CN101156780A - Maximum posteriori optimizing image rebuilding method in PET imaging - Google Patents
Maximum posteriori optimizing image rebuilding method in PET imaging Download PDFInfo
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Abstract
The invention discloses a maximal posteriori optimized image reconstruction method for leading in a general Gibbs experiment in the PET imaging. The method comprises the following procedures: (1) PET imaging equipment is utilized to collect detector data before imaging, and the corrective parameter value and the system matrix of various data in the imaging equipment are obtained simultaneously; (2) a mathematical statistic statistical model used for reconstructing an image is reconstructed according to a statistical feature that is met by the corrective data acquainted by the procedure (1) before imaging; (3) the general Gibbs experiment is led in aiming at the compute of a mathematical model in the procedure (2) , a maximal posteriori estimate method is adopted to perform the conversion of a reconstruction model, to obtain an optimized equation with a constrained objective function used for obtaining a PET reconstruction image; (4) a parabola is adopted to replace a coordinate descent algorithm, to perform the iterative computation treatment and to reconstruct the image based on the selection of a global parameter in the optimized equation through a result obtained by the procedure (3). The invention can greatly improve the quality of the PET reconstruction image.
Description
Technical field
The present invention relates to a kind of medical image image processing method, especially relate to a kind of maximum posteriori optimizing image rebuilding method of in the PET imaging, introducing Generalized Gibbs priori.
Background technology
Positron emission imaging (PET) is one of important inspection means of current Medical Imaging, owing to be subjected to low counting rate and effect of noise, being reconstituted in from the detection data to the image in most cases is the problem of a morbid state.According to the literature, existing most PET imaging algorithms still can not obtain satisfied image.Therefore promoting the PET image quality effectively exists huge needs clinically, also is that the research focus of medical science PET imaging also is one of technical barrier simultaneously always.
As the effective ways that solve the ill-conditioning problem in the image reconstruction, the maximum a posteriori method is widely accepted.Based on the Gibbs Random Field Theory, Gibbs priori energy term can be introduced in and suppress the reconstructed image noise in the image reconstruction.Priori can be divided rough segmentation according to the difference of Gibbs priori energy equation form is two classes: secondary Gibbs priori and non-secondary Gibbs priori.Be easy to simply, in theory on the secondary Gibbs transcendental form commonly used analyze, and can not influence the whole concavity of whole energy equation in the image reconstruction; And have the maximum a posteriori method that the edge keeps effect mostly, and comprise line position model and discontinuous adaptive model, then can realize keeping the image reconstruction at edge by the Gibbs priori energy function of non-secondary.Yet owing to treat that reconstructed image does not always possess whole smoothness properties, edge that exists in the image and inevitable additional noise are often brought some regional conforming sudden change.The simple level and smooth priori of secondary Gibbs also will make in the reconstructed image edge details fuzzy when eliminating noise, produce level and smooth negative effect.And for non-secondary Gibbs priori, if treat that reconstructed image has obvious simple edges by some and some homogeneous areas are formed, non-secondary Gibbs priori will produce result relatively preferably, if but treat that reconstructed image character is tending towards complicated, when often not having significantly the border between the zone (this is the feature of PET imaging just), it is the stepped homogeneous area of pseudo-shadow that non-secondary Gibbs priori is easy to generation by mistaken diagnosis when the PET imaging.Non-in addition secondary Gibbs priori will be introduced amount of calculation and the complexity that new undetermined parameter and correlation values solution will increase whole reconstruction greatly.
Simple secondary Gibbs priori smoothly contains the reconstructed image of noise by the average effect of pixel value in a regional area; Non-secondary Gibbs priori with edge maintenance effect also need according in the local neighborhood between pixel value residual quantity information determine the degree and the form of the priori energy of each pixel in the target image.For simplicity, the priori that only depends on local neighborhood information more than the title is traditional Gibbs priori.
Level and smooth or the stepped effect of negative mistake that tradition Gibbs priori is brought all is because the pixel grey scale value information in adjacent 0 territory of the image local that it relied on can't effectively be distinguished marginal information and noise.For overcoming the above-mentioned shortcoming of local priori, once some had occurred and called oneself and use the maximum a posteriori method of global information in images, for example based on the Gibbs transcendental method in zone with obtain the Gibbs transcendental method based on the border of global information in the image by Level Set Method.Yet in fact based on the Gibbs transcendental method in zone owing to be subjected to that complicated area identification calculates or the restriction of required anatomy prior information, have certain limitation in actual applications.And depending on the parametrization design of level set by force based on the Gibbs transcendental method on border, this process may produce unpredictable results.
Summary of the invention
The objective of the invention is to propose to introduce in a kind of PET imaging the maximum posteriori optimizing image rebuilding method of Generalized Gibbs priori, can increase substantially the PET reconstructed image quality.
The object of the invention can realize by following technical measures, comprises that step is as follows:
1. utilize the detector data before the PET imaging device is gathered imaging, obtain various data correction parameter values and sytem matrix in the imaging device simultaneously;
2. the statistical nature that correction data satisfies before the imaging of obtaining according to step 1 makes up the mathematical statistical model that is used for reconstructed image;
3. at the finding the solution of mathematical model in the step 2, introduce Generalized Gibbs priori, adopt the maximum a posteriori method of estimation to carry out reconstruction model and transform, obtain being used to obtaining the optimization equation of the belt restraining object function of PET reconstructed image;
4. the result who is obtained by step 3 based on to optimizing on the basis that global parameter is selected in the equation, adopts parabola to replace the coordinate descent algorithm and carries out the iterative computation processing, reconstructs fine image.
The mathematical statistical model of using in the step 2 of the present invention is Poisson distribution or Gauss distribution, and promptly the detection process of positron is a counting process in fact, these probe values is interpreted as the stochastic variable of obeying independent Poisson distribution or Gauss distribution.
The image reconstruction model that obtains in the step 3 of the present invention is the optimization problem of a belt restraining in fact, and wherein the specific design process of Generalized Gibbs priori is:
A, at first select one comprise in the image abundant geological information than the large square neighborhood; Design the similarity that a similarity measure is used for the little square neighborhood of interior pixel k of comparison large square neighborhood and pixel j place correspondence simultaneously;
B, subsequently in selected large square neighborhood, carry out between two pixels gray value relatively in, utilize similarity between two pixels to obtain weights amount in the potential-energy function.
Definite process of above-mentioned parameter h is: at first directly adopt filter back-projection algorithm to obtain being used for the initial pictures that parabola is replaced coordinate decline iterative algorithm to correction data; To this image adopt pyramid structure by roughly to meticulous carry out variance analysis obtain in initial pictures variance yields σ than smooth region thereafter; Get at last the h value for the multiple of variances sigma Generalized Gibbs priori formula w during as iterative
Kj GGIn preset parameter.
Step 4 of the present invention adopts the detailed process of parabola replacement coordinate decline iterative processing as follows: the first step, at first the reconstructed image that obtains based on the previous step iteration is with reference to image, obtains to treat the weights amount w by pixel Generalized Gibbs priori of reconstructed image
Kj GG, with usefulness as next step iteration; In second step, on the weights amount basis that the first step is obtained, utilize parabola to replace coordinate decline iterative algorithm and carry out iterative approximation; In the 3rd step, first and second step of hocketing obtains final reconstructed image until convergence.
It is as follows that the experiment of the technology of the present invention and prior art relatively reaches the result:
At first use the technology of the present invention analogue body modulus certificate is rebuild experiment, Fig. 2 is that desirable phantom image is used to illustrate simulation experiment object of the present invention.Wherein (a) is phantom image 1 among Fig. 2, represents a Zubal abdominal part sectional view; (b) be phantom image 2, form by the fuzzy circular bright area of a uniform background, a square bright area, an embedded square dark areas; (c) be phantom image 3, the Shepp-Logan phantom of a standard of expression.The reconstruction of setting these three phantom image in the present invention's experiment has identical reconstruction environment, has all added 10% random noise of obeying Poisson distribution in the sinogram data.Matrix of transition probabilities A, corresponding to a parallel banded integral geometry model, this geometric model is represented 128 radially sampling and 128 systems that sample in the angle of having in one 180 ° the homogeneous area.The ASPIRE software system that is provided by people such as Fessler generates.
Among Fig. 3 1), 2), 3) be shown as respectively and adopt filtered back projection's (FBP) algorithm and the level and smooth priori of secondary Gibbs, the maximum a posteriori method of the Generalized Gibbs priori that non-secondary Huber priori and the present invention propose is to the reconstructed image of three phantoms among Fig. 2.As seen from Figure 3, no matter the reconstructed results of visually using the Generalized Gibbs priori that the present invention proposes still keeps all obviously being better than other three kinds of reconstructed results aspect the edge suppressing noise.The introducing of Generalized Gibbs priori not only can overcome the smoothing effect of crossing of secondary Gibbs priori, and can separate the problem of the stepped pseudo-shadow that secondary priori by no means caused to a great extent.
Among Fig. 4 1), 2), 3) described desirable phantom image and used secondary Gibbs priori respectively, the horizontal profile diagram in side of the maximum a posteriori reconstructed image of the Generalized Gibbs priori that non-secondary Huber priori and the present invention propose.Shown in profile diagram, with respect to FBP algorithm for reconstructing, secondary Gibbs priori, the image that the maximum a posteriori algorithm for reconstructing of non-secondary Huber priori is rebuild, the side profile figure of the image that the Generalized Gibbs priori of using the present invention to propose is rebuild still is the side profile figure that edge region all more approaches true picture in the background area, thereby the algorithm for reconstructing that the Generalized Gibbs priori of using the present invention's proposition is described can better overcome the ill-conditioning problem in the reconstruction, thereby can reconstruct the image that more approaches true phantom.Following table has provided the signal to noise ratio of all above reconstructed images with respect to its true picture.Use the reconstructed image of the Generalized Gibbs priori that the present invention proposes to have higher signal to noise ratio as can be seen.
For further specifying the effectiveness of the Generalized Gibbs priori maximum a posteriori algorithm for reconstructing that the present invention proposes, real PET heart perfusion detection data is rebuild experiment.Fig. 5 uses the reconstructed image of four kinds of different method for reconstructing respectively to real detection data, (a) be the FBP reconstructed image; (b) be secondary Gibbs priori reconstructed image; (c) be non-secondary Huber priori reconstructed results; (d) the Generalized Gibbs priori reconstructed results that proposes for the present invention.As can be seen, the Generalized Gibbs priori reconstructed image of the present invention's proposition is suppressing noise and is keeping all obviously being better than other three kinds of reconstructed images aspect the edge.
Description of drawings
Fig. 1 is using under the situation of Generalized Gibbs prior model of the present invention center neighborhood of a point weights scattergram (right figure in every picture group) among the target figure (left figure in every picture group).(a) when central point is positioned at relatively uniformly the zone, weights are approximately a kind of result's (as gaussian filtering) of image convolution filtering, (b) when central point is positioned on the vertical edge, weights are distributed on this vertical edge line basically, (c) be positioned on the edge of a bending when central point, the point that is positioned among the former figure on this crooked edge line has bigger weights equally, (d) when central point is arranged in the background that a lot of analog structures are arranged, weights similar morphosis in the figure distributes;
Analogue body modulus certificate in Fig. 2 experiment.(a) phantom image 1, and (b) phantom image 2, and (c) phantom image 3;
Fig. 3 (1)～(3) are respectively to the reconstructed image of four kinds of different method for reconstructing of use of three analogue body modulus certificates among Fig. 2.(a) FBP rebuilds, and (b) secondary Gibbs priori is rebuild, and (c) non-secondary Huber priori is rebuild, and (d) the Generalized Gibbs priori of the present invention's proposition is rebuild;
Fig. 4 (1)～(3) are the horizontal profile diagram of maximum a posteriori reconstructed image in corresponding diagram 3 (1)～(3);
Fig. 5 uses the reconstructed image of four kinds of different method for reconstructing respectively to true detection data.(a) FBP rebuilds, and (b) secondary Gibbs priori is rebuild, and (c) non-secondary Huber priori is rebuild the Generalized Gibbs priori reconstruction that (d) the present invention proposes.
The concrete implementing procedure figure of Fig. 6 the present invention.
The specific embodiment
The invention process has four step (see figure 6)s, and is specific as follows:
1, utilize the PET imaging system to gather the preceding detector data of imaging.Concrete acquisition mode can be set by user flexibility.Data acquisition modes is designed in the experiment: in one 180 ° angular interval, get 128 radially sampling and 128 angle samplings; Sytem matrix A is corresponding to the banded integral geometry model of parallel beam.Sampled data is deposited in the array.
2, data are proofreaied and correct.The correction coefficient c in calibration factor sweep time that obtains by system, efficient, attenuation quotient and the dead time of detector
iAnd counting at random that all detects and scattering counting r
iAccording to parameter c
iAnd r
iCarry out detector data and proofread and correct, obtain being used for the data of Generalized Gibbs priori maximum a posteriori image reconstruction.
3, design of graphics is as reconstruction model.Adopt the maximum a posteriori method, the correction data that step 2 obtains carried out mathematical modeling, finish the design of Generalized Gibbs priori, obtain being used to obtaining the optimization equation of the belt restraining object function Φ (λ) of PET reconstructed image,
, Φ (λ)=L (y, λ)-β U
GG(λ), wherein L (y λ) is the log-likelihood energy equation of correction data y;
Be Generalized Gibbs priori item, N
jThe neighborhood system of expression pixel j, w
Kj GGBe the weights amounts; β is a global parameter.
The specific design process of Generalized Gibbs priori in the above-mentioned steps 3: at first select a bigger square neighborhood to comprise geological information abundanter in the image, but also can not be excessive, generally get 11 * 11 or 15 * 15 large square neighborhood.The value of large square neighborhood is 11 * 11 square neighborhood in the experiment; Design the similarity that a similarity measure is used for interior pixel k of comparison large square neighborhood and pixel j place small neighbourhood simultaneously, small neighbourhood is generally got 5 * 5 or 7 * 7 square neighborhood, and similarity measure adopts the inverse proportion function of the weighting Euclidean distance of all pixel gray values in two neighborhood of pixel points.This similarity measure calculating small neighbourhood value is 7 * 7 square neighborhood in the experiment; In selected small neighbourhood, carry out subsequently between two pixels gray value relatively in, utilize similarity between two pixels to obtain weights amount in the potential-energy function.The weights amount is defined as
w
KjBe defined as the weights between the pixel k and pixel j in traditional Gibbs priori, determine V by the inverse ratio function of the Euclidean distance between two picture points in the image area
kAnd V
jThen being set at pixel k and pixel j is the little square neighborhood at center, λ (V
k) and λ (V
j) be all grey scale pixel value arrays in these two neighborhoods, ‖ ‖ represents the weighting Euclidean distance of these two pixel regions.Parameter h is used for the inverse proportion attenuation relation that the exponential function of weights between calculating pixel point is estimated with neighborhood similarity.
For further specifying choosing of weights amount, as shown in Figure 1, in every picture group, the figure on the left side is former figure, the figure on the right has described the value condition of each point weights in the Generalized Gibbs prior model in the left figure central point neighborhood, the bright more then corresponding weights of color are big more, and this neighborhood is set at the zone that covers entire image.As can be seen, weights generally are distributed in more similar structure place, two pixels structure on every side is similar more, then the weights of these two pixels in priori are just big more, show that the Generalized Gibbs prior information can consider the information of some the abundanter geometry forms in the image, thereby overcome the relevant less shortcoming of traditional Gibbs prior information amount, therefore can provide more efficiently regularization to handle the ill-conditioning problem of PET image reconstruction.
Generalized Gibbs priori formula w in the step 3
Kj GGThe process of choosing of middle h is: at first directly adopt filter back-projection algorithm to obtain being used for the initial pictures that parabola is replaced coordinate decline iterative algorithm to correction data; To this image adopt pyramid structure by roughly to meticulous carry out variance analysis obtain in initial pictures variance yields σ than smooth region thereafter; Get at last the h value for 10 times of variances sigma as Generalized Gibbs priori formula w
Kj GGPreset parameter in parabola replacement coordinate decline iterative algorithm iterative process.
Global parameter β method of estimation in the step 3: because the data volume counts decision that quality of reconstructed images is detected by detector to a great extent in the PET imaging.Through lot of experiment validation, global parameter β can be by empirical equation among the present invention
Determine that wherein c is a constant, #counts represents total counts number of being used to rebuild.C value 20 in the simulation experiment (see figure 3) of the present invention, #counts value 3 * 10
5C value 10 in the heart perfusion truthful data experiment (see figure 5), #counts value 1.4876 * 10
5
4, finish reconstruction.On the basis of step 2 and processing of step 3 related data and modelling, adopting parabola replacement coordinate decline iterative algorithm that object function is carried out two-step type optimization finds the solution, specific as follows: the first step, at first the reconstructed image that obtains based on the previous step iteration is with reference to image, treats the weights amount w by pixel Generalized Gibbs priori of reconstructed image
Kj GGCalculate, with usefulness as next step iteration; In second step, on the weights amount basis that the first step is obtained, this weights amount is utilized parabola to replace coordinate decline iterative algorithm and is carried out iterative approximation as constant in second step.Two steps hocketed until convergence, obtained final reconstructed image.In the experiment of the present invention, the reconstruction figure that all can obtain when iterations is 150 times.
Claims (7)
1. a maximum posteriori optimizing image rebuilding method of introducing Generalized Gibbs priori in the PET imaging is characterized in that comprising the steps:
(1) utilizes the PET imaging device to gather the preceding detector data of imaging, obtain various data correction parameter values and sytem matrix in the imaging device simultaneously;
(2) statistical nature that correction data satisfies before the imaging of obtaining according to step 1 makes up the mathematical statistical model that is used for reconstructed image;
(3) at the finding the solution of mathematical model in the step 2, introduce Generalized Gibbs priori, adopt the maximum a posteriori method of estimation to carry out reconstruction model and transform, obtain being used to obtaining the optimization equation of the belt restraining object function of PET reconstructed image;
(4) result who is obtained by step 3 based on to optimizing on the basis that global parameter is selected in the equation, adopts parabola to replace the coordinate descent algorithm and carries out iterative computation processing, the image that reconstructs.
2. the maximum posteriori optimizing image rebuilding method of introducing Generalized Gibbs priori in the PET imaging according to claim 1, it is characterized in that: the mathematical statistical model of using in the step 2 is Poisson distribution or Gauss distribution.
3. the maximum posteriori optimizing image rebuilding method of in the PET imaging, introducing Generalized Gibbs priori according to claim 1, it is characterized in that: the specific design process of Generalized Gibbs priori is in the step 3:
A, at first select one comprise in the image abundant geological information than the large square neighborhood; Design the similarity that a similarity measure is used for the little square neighborhood of interior pixel k of comparison large square neighborhood and pixel j place correspondence simultaneously;
B, subsequently in selected little square neighborhood, carry out between two pixels gray value relatively in, utilize similarity between two pixels to obtain weights amount in the potential-energy function.
4. the maximum posteriori optimizing image rebuilding method of introducing Generalized Gibbs priori in the PET imaging according to claim 3, it is characterized in that: the weights amount among the step b is defined as
w
KjBe defined as the weights between the pixel k and pixel j in traditional Gibbs priori, determine by the inverse proportion function of the Euclidean distance between two picture points in the image area; V
kAnd V
jThen be set at pixel k and pixel j is the little square neighborhood at center; λ (V
k) and λ (V
j) be all grey scale pixel value arrays in these two neighborhoods; ‖ ‖ represents the weighting Euclidean distance of these two pixel regions; Parameter h is used for the inverse proportion attenuation relation that the exponential function of weights between calculating pixel point is estimated with neighborhood similarity.
5. the maximum posteriori optimizing image rebuilding method of in the PET imaging, introducing Generalized Gibbs priori according to claim 4, it is characterized in that: definite process of above-mentioned parameter h is: at first directly adopt filter back-projection algorithm to obtain being used for the initial pictures that parabola is replaced coordinate decline iterative algorithm to correction data; To this image adopt pyramid structure by roughly to meticulous carry out variance analysis obtain in initial pictures variance yields σ than smooth region thereafter; Get at last the h value for the multiple of variances sigma Generalized Gibbs priori formula w during as iterative
Kj GGIn preset parameter.
6. the maximum posteriori optimizing image rebuilding method of introducing Generalized Gibbs priori in the PET imaging according to claim 3 is characterized in that: the similarity measure among the step a adopts the inverse proportion function of the weighting Euclidean distance of all pixel gray values in two neighborhood of pixel points.
7. the maximum posteriori optimizing image rebuilding method of in the PET imaging, introducing Generalized Gibbs priori according to claim 1, it is characterized in that: step 4 adopts the detailed process of parabola replacement coordinate decline iterative processing as follows: the first step, at first the reconstructed image that obtains based on the previous step iteration is with reference to image, the weights amount of each pixel place Generalized Gibbs priori of reconstructed image is treated in acquisition, with the usefulness as next step iteration; In second step, on the weights amount basis that the first step is obtained, utilize parabola to replace coordinate decline iterative algorithm and carry out iterative approximation; In the 3rd step, first and second step of hocketing obtains final reconstructed image until convergence.
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