) scanner.

3, method according to claim 2, it is characterized in that: the PET PET (positron emission tomography) scanner is carried out transmission scan and emission scan, transmission scan obtains the attenuation correction coefficient of image, and emission scan is chosen radially unit of 48 sampling angles and 34 in 180 degree.

4, method according to claim 1 is characterized in that: described step (3) may further comprise the steps:

1) the at first initial value of set condition and initially covariance X ₀, P ₀

1. and 2. 2) utilize time renewal equation equation in time to extrapolate the priori estimates of current state and error covariance forward;

3) 5., 6. the observed reading Z (t) that utilizes the discrete acquisitions time point to record upgrades priori value according to the state renewal equation, obtains this optimal estimation constantly;

4) repeat alternate steps 2) and step 3) until the optimum reconstructed results of acquisition.

Images