CN117788625A - Scattering correction method and system for PET image - Google Patents
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Abstract
The invention relates to a scattering correction method of PET images, comprising the following steps: modeling the PET acquisition process to obtain a PET reconstructed image x without attenuation correction nac The method comprises the steps of carrying out a first treatment on the surface of the Extraction of x based on Canny operator nac The method comprises the steps of generating a mask matrix Q of an interested region according to object edge information; according to x nac And linear attenuation coefficient distributions μ and Q to determine an initial scattering distribution S 0 The method comprises the steps of carrying out a first treatment on the surface of the Determining a log-likelihood function of the detection data according to the PET images x, mu, the scattering distribution S and the scattering correction factor alpha in the iterative reconstruction process; keeping mu and alpha constant, and maximizing log-likelihood function to obtain PET iterative image x j (n+1) The method comprises the steps of carrying out a first treatment on the surface of the Keeping x and alpha constant, maximizing log-likelihood function to obtain iterative attenuation systemNumber distribution mu n+1 The method comprises the steps of carrying out a first treatment on the surface of the Keeping x and mu constant, maximizing the log-likelihood function to obtain an iterative scattering correction factor alpha it n+1 The method comprises the steps of carrying out a first treatment on the surface of the For x j (n+1) 、μ n+1 And alpha it n+1 Alternately iterating to obtain estimated values of x, mu and alpha; from the estimated values of x, μ, α, scatter corrected PET images are obtained. Compared with the traditional scattering correction algorithm, the method has the advantages of being higher in correction precision and beneficial to improving the image quality.
Description
Technical Field
The invention relates to the technical field of medical imaging, in particular to a scattering correction method and system for PET images.
Background
Positron emission tomography PET (Positron Emission Tomography) is a high-end nuclear medicine image diagnostic device. In practice using radionuclides (e.g 18 F、 11 C) marking metabolic substances, injecting nuclides into a human body, and then carrying out functional metabolism imaging on a patient through a PET system to reflect the condition of life metabolism activities, thereby achieving the purpose of diagnosis. The current commercial positron emission tomography PET is generally integrated with other modality imaging systems, such as a computer tomography CT (Computed Tomography) or a magnetic resonance imaging MRI (Magnetic Resonance Imaging), so that the aim of simultaneously imaging the anatomical structure of a patient is fulfilled, the PET nuclide distribution imaging can be accurately positioned, and the focus positioning accuracy is improved. The final function imaging and the anatomical imaging are integrated with each other, so that the advantages of dual-mode imaging are compatible, the whole condition of the whole body can be known at a glance, the purposes of early finding focus and diagnosing diseases are achieved, and the method has more advantages for guiding diagnosis and treatment of tumor, heart and brain diseases.
During acquisition in a positron emission tomography system, photons may undergo Compton scattering inside the human body before reaching the detector, changing the direction of flight. Due to the limited energy resolution of the detector, these scattering events are erroneously recorded as true coincidence events, confounding annihilation position information of the nuclide, thereby generating scattering artifacts in the image, and seriously affecting image quality. Especially in three-dimensional data acquisition, the number of scatter coincidences may reach 30% -60% of the total count, which makes scatter correction one of the key links in PET reconstruction.
At present, a few factors influencing the accuracy of scattering distribution and further seriously influencing the image quality often exist in a commonly used PET acquisition mode:
single scatter analog correction (SSS) methods are widely used for scatter correction in PET reconstruction. The method simulates a scattering distribution by calculating the probability that a coincident gamma photon will undergo a single scattering event before being detected. Due to the presence of multiple scattering components in the real detection data, SSS alone is not able to accurately determine the proportional relationship of the scattering components to the total detected coincidence. The relative amount of scatter contribution is typically determined by a sinogram radial tail fitting method or a method based on Monte Carlo simulation. In practical use, since the tail fitting method only selects part of data outside the object, the tail fitting is sometimes unstable for the case of small data volume, especially when the scanned target volume is large, the data volume reserved for fitting is small, the noise is increased, and underestimation or overestimation is easy to occur.
For multi-modality acquisition modes, images of different modalities tend to provide attenuation information required for scatter correction. In actual clinical practice, there may be relative deviations in the multi-modality image positions, with inaccurate range of tail fitting, resulting in scatter artifacts on the PET image. Taking the example of a PET/CT system, the scan range of PET is typically greater than the scan range of other modalities (e.g., CT or MRI). Other modality imaging is likely not to provide a sufficiently large imaging range when scanning patients of relatively large body weight, which can lead to truncation of the linear attenuation coefficient image, and mismatch of PET image and CT image imaging ranges.
In addition, CT scanning can typically be accomplished in a short period of time, with the acquired image being almost a snapshot of the moment in time. However, PET scanning is slow, and each position typically takes several minutes, so that it is impossible to complete data acquisition while the patient is in a breath-hold state, and respiratory motion can result in a positional mismatch between the PET and CT images. In addition, in long-time PET scanning, the patient may move (such as arm, head, etc. may move when the scanning time is long), and the PET and CT images may be phase-mismatched. Meanwhile, obvious high-brightness metal artifacts exist in CT images (such as cardiac pacemakers, metal dental sleeves and the like) of patients containing metal substances in the body during the scanning process, and obvious errors can occur in the CT images.
In summary, under clinical conditions, PET truncation or mismatch of PET and other modality images can produce erroneous linear attenuation information, resulting in erroneous scatter correction, even with severe scatter artifacts on the PET image, with the accuracy of the scatter correction remaining to be further improved.
Disclosure of Invention
First, the technical problem to be solved
In view of the above-mentioned drawbacks and disadvantages of the prior art, the present invention provides a method and a system for scatter correction of PET images, which solve the technical problem of how to further improve the accuracy of scatter correction of PET images.
(II) technical scheme
In order to achieve the above purpose, the main technical scheme adopted by the invention comprises the following steps:
in a first aspect, the present invention provides a method for scatter correction of PET images, comprising:
modeling the PET acquisition process to obtain a PET reconstructed image x without attenuation correction nac ；
Extraction of x based on Canny operator nac Generating a mask matrix Q of the region of interest according to the object edge information;
according to x nac And linear attenuation coefficient distributions μ and Q to determine an initial scattering distribution S 0 ；
Determining a log-likelihood function of the detection data according to the PET images x, mu, the scattering distribution S and the scattering correction factor alpha in the iterative reconstruction process;
keeping mu and alpha constant, maximizing log-likelihood function, and obtaining PET iterative image x j (n+1) ；
Keeping x and alpha constant, maximizing log-likelihood function, and obtaining iterative attenuation coefficient distribution mu n+1 ；
Keeping x and mu constant, maximizing log-likelihood function, and obtaining iterative scattering correction factor alpha it n+1 ；
For x j (n+1) 、μ n+1 And alpha it n+1 Alternating iteration is carried out, and estimated values of x, mu and alpha meeting the requirement of the maximized log-likelihood function are obtained;
according to x, mu, alpha estimated values, scattering corrected PET images;
where n is the number of iterations.
Alternatively, Q is obtained according to the following formula:
wherein, (x) nac ) j X for a single pixel of a PET reconstructed image without attenuation correction b The object region in the image is reconstructed for PET.
Optionally, the modeling of the PET acquisition process results in a PET reconstructed image x nac Comprising:
modeling a PET acquisition process according to the following formula to obtain a PET reconstructed image x nac ：
Wherein,is the average value of the detected data; j is a variable index of the radioactivity distribution image space; m is the size of the radioactivity distribution image space; a is that ijt Is a system matrix; i is the variable index of a response line LOR of the sine graph of the detection data; t is the variable index of the time-of-flight TOF discrete space; x is x j Reconstructing an image for the unknown PET; l (L) ik Is a linear attenuation coefficient matrix; k is the variable index of the linear attenuation coefficient image space; k is the size of the linear attenuation coefficient image space; mu (mu) k Is a linear attenuation coefficient image, x nac The medium attenuation correction parameter is mu k ＝0；α it Correction factors for each scattering point; s is S it Is the average of the scattered noise; n is the size of the sinogram of the detected data; t is the size of the time-of-flight TOF discrete space.
Optionally, the scattering distribution S is determined according to the following formula:
wherein I is A Indicating that positron annihilates at any point on S1 to emit a pair of gamma photons, one photon is not scattered and moves along path S1 and is detected by detector A, the photon energy is 511keV, and the detection efficiency is epsilon AS The linear attenuation coefficient image is mu, the other photon moves along the path S2 after being scattered by the S point, the photon energy is smaller than 511keV, and the detection efficiency is epsilon' BS The linear attenuation coefficient image is μ';
I B indicating that the annihilation of the positive and negative electrons at any point on S2 emits a pair of gamma photons, one of which is not scattered and moves along the path S2 and is detected by the detector B, and the photon energy is 511keV, and the detection efficiency is epsilon BS The linear attenuation coefficient image is mu, the other photon moves along the path S1 after being scattered by the S point, the photon energy is smaller than 511keV, and the detection efficiency is epsilon A ′ B The linear attenuation coefficient image is μ';
vs is the total scattering volume, σ AS For the geometrical cross section of detector a along gamma rays, σ BS A geometric section of the detector B along the ray γ;
σ c for the compton scattering cross-section,for Compton scattering, Ω represents the scattering solid angle.
Optionally, the log-likelihood function is:
optionally, the saidThe method comprises the following steps:
optionally, the μ n+1 The method comprises the following steps:
optionally, the values of x and μ are kept constant, and the log-likelihood function is maximized to obtain an iterative scatter correction factor α it n+1 Comprising:
keeping x and mu constant, maximizing a log-likelihood function, and calculating to obtain a three-dimensional iterative scattering correction factor according to the following formula:wherein (1)>
The three-dimensional data are recombined into two-dimensional data, and a two-dimensional correction factor is applied to each layer of data to obtain a conversion formula:wherein d is the number of layers of direct incidence, +.>Representing data reorganization;
according toAlpha is obtained by reverse recombination it n+1 。
In a second aspect, the present invention provides a scatter correction system for PET images, comprising:
the image reconstruction module is used for modeling the PET acquisition process to obtain a PET reconstructed image x without attenuation correction nac ；
Mask matrix generation module, extracting x based on Canny operator nac Generating a mask matrix Q of the region of interest according to the object edge information;
a first determination module according to x nac And linear attenuation coefficient distributions μ and Q to determine an initial scattering distribution S 0 ；
The second determining module is used for determining a log-likelihood function of the detection data according to the PET images x, mu, the scattering distribution S and the scattering correction factor alpha in the iterative reconstruction process;
a first iteration module for keeping mu and alpha constant and maximizing log-likelihood function to obtain PET iteration image x j (n+1) ；
A second iteration module for keeping x and alpha constant and maximizing log-likelihood function to obtain an iteration attenuation coefficient distribution mu n+1 ；
A third iteration module for keeping x and mu constant and maximizing log-likelihood function to obtain an iteration scattering correction factor alpha it n+1 ；
Alternate iteration module for x j (n+1) 、μ n+1 And alpha it n+1 Alternating iteration is carried out, and estimated values of x, mu and alpha meeting the requirement of the maximized log-likelihood function are obtained;
the scattering correction module is used for correcting the PET image after scattering according to the estimated values of x, mu and alpha;
where n is the number of iterations.
(III) beneficial effects
The beneficial effects of the invention are as follows: according to the scattering correction method for the PET image, the characteristic tissue of the object is extracted in the iteration process, and the attenuation coefficient distribution and the scattering correction factors are adjusted, so that the iteration result approaches to an ideal value, and the accuracy of final scattering correction is ensured. Compared with the related art, the invention provides a more accurate scattering correction method, which not only overcomes the defects of smaller data size and larger weight and poor stability of a patient in the traditional scattering algorithm, but also gets rid of dependence on other mode images, obtains more accurate scattering distribution under the condition that no other mode images or other mode images have obvious artifacts, greatly reduces the radiation dose of the patient, and simultaneously obtains higher-quality images, thereby having stronger applicability. Compared with the traditional scattering correction algorithm, the method has higher correction precision and contributes to improving the image quality.
Drawings
Fig. 1 is a flowchart of a method for correcting scattering of a PET image according to an embodiment of the present invention;
FIG. 2 is a PET image obtained by calculating a scattering distribution using a conventional algorithm according to an embodiment of the present invention;
FIG. 3 is a PET image obtained by calculating a scatter distribution using a scatter correction method for PET images of the present application according to an embodiment of the present invention;
fig. 4 is a block diagram of a scatter correction system for PET images according to an embodiment of the present invention.
[ reference numerals description ]
400: a scatter correction system for PET images;
401: an image reconstruction module;
402: a mask matrix generation module;
403: a first determination module;
404: a second determination module;
405: a first iteration module;
406: a second iteration module;
407: a third iteration module;
408: alternating iteration modules;
409: and a scatter correction module.
Detailed Description
The invention will be better explained by the following detailed description of the embodiments with reference to the drawings.
In PET image reconstruction, an SSS method is generally used for estimating scattering distribution, however, under the condition of small data volume or mismatching of multi-mode images, the method has poor stability, and artifacts are easy to generate to influence diagnosis of doctors. According to the method, firstly, matched attenuation coefficient distribution and scattering correction factors are obtained from PET data, and after multiple iterations, accurate attenuation correction and scattering correction are obtained.
In order that the above-described aspects may be better understood, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
In a first aspect, referring to fig. 1, the present embodiment provides a method for correcting scattering of a PET image, including:
s101, modeling a PET acquisition process to obtain a PET reconstructed image x without attenuation correction nac 。
Optionally, the modeling of the PET acquisition process results in a PET reconstructed image x nac Comprising:
modeling a PET acquisition process according to the following formula to obtain a PET reconstructed image x nac ：
Wherein,is the average value of the detected data; j is a variable index of the radioactivity distribution image space and represents a point source corresponding to the space position; m is the size of the radioactivity distribution image space; a is that ijt The probability that the space point source j is detected by a response line LOR i and the time of flight TOF is t in the PET system is expressed in a mathematical form as a system matrix, and the physical characteristics of the system are reflected; i is the variable index of a response line LOR of the sine graph of the detection data; t is the variable index of the time-of-flight TOF discrete space; x is x j Reconstructing an image for the unknown PET; l (L) ik A linear attenuation coefficient matrix is used for representing the track crossing length of LOR i when the LOR i passes through a space position point source k; k is the variable index of the linear attenuation coefficient image space; k is the size of the linear attenuation coefficient image space; mu (mu) k Is a linear attenuation coefficient image, x nac Attenuation correction parameters used in reconstruction are taken μ k ＝0；α it Correction factors for each scattering point; s is S it Is the average of the scattered noise; n is the size of the sinogram of the detected data; t is the size of the time-of-flight TOF discrete space.
S102, extracting x based on Canny operator nac The mask matrix Q of the region of interest is generated.
Alternatively, Q is obtained according to the following formula:
wherein, (x) nac ) j X for a single pixel of a PET reconstructed image without attenuation correction b The object region in the image is reconstructed for PET.
S103, according to x nac And linear attenuation coefficient distributions μ and Q to determine an initial scattering distribution S 0 。
Optionally, the scattering distribution S is determined according to the following formula:
wherein I is A Indicating that positron annihilates at any point on S1 to emit a pair of gamma photons, one photon is not scattered and moves along path S1 and is detected by detector A, the photon energy is 511keV, and the detection efficiency is epsilon AS The linear attenuation coefficient image is mu, the other photon moves along the path S2 after being scattered by the S point, the photon energy is smaller than 511keV, and the detection efficiency is epsilon' BS The linear attenuation coefficient image is μ';
I B indicating that the annihilation of the positive and negative electrons at any point on S2 emits a pair of gamma photons, one of which is not scattered and moves along the path S2 and is detected by the detector B, and the photon energy is 511keV, and the detection efficiency is epsilon BS The linear attenuation coefficient image is mu, the other photon moves along the path S1 after being scattered by the S point, the photon energy is smaller than 511keV, and the detection efficiency is epsilon A ′ B The linear attenuation coefficient image is μ';
vs is the total scattering volume, σ AS For the geometrical cross section of detector a along gamma rays, σ BS A geometric section of the detector B along the ray γ;
σ c for the compton scattering cross-section,the differential cross section for Compton scattering can be obtained by the Klein-Nishina formula, where Ω represents the scattering solid angle.
In particular, single Scatter Simulation (SSS) methods are typically used to estimate scatter distribution during PET image reconstruction.
The general idea of SSS is to determine all possible scattering points first, calculate the scattering value on the fold line formed by each scattering point and any two crystals, and calculate the scattering value on each crystal pair after traversing the combination of all scattering points and crystal pairs. The number of scattering points thus has a direct influence on the calculation time and accuracy of the scatter correction. The number of scattering points is determined by the size of the object, the number of scattering points is large when the object is large, and the time consumed for scattering correction is long, and vice versa. The object range of the scattering correction generally utilizes images of other modes to approximate and select an external maximum cube range, and the number of scattering points in the range is often larger than that of the actual object scattering points, so that the calculation time of the scattering is increased, and the accuracy of the scattering correction is reduced.
In order to reduce the calculation time of the scatter correction and increase the accuracy of the scatter correction, the patent applies a Canny operator to the PET image x without attenuation correction nac And extracting edge information of the object to generate a mask matrix Q of the region of interest. X is x nac The attenuation correction parameters used in the reconstruction can be taken μ using conventional reconstruction algorithms k =0, k=1 to K, such as OSEM or FBP. For the selection of the region, other edge detection operators can be selected, the manual sketching can be directly performed, and different selection sketching methods such as automatic sketching by using a threshold value, artificial intelligent recognition and the like can be used.
S104, determining a log-likelihood function of the detection data according to the PET images x, mu, the scattering distribution S and the scattering correction factor alpha in the iterative reconstruction process.
Optionally, the log-likelihood function is:
the PET detection data obey poisson distribution, and unknowns are x and μ and a scattering correction factor α. The log-likelihood function of the probe data is expressed as:
bringing the above formula into the formula Ignoring terms that are not related to unknowns, the log-likelihood function can be written as the above formula L (x, μ, α, y).
S105, keeping mu and alpha as constants, maximizing a log-likelihood function, and obtaining a PET iterative image x j (n+1) 。
Optionally, the saidThe method comprises the following steps:
since the above log-likelihood function is a very complex function for the unknowns x, α, μ, the formula L (x, μ, α, y) is difficult to obtain an analytical solution, so it is necessary to gradually approach the optimal solution using an iterative algorithm. Before iterative algorithm operation, the unknown numbers x, alpha and mu are initialized to obtain the initialization results x respectively 0 ，α 0 ，μ 0 The iteration is guaranteed to converge as soon as possible. The log-like function is maximized for the unknown PET radioactivity distribution x, α.
The initial value of x can be set as a constant, or can be an image obtained by other reconstruction methods or a PET image without correction, and the initial value of x is set as constant distribution in an imaging visual field, and the constant is selected to be 1000.
S106, keeping x and alpha constant, maximizing a log-likelihood function, and obtaining an iterative attenuation coefficient distribution mu n+1 。
Optionally, aSaid mu n+1 The method comprises the following steps:
and keeping PET activity distribution x, wherein a scattering correction factor alpha is constant, maximizing a log-likelihood function aiming at unknown attenuation coefficient distribution mu, and directly calculating by using PET data to obtain new linear attenuation coefficient distribution mu. Where l represents the projection of the full 1 image, n represents the number of iterations, and the initial value of μ in the set may be a constant or may be a linear attenuation coefficient distribution of incomplete matching obtained by other modalities, which is set to be a constant 0 in this application.
S107, keeping x and mu constant, maximizing log-likelihood function, obtaining iterative scattering correction factor alpha it n+1 。
Optionally, the α it n+1 The method comprises the following steps:
formula (VI)T is more than or equal to 1 and less than or equal to T is written in a matrix form as follows: y=a×x+smatrix×α.
Smatrix is a diagonal arrayAs can be seen from the above formula, the unknowns x and α are symmetrical in the formula, so solving the unknowns α can be used to reference the iterative algorithm of the unknowns x, and thus the formula can be simplified as follows: />
Namely, the PET activity distribution x is kept, the linear attenuation coefficient distribution mu is constant, the log-like hood function is maximized aiming at the unknown scattering correction factor alpha, and the new scattering correction factor alpha is obtained by directly calculating PET data.
In order to reduce noise, the method is more suitable for the condition of small data volume and simultaneously reduces calculation time, and generally adopts a data reorganization technology to reorganize three-dimensional data into two dimensionsData, two-dimensional factors are applied to each layer of data, namely, a formulaThe method comprises the following steps of: /> Obtaining a two-dimensional scattering correction factor->And then, the three-dimensional scattering correction factor alpha is restored by an inverse recombination mode and is directly applied to scattering correction and data reconstruction.
The present application applies monolayer recombination (SSRB), inverse monolayer recombination (reverse SSRB), also multilayer recombination (MSRB), inverse multilayer recombination (reverse MSRB) or fourier recombination (fire), inverse fourier recombination (reverse fire).
Formula (VI)The initial value of α in (a) may be set to be a constant or may be a scatter correction factor distribution obtained by other fitting methods, and in this patent is set to be a constant 1.
S108, for x j (n+1) 、μ n+1 And alpha it n+1 And (5) carrying out alternate iteration to obtain estimated values of x, mu and alpha meeting the requirement of the maximized log-likelihood function.
S109, according to the estimated value of x, mu and alpha, the PET image after the scattering correction is obtained.
Where n is the number of iterations.
According to the scattering correction method for the PET image, the characteristic tissue of the object is extracted in the iteration process, and the attenuation coefficient distribution and the scattering correction factors are adjusted, so that the iteration result approaches to an ideal value, and the accuracy of final scattering correction is guaranteed. Compared with the related art, the invention provides a more accurate scattering correction method, which not only overcomes the defects of smaller data size and larger and stable weight of a patient of the traditional scattering algorithm, but also gets rid of dependence on other mode images, obtains more accurate scattering distribution under the condition that no other mode images or other mode images have obvious artifacts, greatly reduces the radiation dose of the patient, and simultaneously obtains higher-quality images, thereby having stronger applicability. Compared with the traditional scattering correction algorithm, the method has higher correction precision and contributes to improving the image quality.
The method for correcting the scattering of the PET image provided by the present embodiment is further described below with reference to specific embodiments:
whole body scanning of a patient with a PET apparatus, wherein the PET scan field of view is 600mm, the ct field of view is 500mm, the PET image is reconstructed using an ordered subset maximum likelihood method (OSEM), 17 subsets, 2 iterations, image matrix 192x nac 92, gaussian filter half width 4mm.
The uncorrected PET image was gaussian filtered at half-width 5 mm.
The upper threshold ratio value of the Candy operator is set to be 0.65, the lower threshold ratio value is set to be 0.32, the edge difference operator is selected from the Sobel operator, the difference between the horizontal direction and the vertical direction is calculated, the convolution kernel 3 is used for scaling the derivative, and the ratio of the derivative is 1.
x is set as a default initial value 1000, mu is set as an initial value 1, alpha is set as an initial value 1, the number of alternative iteration subsets is 17, the iteration number of PET images is 2, the iteration number of linear attenuation coefficients is 3, the iteration number of scattering correction factors is 2, and the reconstruction result is shown in figures 2 and 3. FIG. 2 is a reconstructed image of PET obtained by calculating the scatter distribution using a conventional algorithm, with a large patient weight and a small data volume, with significant artifacts in the patient's body; fig. 3 shows a PET image obtained by the method of the present invention under the same reconstruction method and parameters, with more accurate scatter distribution, no significant artifacts, and better image quality.
In a second aspect, as shown in fig. 4, the present embodiment provides a scatter correction system 400 for PET images, comprising: image reconstruction module 401, mask matrix generation module 402, first determination module 403, second determination moduleA module 404, a first iteration module 405, a second iteration module 406, a third iteration module 407, an alternating iteration module 408, and a scatter correction module 409. The image reconstruction module 401 models the PET acquisition process to obtain a PET reconstructed image x without attenuation correction nac . Mask matrix generation module 402 extracts x based on Canny operator nac The mask matrix Q of the region of interest is generated. The first determination module 403 is based on x nac And linear attenuation coefficient distributions μ and Q to determine an initial scattering distribution S 0 . The second determination module 404 determines a log-likelihood function of the detection data from the PET images x, μ, the scatter distribution S, and the scatter correction factor α in the iterative reconstruction process. The first iteration block 405 keeps μ and α constant, maximizes the log-likelihood function, and obtains the PET iteration image x j (n+1) . The second iteration block 406 keeps x and α constant, maximizes the log-likelihood function, and obtains an iterative attenuation coefficient distribution μ n+1 . The third iteration block 407 keeps x and μ constant, maximizes the log-likelihood function, and obtains the iterative scatter correction factor α it n+1 . Alternate iteration module 408 pair x j (n+1) 、μ n+1 And alpha it n+1 And (5) carrying out alternate iteration to obtain estimated values of x, mu and alpha meeting the requirement of the maximized log-likelihood function. The scatter correction module 409 derives scatter corrected PET images from the estimated values of x, μ, α. Where n is the number of iterations. According to the scatter correction system for PET image provided in this embodiment, since the scatter correction system for PET image is used to implement the steps of the scatter correction method for PET image provided in the first embodiment of the present invention, the scatter correction system for PET image has all the technical effects of the scatter correction method for PET image, which are not described herein.
In a third aspect, an embodiment of the present invention provides a computer readable storage medium having stored thereon a computer program that, when executed, implements the method for scatter correction of PET images according to any of the first aspects above.
In a fourth aspect, an embodiment of the present invention provides a storage device including a storage medium and a processor, the storage medium storing a computer program, the program when executed by the processor implementing the method for scatter correction of a PET image according to any one of the first aspects.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, the present invention should also include such modifications and variations provided that they come within the scope of the following claims and their equivalents.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that alterations, modifications, substitutions and variations may be made in the above embodiments by those skilled in the art within the scope of the invention.
Claims (9)
1. A method for scatter correction of a PET image, comprising:
modeling the PET acquisition process to obtain a PET reconstructed image x without attenuation correction nac ；
Extraction of x based on Canny operator nac Generating a mask matrix Q of the region of interest according to the object edge information;
according to x nac And linear attenuation coefficient distributions μ and Q to determine an initial scattering distribution S 0 ；
Determining a log-likelihood function of the detection data according to the PET images x, mu, the scattering distribution S and the scattering correction factor alpha in the iterative reconstruction process;
keeping μ and α constant, maximizing log-likeihood function to obtain PET iterative image x j (n+1) ；
Keeping x and alpha constant, maximizing log-likelihood function, and obtaining iterative attenuation coefficient distribution mu n+1 ；
Keeping x and mu constant, maximizing log-likelihood function, and obtaining iterative scattering correction factor alpha it n+1 ；
For x j (n+1) 、μ n+1 And alpha it n+1 Alternating iteration is carried out, and estimated values of x, mu and alpha meeting the requirement of the maximized log-likelihood function are obtained;
according to x, mu, alpha estimated values, scattering corrected PET images;
where n is the number of iterations.
2. The scatter correction method of a PET image according to claim 1, wherein Q is obtained according to the following formula:
wherein, (x) nac ) j X for a single pixel of a PET reconstructed image without attenuation correction b The object region in the image is reconstructed for PET.
3. The method of claim 2, wherein modeling the PET acquisition process yields a PET reconstructed image x nac Comprising:
modeling a PET acquisition process according to the following formula to obtain a PET reconstructed image x nac ：
Wherein,is the average value of the detected data; j is a variable index of the radioactivity distribution image space; m is the size of the radioactivity distribution image space; a is that ijt Is a system matrix; i is the variable index of a response line LOR of the sine graph of the detection data; t is the variable index of the time-of-flight TOF discrete space; x is x j Reconstructing an image for the unknown PET; l (L) ik Is a linear attenuation coefficient matrix; k is the variable index of the linear attenuation coefficient image space; k is the size of the linear attenuation coefficient image space; mu (mu) k Is a linear attenuation coefficient image, wherein mu k ＝0；α it Correction factors for each scattering point; s is S it Is the average of the scattered noise; n is the size of the sinogram of the detected data; t is the size of the time-of-flight TOF discrete space.
4. A method for scatter correction of PET images according to claim 3, characterized in that,
the scattering distribution S is determined according to the following formula:
wherein I is A Indicating that positron annihilates at any point on S1 to emit a pair of gamma photons, one photon is not scattered and moves along path S1 and is detected by detector A, the photon energy is 511keV, and the detection efficiency is epsilon AS The linear attenuation coefficient image is mu, the other photon moves along the path S2 after being scattered by the S point, the photon energy is smaller than 511keV, and the detection efficiency is epsilon' BS Linear attenuation coefficient imageMu';
I B indicating that the annihilation of the positive and negative electrons at any point on S2 emits a pair of gamma photons, one of which is not scattered and moves along the path S2 and is detected by the detector B, and the photon energy is 511keV, and the detection efficiency is epsilon BS The linear attenuation coefficient image is mu, the other photon moves along the path S1 after being scattered by the S point, the photon energy is smaller than 511keV, and the detection efficiency is epsilon A ′ B The linear attenuation coefficient image is μ';
vs is the total scattering volume, σ AS For the geometrical cross section of detector a along gamma rays, σ BS A geometric section of the detector B along the ray γ;
σ c for the compton scattering cross-section,for Compton scattering, Ω represents the scattering solid angle.
5. The method of claim 4, wherein the log-likelihood function is:
6. the method of scatter correction of a PET image of claim 5, wherein theThe method comprises the following steps:
7. the method of scatter correction of PET images of claim 6, wherein the μ is n+1 The method comprises the following steps:
8. the method of claim 7, wherein the maintaining x and μ constant maximizes the log-likelihood function to obtain an iterative scatter correction factor α it n+1 Comprising:
keeping x and mu constant, maximizing a log-likelihood function, and calculating to obtain a three-dimensional iterative scattering correction factor according to the following formula:wherein (1)>
The three-dimensional data are recombined into two-dimensional data, and a two-dimensional correction factor is applied to each layer of data to obtain a conversion formula:wherein d is the number of layers of direct incidence, +.>Representing data reorganization;
according toAlpha is obtained by reverse recombination it n+1 。
9. A scatter correction system for PET images, comprising:
image processing apparatusThe reconstruction module is used for modeling the PET acquisition process to obtain a PET reconstructed image x without attenuation correction nac ；
Mask matrix generation module, extracting x based on Canny operator nac Generating a mask matrix Q of the region of interest according to the object edge information;
a first determination module according to x nac And linear attenuation coefficient distributions μ and Q to determine an initial scattering distribution S 0 ；
The second determining module is used for determining a log-likelihood function of the detection data according to the PET images x, mu, the scattering distribution S and the scattering correction factor alpha in the iterative reconstruction process;
a first iteration module for keeping mu and alpha constant and maximizing log-likelihood function to obtain PET iteration image x j (n +1) ；
A second iteration module for keeping x and alpha constant and maximizing log-likelihood function to obtain an iteration attenuation coefficient distribution mu n+1 ；
A third iteration module for keeping x and mu constant and maximizing log-likelihood function to obtain an iteration scattering correction factor alpha it n+1 ；
Alternate iteration module for x j (n+1) 、μ n+1 And alpha it n+1 Alternating iteration is carried out, and estimated values of x, mu and alpha meeting the requirement of the maximized log-likelihood function are obtained;
the scattering correction module is used for correcting the PET image after scattering according to the estimated values of x, mu and alpha;
where n is the number of iterations.
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