CN114677455A - Method for acquiring normalization correction factor for PET image reconstruction - Google Patents
Method for acquiring normalization correction factor for PET image reconstruction Download PDFInfo
- Publication number
- CN114677455A CN114677455A CN202210358814.7A CN202210358814A CN114677455A CN 114677455 A CN114677455 A CN 114677455A CN 202210358814 A CN202210358814 A CN 202210358814A CN 114677455 A CN114677455 A CN 114677455A
- Authority
- CN
- China
- Prior art keywords
- pet
- epsilon
- correction factor
- vector
- radioactivity
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000010606 normalization Methods 0.000 title claims abstract description 134
- 238000012937 correction Methods 0.000 title claims abstract description 108
- 238000000034 method Methods 0.000 title claims abstract description 80
- 238000001514 detection method Methods 0.000 claims abstract description 126
- 238000009826 distribution Methods 0.000 claims abstract description 82
- 238000007476 Maximum Likelihood Methods 0.000 claims abstract description 44
- 230000000694 effects Effects 0.000 claims abstract description 31
- 230000008569 process Effects 0.000 claims abstract description 24
- 230000006870 function Effects 0.000 claims description 75
- 239000013598 vector Substances 0.000 claims description 71
- 230000002285 radioactive effect Effects 0.000 claims description 26
- 238000011478 gradient descent method Methods 0.000 claims description 9
- 238000005457 optimization Methods 0.000 claims description 7
- 238000012545 processing Methods 0.000 claims description 7
- 238000004590 computer program Methods 0.000 claims description 6
- 239000011159 matrix material Substances 0.000 claims description 4
- 230000009286 beneficial effect Effects 0.000 abstract 1
- 238000012636 positron electron tomography Methods 0.000 description 104
- 239000013078 crystal Substances 0.000 description 12
- 238000010586 diagram Methods 0.000 description 5
- 238000012986 modification Methods 0.000 description 5
- 230000004048 modification Effects 0.000 description 5
- 230000008859 change Effects 0.000 description 4
- 239000000284 extract Substances 0.000 description 4
- 230000006872 improvement Effects 0.000 description 3
- 230000002503 metabolic effect Effects 0.000 description 3
- 230000005855 radiation Effects 0.000 description 3
- 230000009467 reduction Effects 0.000 description 3
- 239000007787 solid Substances 0.000 description 3
- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 description 2
- 230000008878 coupling Effects 0.000 description 2
- 238000010168 coupling process Methods 0.000 description 2
- 238000005859 coupling reaction Methods 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 238000005259 measurement Methods 0.000 description 2
- 229910052710 silicon Inorganic materials 0.000 description 2
- 239000010703 silicon Substances 0.000 description 2
- 238000012879 PET imaging Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000003745 diagnosis Methods 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 230000001678 irradiating effect Effects 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
- 238000004020 luminiscence type Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000004806 packaging method and process Methods 0.000 description 1
- 238000002600 positron emission tomography Methods 0.000 description 1
- 238000005316 response function Methods 0.000 description 1
- 239000000523 sample Substances 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/008—Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T5/00—Image enhancement or restoration
- G06T5/73—Deblurring; Sharpening
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10072—Tomographic images
- G06T2207/10104—Positron emission tomography [PET]
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Nuclear Medicine (AREA)
Abstract
The invention relates to a PET image reconstruction normalization correction factor acquisition method and a PET image reconstruction method, wherein the normalization correction factor acquisition method comprises the following steps: acquiring PET detection data, a preset normalization correction factor and an initial value of radioactivity activity distribution; and constructing an objective function with the unknown numbers of the normalized correction factors and the radioactivity activity distribution, carrying out iterative solution on the objective function to ensure that the normalized correction factors are converged to the maximum likelihood estimation value, obtaining the normalized correction factors after iteration, and carrying out PET image reconstruction to obtain a reconstructed PET radioactivity activity distribution image. The invention utilizes the maximum likelihood reconstruction process to adjust the normalization factor, reduces the influence caused by the error of the traditional normalization algorithm, is beneficial to improving the uniformity of the image quality, does not need additional source cost and complex mechanical positioning equipment, and is suitable for various PET detection systems.
Description
Technical Field
The invention relates to the technical field of computers, in particular to a method for acquiring a normalization correction factor for PET image reconstruction and a PET image reconstruction method.
Background
Positron Emission tomography (pet) is a high-end nuclear medical image diagnostic device. In practice using radionuclides (e.g. of the type18F、11C, etc.) to mark the metabolic substance and inject the nuclide into the human body, and then the PET is used for carrying out functional metabolic imaging on the patient to reflect the condition of the metabolic activity of the life, thereby achieving the purpose of diagnosis.
A PET imaging system is typically a ring-shaped detection system comprising tens of thousands of detection units. Due to the influence of geometrical position and performance differences, such as the crystal luminous efficiency, the crystal package, the coupling between the crystal and PMT (photomultiplier tube) or silicon photomultiplier tube (SiPM), the electronic system, the incident angle of photon pairs, etc., the detection efficiency of the detection unit is inconsistent, so that the output of the detection unit cannot accurately reflect the intensity of the input photon beam, which inevitably introduces artifacts in the reconstruction process. In order to accurately model the detection system, the user must correct the detection efficiency of the detector in advance, i.e., normalized correction.
In the conventional normalization correction, a uniform source (such as a rod source rotating at a constant speed, a cylinder barrel source filled with an FDG solution, and a solid cylinder Ge barrel source) placed in the center of a system is used for uniformly irradiating each detection unit, detection data are processed by a model-based normalization method, intrinsic detection efficiency of a crystal, a normalization factor influenced by system geometric factors and a normalization factor related to a counting rate are respectively extracted from the data, and are finally integrated into a normalization correction factor reflecting the overall detection efficiency, and normalization correction is performed on the measurement data.
The detection efficiency of the detector can change slowly along with the change of working conditions such as time, temperature, humidity and the like, and the detection efficiency of the corresponding position can also change greatly due to the replacement of the detector module. The normalization correction needs to be done often to accurately account for variations in the performance of the PET system. However, the conventional normalization correction method has the following problems in practical application: the uniform source needs to be placed in the center of the detector to ensure that all detector units can be uniformly irradiated, the requirement on position precision is high, the operation is complex when the position is finely adjusted, and meanwhile, the radioactive irradiation risk also exists for operators; the FDG bucket source needs to be manually poured, and this process also has the risk of radioactive irradiation; whether a solid Ge source or an FDG liquid source is used, additional purchase is required, and because the radioactive source decays, repeated purchase is required for normalization correction, so that the operation cost is increased; the axial visual field of the current PET system is larger and larger, in order to ensure that a radioactive source can still uniformly irradiate all detector crystals in a normalization test, the axial size of the radioactive source is designed to be longer and longer correspondingly, so that the weight is greatly increased, and meanwhile, the positioning and moving operation is very difficult, so that the manufacturing and mechanical positioning of a uniform source are challenged more and more; the traditional normalization correction algorithm generally utilizes a Variance Reduction (Variance Reduction) technology to average and reduce noise of acquired data and extract a normalization correction factor from the acquired data, and the normalization correction process and the reconstruction process are independent from each other, so that errors generated by modeling precision deviation and noise influence in the normalization correction process are transmitted to image reconstruction, the image quality is reduced, and image artifacts are generated in severe cases.
Disclosure of Invention
Technical problem to be solved
In view of the above disadvantages and shortcomings of the prior art, the present invention provides a normalized correction factor acquisition method for PET image reconstruction and a PET image reconstruction method.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
in a first aspect, an embodiment of the present invention provides a normalized correction factor obtaining method for PET image reconstruction, including:
s10, acquiring PET detection data y for PET image reconstruction, and a preset normalization correction factor and an initial value of radioactivity distribution x for reconstructing the PET image; the PET detection data does not need to be a uniform radioactive central source, and can be data collected by a detection device of a non-uniform radioactive source or a non-central positioning radioactive source;
s20, constructing an objective function with the unknowns as a normalized correction factor and a radioactivity distribution x according to the PET detection data and based on the Poisson distribution principle, wherein the objective function is composed of a log-likelihood function with the normalized correction factor and the radioactivity distribution x as the unknowns and a penalty function R (x) with the radioactivity distribution x as the unknowns;
s30, carrying out iterative solution on the objective function according to the normalization correction factor and the initial value of the radioactivity activity distribution x, so that the normalization correction factor is converged to a maximum likelihood estimation value, and the normalized correction factor after iteration is obtained and used as a normalization correction factor for PET image reconstruction;
the maximum likelihood estimation value is a numerical value obtained by performing maximum likelihood estimation on the log-likelihood function;
and keeping the current value of the normalization factor known in iterative solution, acquiring the latest estimation result of the radioactivity activity distribution x by adopting a MAP iterative reconstruction algorithm, and then acquiring the latest estimation result of the normalization factor by adopting a gradient descent method when the latest estimation result of the radioactivity activity distribution x is kept known.
The method of the embodiment can realize the normalization correction of the detection data of various radioactive sources, and the acquisition process of the detection data does not need or specially sets a uniform central source, thereby being greatly convenient for practical operation, such as using clinical scanning data and the like.
Optionally, the normalizing correction factor comprises: a geometric normalization factor vector f and an intrinsic detection efficiency vector epsilon of the PET system;
the objective function Φ (y | x, f, ε) is:
Φ (y | x, f, ∈) ═ L (y | x, f, ∈) - β · r (x); formula (A1)
R (x) is a penalty function; β is a non-negative weight factor; l (y | x, f, epsilon) is the log-likelihood function of the PET detection data;
the log-likelihood function L (y | x, f, ε) of the PET detection data is:
wherein the PET radioactivity distribution x ═ x1,x2,…,xM]TAnd the intrinsic detection efficiency vector ε ═ ε1,ε2,…,εN]TAnd the geometric normalization factor vector f is ═ f11,f12,…,fNN]T，y＝[y11,y12,…,yNN]TRepresenting data actually detected, a ═ aikj]Taking j as 1 … … M as a system matrix, and taking j as a position of a spatial point source in the PET system; y isikRepresenting photon pair instances collected by detector i and detector k; p is a radical ofrRefers to the poisson probability distribution; epsiloniAnd εkExpressed as intrinsic detection efficiency of detector i and detector k; f. ofikIs a geometric normalization factor.
Optionally, the S30 includes:
s31, based on the objective function, adopting a formula (A3) to obtain a maximum likelihood estimation value of the radioactivity activity distribution x;
s32, maximizing the log-likelihood function L (y | x, f, epsilon) aiming at the geometric normalization factor vector f to obtain the geometric normalization factor fikThe maximum likelihood estimate of (a), as in equation (a 4);
rikmean values representing random noise and scatter noise for detector i and detector k;
s33, maximizing a log-likelihood function L (y | x, f, epsilon) according to the intrinsic detection efficiency vector epsilon to obtain the intrinsic detection efficiency epsiloniThe maximum likelihood estimate of (a), as in equation (a 5);
s34, when the radioactivity distribution x is unknown based on the known initial values of the geometric normalization factor vector f and the intrinsic detection efficiency vector epsilon, maximizing a target function phi (y | x, f, epsilon) by adopting a MAP iterative reconstruction algorithm to obtain the latest estimation result of the radioactivity distribution x;
based on the latest estimation result of the known radioactivity activity distribution x and the initial value of the intrinsic detection efficiency epsilon, when the geometric normalization factor vector f is unknown, iteratively solving the geometric normalization factor and maximizing the objective function phi (y | x, f, epsilon), and optimizing to obtain the latest estimation result of the geometric normalization factor vector f;
iteratively solving intrinsic detection efficiency and maximizing a target function phi (y | x, f, epsilon) based on the latest estimation result of the known radioactivity distribution x and the latest estimation result of the geometric normalization factor vector f, and optimizing to obtain the latest estimation result of the intrinsic detection efficiency vector epsilon;
iteration is carried out in the alternating mode, so that f in the geometric normalization factor vector fikConvergence to a geometric normalization factor fikOf the vector of intrinsic detection efficiencies, epsilon in the vector of intrinsic detection efficienciesiConvergence to intrinsic detection efficiency epsiloniThe maximum likelihood estimate of (2).
Optionally, based on the latest estimation result of the known radioactivity distribution x and the initial value of the intrinsic detection efficiency vector epsilon, when the geometric normalization factor vector f is unknown, performing iterative processing by adopting a gradient descent method and a first search step length and maximizing the objective function phi (y | x, f, epsilon), and optimizing to obtain the latest estimation result of the geometric normalization factor vector f;
and based on the latest estimation result of the known radioactivity distribution x and the latest estimation result of the geometric normalization factor vector f, performing iterative processing by adopting a gradient descent method and a second search step length and maximizing the objective function phi (y | x, f, epsilon), and optimizing to obtain the latest estimation result of the intrinsic detection efficiency vector epsilon.
Optionally, the S34 includes:
the radioactivity activity distribution x is a result reconstructed by other algorithms, and if the radioactivity activity distribution x in each iteration is a known fixed value, the geometric normalization factor and the intrinsic detection efficiency are iterated alternately;
alternatively, the first and second electrodes may be,
the intrinsic detection efficiency vector epsilon is a designated numerical value, and the intrinsic detection efficiency epsilon in each iteration is a known fixed value, so that a geometric normalization factor f and the radioactivity distribution x are iterated alternately;
or, if the geometric normalization factor vector f is a designated numerical value and the geometric normalization factor in each iteration is a known fixed value, the intrinsic detection efficiency and the radioactivity distribution x are alternately iterated.
In the embodiment, the sequence of the three variables is not fixed, so that free combination can be realized, and adjustment and setting can be performed according to actual needs.
Optionally, the S30 further includes:
s35, carrying out normalization processing on the geometric normalization factor vector f of iterative convergence according to the following formula (A6) to obtain a geometric normalization correction factor f for PET image reconstructionik；
Normalizing the intrinsic detection efficiency epsilon of iterative convergence according to the following formula (A6) to obtain the intrinsic detection efficiency epsilon for PET image reconstructioni；
Optionally, S34 includes:
geometric normalized correction factor fikIs the formula (a 7):
search step size
m represents the number of iterations;
intrinsic detection efficiency epsiloniIs the formula (A8):
wherein the step size of the search
n denotes the number of iterations o
Optionally, the initial value of the normalized correction factor for reconstructing the PET image is preset as a PET system use parameter value;
if the PET detection data used for the PET image reconstruction is data of a reconstructed image, taking the radioactivity activity distribution x of the reconstructed image as an initial value of the radioactivity activity distribution x;
if the PET detection data used for PET image reconstruction is data of an unrecognized image, the initial value of the radioactivity activity distribution x is a given value. It will be appreciated that a fully spatially uniform value is typically chosen, such as all pixels initially set to 1000+ -150.
In a second aspect, an embodiment of the present invention further provides a PET image reconstruction method, which includes:
acquiring PET detection data for PET image reconstruction;
acquiring a normalized correction factor for PET image reconstruction by using the method for acquiring the normalized correction factor for PET image reconstruction in the first aspect;
and reconstructing to obtain the radioactivity distribution x of the corresponding PET image based on the normalized correction factor and the PET detection data.
In a third aspect, embodiments of the present invention further provide a PET system, including: a memory and a processor; the memory stores computer program instructions, and the processor executes the computer program instructions stored in the memory, in particular, executes the PET image reconstruction method according to the second aspect.
(III) advantageous effects
The method of the embodiment of the invention simultaneously carries out the joint maximum likelihood estimation on the PET radioactive image and the normalization correction factor in the reconstruction process, iteratively extracts the normalization correction factor, and is applied to the reconstruction of the PET radioactive activity distribution image in real time.
The method extracts the normalization factor and simultaneously satisfies the maximum likelihood estimation of the PET radioactivity distribution, the normalization correction process and the image reconstruction process are fused together, the maximum likelihood reconstruction process is utilized to simultaneously estimate the normalization factor and the PET radioactivity distribution, the variance is reduced, the influence of the error of the algorithm on the image reconstruction is reduced, and the improvement of the image quality uniformity is facilitated. The method has the advantages that the influence caused by errors of the traditional normalization algorithm is reduced, the improvement of the image quality uniformity is facilitated, and the process does not need extra source cost or complex mechanical positioning equipment.
Compared with the normalization correction method in the prior art, the method does not need additional source cost and complex mechanical positioning devices, and is suitable for various PET detection systems, such as long-axis PET systems. The method provided by the embodiment of the invention has no limitation on the radioactive source, does not require a uniform radioactive source any more, can also perform normalization correction by using the patient data of conventional scanning, and does not limit the type and other requirements of PET detection data.
Drawings
Fig. 1 is a schematic flowchart of a normalized correction factor obtaining method for PET image reconstruction according to an embodiment of the present invention;
FIG. 2 is a schematic representation of a PET radioactively reconstructed image obtained by joint maximum likelihood estimation using the method of the present invention;
FIG. 3 is a schematic diagram of the intrinsic detection efficiency obtained by joint maximum likelihood estimation using the method of the present invention;
fig. 4 is a schematic diagram of geometric normalization factors obtained by joint maximum likelihood estimation using the method of the present invention.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
Embodiments of the present invention achieve the goal of optimizing the PET system normalization correction factor independently of the time-of-flight measurements, without regard to the time-of-flight dimension as described below.
In addition, the method for acquiring the normalization correction factor of the embodiment of the invention simultaneously performs the joint maximum likelihood estimation on the PET radioactive image and the normalization correction factor in the reconstruction process, iteratively extracts the normalization correction factor, and is applied to the PET radioactive image reconstruction in real time, thereby saving the process of algorithm processing and improving the quality of the reconstructed image. The vectors are shown in italics and bold in the following examples. In addition, in some embodiments, the estimated values are used, in some embodiments, the estimated results are used, which means they are consistent, and the PET image reconstruction is the reconstruction of the PET radioactivity distribution image.
Example one
As shown in fig. 1, an embodiment of the present invention provides a normalized correction factor obtaining method for PET image reconstruction, and an implementation subject of the method of the present embodiment may be a control device/electronic device of the normalized correction factor obtaining method for PET image reconstruction, the control device may be integrated in an acquisition device of a PET system or a separate computer processing device, and the normalized correction factor obtaining method includes the following steps:
s10, acquiring PET detection data for PET image reconstruction, a preset normalization correction factor for PET image reconstruction and an initial value of radioactivity distribution x;
in this step, the PET detection data is data collected by a detection device for a uniform radiation source, a non-uniform radiation source, or a non-centrally located radiation source. Generally, in the prior art, the PET detection data must be limited to data acquired by the detection device of the uniform radioactive source, but in the embodiment, data acquired by the detection device of the non-uniform radioactive source can be selected, so that the quality of the PET image reconstructed by the method of the embodiment is high, the requirement is met, and the uniformity of the reconstructed image can be realized.
S20, constructing an objective function phi (y | x, f, epsilon) with unknowns as a normalization correction factor (such as a geometric normalization factor f and the intrinsic detection efficiency epsilon of the PET system) and a radioactivity distribution x according to the PET detection data and based on the principle of Poisson distribution, wherein the objective function consists of a log-likelihood function with the normalization correction factor and the radioactivity distribution x as unknowns and a penalty function R (x) with the radioactivity distribution x as unknowns;
s30, according to the normalization correction factor and the initial value of the radioactivity activity distribution x, carrying out iterative solution on the objective function phi (y | x, f, epsilon) to make the normalization correction factor converge to a maximum likelihood estimation value, and obtaining the iterative normalization correction factor as the normalization correction factor for PET image reconstruction;
the maximum likelihood estimation value is a numerical value obtained by performing maximum likelihood estimation on a log-likelihood function;
and keeping the current value of the normalization factor known in iterative solution, acquiring the latest estimation result of the radioactivity activity distribution x by adopting a MAP iterative reconstruction algorithm, and then acquiring the latest estimation result of the normalization factor by adopting a gradient descent method when the latest estimation result of the radioactivity activity distribution x is kept known.
Compared with the normalization correction method in the prior art, the normalization factor is extracted and the maximum likelihood estimation of the PET radioactivity distribution is satisfied, the normalization correction process can be fused with the image reconstruction process, the maximum likelihood reconstruction process is used for adjusting the normalization factor, the influence caused by the error of the variance reduction algorithm is reduced, and the improvement of the image quality uniformity is facilitated.
The normalization correction method of the embodiment has no limitation on the radioactive source, does not need a uniform radioactive source, can perform normalization correction by using patient data of conventional scanning, does not need additional source cost or complex mechanical centering equipment, and is suitable for various PET detection systems, such as a long-axis PET system.
Example two
In the method for acquiring the normalization correction factor, joint maximum likelihood estimation is simultaneously performed on the PET radioactive image and the normalization correction factor in the reconstruction process, the normalization correction factor is extracted in an iterative manner, and the method is applied to PET image reconstruction in real time.
For a better understanding of the method of the first embodiment, the following detailed description of the various steps and principles is provided:
the first step is as follows: PET detection data for PET image reconstruction is acquired.
The second step is that: the PET acquisition process can be modeled as the following equation:
the meaning of each parameter in the formula is as follows:
x＝[x1,x2,…,xM]TRepresenting the unknown PET radioactivity distribution, and M is the size of the radioactivity distribution image space.
A＝[Aikj]The probability that a spatial position point source j is detected by a detector i and a detector k in the PET system simultaneously is expressed in a mathematical form as a system matrix, and the probability comprises a geometrical detection efficiency factor, a photon detection point diffusion factor and a photon attenuation factor in the detection process of photon pairs. The geometric detection efficiency, expressed as the probability of a photon pair arriving at the detector pair surface, depends on the variation of the geometric solid angle of the detector pair with respect to each pixel position; the photon point spread function is expressed as a response function of the detector crystal to photon incidence; photon attenuation is expressed as the probability that a photon pair will decay before being detected.
In addition, to reduce the requirement of statistical data volume, the normalized correction parameter evaluation usually employs a model-based method. The normalized correction parameters can be modeled as:
wherein epsiloniAnd εkExpressed as the intrinsic detection efficiency of detector i and detector k, to correct for inconsistencies in detection efficiency of the crystal due to individual luminescence efficiencies, crystal packaging, coupling of the crystal to a photomultiplier tube (PMT) or silicon photomultiplier tube (SiPM), electronics systems, and the like. Generally, before the detection device leaves the factory, normalization correction is performed to obtain the detection efficiency of the system, but the detection efficiency changes along with the system operation, so that the detection efficiency needs to be updated regularly.
Geometric normalization factor fikReflecting the non-uniformity of detection efficiency of photon pairs detected by detectors i and k due to the geometry of the PET system, depends on the position of the two detectors, the angle of incidence of the detector line with respect to the detector plane (i.e., the actual surface of the detectors), and the distance of the detector line from the center of the field of view of the scanner. It will be appreciated that for a PET system, the normalized correction is to correct for the above-described effects of detector detection efficiency and system geometry on the acquired data. In addition, the correction factor (dead time correction factor, pile-up effect correction factor) related to the count rate is determined by other experiments, which are not referred to in the embodiments of the present invention. Namely, the intrinsic detection efficiency and the geometric normalization factor to be solved are independent of the activity of the radioactive source, namely independent of the counting rate acquired in real time.
The third step: construction ofAn objective function with unknowns.
1) The PET detection data obeys Poisson distribution, and the unknown number is the PET radioactivity distribution x ═ x1,x2,…,xM]TAnd intrinsic detection efficiency e ═ e1,ε2,…,εN]TAnd the geometric normalization factor f ═ f11,f12,…,fNN]TThen, the log-likelihood function (log-likelihood function) of the probe data is expressed as:
y in formula (3) [ < y >11,y12,…,yNN]TRepresenting the actual detected data.
2) Substituting equation (1) into equation (3), ignoring terms that are not related to unknowns, the log-likelihood function can be written as:
3) in order to improve the data ill-conditioned problem in the log-likelihood function solving process, the objective function can be adjusted by means of an explicit regularization process, i.e. a penalty function r (x) is added to the log-likelihood function to selectively penalize certain undesired features, and the maximum likelihood solution with penalty term is calculated.
The corresponding objective function is:
Φ(y|x,f,ε)＝L(y|x,f,ε)-β·R(x) (5)
beta is a non-negative weight factor that is used to balance the importance of the log-likelihood function and the penalty function.
The fourth step: and determining iteration convergence information and an iteration formula of each unknown number aiming at the target function.
1) When the unknown number of the objective function, such as the PET radioactivity distribution x, is solved iteratively, the regularized maximum likelihood estimation can be obtained by the maximum posterior probability algorithm map (maximum a posteriori):
of course, if the parameter β is 0, the formula (6) becomes the conventional maximum Likelihood Expectation maximization algorithm mlem (maximum Likelihood Expectation maximization optimization) or the ordered Subset Expectation maximization algorithm osem (ordered Subset Expectation maximization optimization) thereof for iterative solution.
2) The normalized correction factor is composed of a geometric normalization factor vector f and an intrinsic detection efficiency vector epsilon, and is characterized by normalized calibration parameters of the detection data y, and the optimized objective function is a log-likelihood function L (y | x, f, epsilon).
The scalar penalty function r (x) is only related to the PET radioactivity distribution x, is independent of the normalized correction factor, and is therefore negligible in the derivation operation for the normalized correction factor.
2-1) first, the log-likelihood function is maximized for the geometric normalization factor vector f (4) to get fikMaximum likelihood estimation of (2):
both scattered and random photons are incident on the detector surface at a wide range of angles, the incident angle of the photon is not limited by the detector location, unlike the case of real photon pairs. Any geometric factors of scattering and random events are therefore averaged over a large angular range and can effectively be ignored, so that rik/fik≈rik. Whereby fikThe maximum likelihood estimate of (c) may be approximated as:
2-2) secondly, selecting a gradient descent method (gradient) as an optimization algorithm for iteratively solving a geometric normalization factor vector f, recursively approximating the maximum likelihood solution of the objective function along the gradient descent direction, wherein the iterative formula can be expressed as:
in the formula, α represents a search step in the gradient direction, and m represents the number of iterations. Since the objective function L (y | x, f, epsilon) is known, the step size variable alpha of the iterative function needs to be solved. Transform equation (8):
comparing equation (10) with equation (9), the iterative equation can be derived as:
wherein the step size of the search
From equation (11), when the iteration converges, the geometric normalization factor fikConverge to its maximum likelihood estimate (8).
2-3) subsequently, a log-likelihood function (4) is maximized for the intrinsic detection efficiency vector ε to obtain εiMaximum likelihood estimation of (2):
2-4) further, selecting a gradient descent method (gradient) as an optimization algorithm for iteratively solving the intrinsic detection efficiency vector epsilon, and recursively approximating the maximum likelihood solution of the objective function epsilon along the gradient descent directioniThe iterative formula can be expressed as:
in the formula, eta represents a search step in the gradient direction, and n represents the number of iterations. Since the objective function L (y | x, f, ε) is known, the step size variable η of the iterative function needs to be solved. Transform equation (12)
Comparing equation (14) with equation (13), the iterative equation can be derived as:
wherein the step size of the search
From equation (15), when the iteration converges, the intrinsic detection efficiency εiConverge to its maximum likelihood estimate (12).
The fifth step: iterating based on the target function, the iteration convergence information of each unknown number and the iteration formula
And (6) solving.
In order to obtain estimates of the unknown PET radioactivity distribution x and the vectors f, epsilon, an objective function (5) of its joint distribution needs to be optimized. Since the objective function is a complex function for the unknowns x, f, and epsilon, the equation (5) is difficult to obtain an analytic solution, and thus an iterative algorithm is required to gradually approximate the optimal solution. For the feasibility of the algorithm implementation, the optimization procedure needs to be simplified and explained as follows:
firstly, keeping vectors f and epsilon as constants, maximizing an objective function aiming at the PET radioactivity distribution x, and adopting a traditional MAP iterative reconstruction algorithm;
then, selecting and keeping the PET radioactivity distribution x and the intrinsic detection efficiency vector epsilon as constants, maximizing an objective function aiming at the geometric normalization factor vector f, and adopting an iterative formula (11);
and finally, selecting the PET radioactivity distribution x and the geometric normalization factor vector f as constants, maximizing an objective function aiming at the intrinsic detection efficiency vector epsilon, and adopting an iterative formula (15).
The maximization operation is performed alternately as described above, and the normalization correction parameters are continuously corrected to approximate to the real normalization condition, so as to finally obtain the estimated values of x, f, and epsilon meeting the requirement of the maximization objective function.
It should be emphasized that the iteration sequence of the three unknowns is not limited in this patent, and the PET radioactivity distribution x may be iteratively solved first, then the intrinsic detection efficiency vector epsilon is iteratively solved, and finally the geometric normalization factor vector f is iteratively solved. The intrinsic detection efficiency vector epsilon can also be selected to use the system default results without solving, and only the PET radioactivity distribution x and the geometric normalization factor vector f are alternately solved iteratively. Alternatively, the result x of the conventional reconstruction may be used without performing the solution, and only the intrinsic detection efficiency vector epsilon and the geometric normalization factor vector f are iteratively solved alternately.
It should be noted that the iteration initial value of the geometric normalization factor vector f or the intrinsic detection efficiency vector epsilon may select the parameter result used before the system, or may select all the parameter values to be 1.
The geometric normalization factor vector f or the intrinsic detection efficiency vector epsilon iteratively solves the maximum likelihood value, and no requirement is made on the radioactivity activity distribution source in the solving process, namely, normalization correction and parameter optimization can be carried out by using any radioactive object, for example, by using patient scanning data.
And a sixth step: intrinsic detection efficiency of iteration solution of the fifth stepεi And geometric normalization factorfik Is subjected to normalization And obtaining a normalized correction factor for reconstructing the PET image.
In equations (1) and (2), if the geometric normalization factor f or the intrinsic detection efficiency ε is multiplied by a constant, the reconstructed PET radioactivity distribution x divided by the same constant can still yield the same measured average. This means that the normalized correction factor estimated by the above algorithm may have a constant multiple with the true normalized correction factor, and this constant cannot be determined by the algorithm itself. However, since the normalization correction factor corrects the relative change of the detection efficiency, the average value can be set to 1, and the information can be used to calculate the geometric normalization factor fikOr intrinsic detection efficiency epsiloniCarrying out normalization, namely:
the variable may be updated after each iteration or only updated in the last iteration, which is not limited in this embodiment.
The seventh step: obtaining the PET radioactivity activity based on the normalization correction factor of the PET image reconstruction
PET image of distribution x.
As shown in fig. 2, fig. 2 is a schematic diagram showing a PET radioactive reconstruction image obtained by using the above method for joint maximum likelihood estimation, fig. 3 is a schematic diagram showing intrinsic detection efficiency obtained by using the above method for joint maximum likelihood estimation, and fig. 4 is a schematic diagram showing a geometric normalization factor obtained by using the above method for joint maximum likelihood estimation.
EXAMPLE III
The embodiment provides a PET image reconstruction method, which includes:
acquiring PET detection data for PET image reconstruction;
acquiring a normalized correction factor for PET image reconstruction by using the method for acquiring the normalized correction factor for PET image reconstruction according to the first embodiment or the second embodiment;
and reconstructing to obtain the radioactivity distribution x of the corresponding PET image based on the normalized correction factor and the PET detection data.
In addition, an embodiment of the present invention further provides a PET system, which includes: a memory and a processor; the memory stores computer program instructions, and the processor executes the computer program instructions stored in the memory, in particular, executes the above PET image reconstruction method.
In general, the above-described PET image reconstruction method may be specifically performed for a control device in a PET system.
It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the terms first, second, third and the like are for convenience only and do not denote any order. These words are to be understood as part of the name of the component.
Furthermore, it should be noted that in the description of the present specification, the description of the term "one embodiment", "some embodiments", "examples", "specific examples" or "some examples", etc., means that a specific feature, structure, material or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, the claims should be construed to include preferred embodiments and all such variations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include such modifications and variations.
Claims (10)
1. A method of normalized correction factor acquisition for PET image reconstruction, comprising:
s10, acquiring PET detection data y for PET image reconstruction, a preset normalization correction factor for PET image reconstruction and an initial value of radioactivity distribution x; the PET detection data is data collected by a detection device of a uniform radioactive source, a non-uniform radioactive source or a non-central positioning radioactive source;
s20, constructing an objective function with the unknowns as a normalized correction factor and a radioactivity distribution x according to the PET detection data and based on the Poisson distribution principle, wherein the objective function is composed of a log-likelihood function with the normalized correction factor and the radioactivity distribution x as the unknowns and a penalty function R (x) with the radioactivity distribution x as the unknowns;
s30, carrying out iterative solution on the objective function according to the normalization correction factor and the initial value of the radioactivity activity distribution x, so that the normalization correction factor is converged to a maximum likelihood estimation value, and the normalized correction factor after iteration is obtained and used as a normalization correction factor for PET image reconstruction;
the maximum likelihood estimation value is a numerical value obtained by performing maximum likelihood estimation on the log-likelihood function;
and keeping the current value of the normalization factor known in iterative solution, acquiring the latest estimation result of the radioactivity activity distribution x by adopting a MAP iterative reconstruction algorithm, and then acquiring the latest estimation result of the normalization factor by adopting a gradient descent method when the latest estimation result of the radioactivity activity distribution x is kept known.
2. The normalized correction factor acquisition method according to claim 1,
the normalized correction factor includes: a geometric normalization factor vector f and an intrinsic detection efficiency vector epsilon of the PET system;
the objective function Φ (y | x, f, ε) is:
Φ (y | x, f, ∈) ═ L (y | x, f, ∈) - β · r (x); formula (A1)
R (x) is a penalty function; β is a non-negative weight factor; l (y | x, f, epsilon) is the log-likelihood function of the PET detection data;
the log-likelihood function L (y | x, f, ε) of the PET detection data is:
wherein the PET radioactivity distribution x ═ x1,x2,…,xM]TAnd the intrinsic detection efficiency vector ε ═ ε1,ε2,…,εN]TAnd the geometric normalization factor vector f is ═ f11,f12,…,fNN]T，y＝[y11,y12,…,yNN]TRepresenting actually detected data, A ═ Aikj]Taking j as 1 … … M as a system matrix, and taking j as a position of a spatial point source in the PET system; y isikRepresenting photon pair instances collected by detector i and detector k; p is a radical ofrRefers to the poisson probability distribution; epsiloniAnd εkExpressed as intrinsic detection efficiency of detector i and detector k; f. ofikIs a geometric normalization factor.
3. The normalized correction factor acquisition method according to claim 2, wherein the S30 includes:
s31, based on the objective function, adopting a formula (A3) to obtain a maximum likelihood estimation value of the radioactivity activity distribution x;
s32, maximizing the log-likelihood function L (y | x, f, epsilon) aiming at the geometric normalization factor vector f to obtain the geometric normalization factor fikThe maximum likelihood estimate of (a), as in equation (a 4);
rikmean values representing random noise and scatter noise for detector i and detector k;
s33, maximizing a log-likelihood function L (y | x, f, epsilon) according to the intrinsic detection efficiency vector epsilon to obtain the intrinsic detection efficiency epsiloniThe maximum likelihood estimate of (a), as in equation (a 5);
s34, when the radioactivity distribution x is unknown based on the known initial values of the geometric normalization factor vector f and the intrinsic detection efficiency vector epsilon, maximizing a target function phi (y | x, f, epsilon) by adopting a MAP iterative reconstruction algorithm to obtain the latest estimation result of the radioactivity distribution x;
based on the latest estimation result of the known radioactivity activity distribution x and the initial value of the intrinsic detection efficiency vector epsilon, when the geometric normalization factor vector f is unknown, iteratively solving the geometric normalization factor and maximizing the objective function phi (y | x, f, epsilon), and optimizing to obtain the latest estimation result of the geometric normalization factor vector f;
iteratively solving intrinsic detection efficiency and maximizing a target function phi (y | x, f, epsilon) based on the latest estimation result of the known radioactivity distribution x and the latest estimation result of the geometric normalization factor vector f, and optimizing to obtain the latest estimation result of the intrinsic detection efficiency vector epsilon;
iteration is carried out in the alternating mode, so that f in the geometric normalization factor vector fikConvergence to a geometric normalization factor fikOf the vector of intrinsic detection efficiencies, epsilon in the vector of intrinsic detection efficienciesiConvergence to intrinsic detection efficiency epsiloniThe maximum likelihood estimate of (2).
4. The normalized correction factor acquisition method according to claim 3,
based on the latest estimation result of the known radioactivity distribution x and the initial value of the intrinsic detection efficiency vector epsilon, when the geometric normalization factor vector f is unknown, the latest estimation result of the geometric normalization factor vector f is obtained through optimization by adopting a gradient descent method and a first search step length iteration process and maximizing a target function phi (y | x, f, epsilon);
and based on the latest estimation result of the known radioactivity distribution x and the latest estimation result of the geometric normalization factor vector f, performing iterative processing by adopting a gradient descent method and a second search step length and maximizing the objective function phi (y | x, f, epsilon), and optimizing to obtain the latest estimation result of the intrinsic detection efficiency vector epsilon.
5. The normalized correction factor acquisition method according to claim 3 or 4, wherein the S34 includes:
the radioactivity activity distribution x is a result reconstructed by other algorithms, and if the radioactivity activity distribution x in each iteration is a known fixed value, the geometric normalization factor and the intrinsic detection efficiency are iterated alternately;
alternatively, the first and second electrodes may be,
and if the intrinsic detection efficiency vector epsilon is a designated numerical value and the intrinsic detection efficiency vector epsilon in each iteration is a known fixed value, alternately iterating the geometric normalization factor and the radioactivity distribution x.
6. The normalized correction factor acquisition method according to claim 3 or 4, wherein the S30 further includes:
s35, carrying out normalization processing on the geometric normalization factor vector f of iterative convergence according to the following formula (A6) to obtain a geometric normalization correction factor f for PET image reconstructionik；
Normalizing the intrinsic detection efficiency vector epsilon of iterative convergence according to the following formula (A6) to obtain the intrinsic detection efficiency epsilon for PET image reconstructioni；
7. The normalized correction factor acquisition method according to claim 3 or 4, wherein S34 includes:
geometric normalized correction factor fikIs the formula (a 7):
search step size
m represents the number of iterations;
intrinsic detection efficiency epsiloniIs the formula (A8):
wherein the step size of the search
n represents the number of iterations.
8. The normalized correction factor acquisition method according to any one of claims 1 to 4, wherein an initial value of the normalized correction factor for reconstructing the PET image is a PET system use parameter value;
if the PET detection data used for the PET image reconstruction is data of a reconstructed image, taking the radioactivity activity distribution x of the reconstructed image as an initial value of the radioactivity activity distribution x;
if the PET detection data used for the PET image reconstruction is data of an unrereconstructed image, the initial value of the radioactivity distribution x is a given value.
9. A PET image reconstruction method, comprising:
acquiring PET detection data for PET image reconstruction;
acquiring a normalized correction factor for PET image reconstruction by using the method for acquiring a normalized correction factor for PET image reconstruction according to any one of claims 1 to 8;
and reconstructing to obtain the radioactivity distribution x of the corresponding PET image based on the normalized correction factor and the PET detection data.
10. A PET system, comprising: a memory and a processor; the memory has stored therein computer program instructions, and the processor executes the computer program instructions stored in the memory, in particular to perform the PET image reconstruction method of claim 9.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210358814.7A CN114677455A (en) | 2022-04-06 | 2022-04-06 | Method for acquiring normalization correction factor for PET image reconstruction |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210358814.7A CN114677455A (en) | 2022-04-06 | 2022-04-06 | Method for acquiring normalization correction factor for PET image reconstruction |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN114677455A true CN114677455A (en) | 2022-06-28 |
Family
ID=82078987
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210358814.7A Pending CN114677455A (en) | 2022-04-06 | 2022-04-06 | Method for acquiring normalization correction factor for PET image reconstruction |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114677455A (en) |
-
2022
- 2022-04-06 CN CN202210358814.7A patent/CN114677455A/en active Pending
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Tong et al. | Image reconstruction for PET/CT scanners: past achievements and future challenges | |
| US8098916B2 (en) | System and method for image-based attenuation correction of PET/SPECT images | |
| Moehrs et al. | Multi-ray-based system matrix generation for 3D PET reconstruction | |
| CN108615250B (en) | Image reconstruction method, device, system and computer readable storage medium | |
| JP7118048B2 (en) | TOF PET image reconstruction using locally modified time-of-flight (TOF) kernels | |
| CN105894525B (en) | Positron emission tomography detector correction method | |
| US10049446B2 (en) | Accelerated statistical iterative reconstruction | |
| WO2014171539A1 (en) | X-ray computed tomography device and correction method | |
| US10126439B2 (en) | Reconstruction with multiple photopeaks in quantitative single photon emission computed tomography | |
| US7915578B2 (en) | Method and apparatus for correcting scattering in SPECT imaging | |
| CN110717951B (en) | cGANs-based PET image direct reconstruction method | |
| US8755586B2 (en) | Image reconstruction including shift-variant blur compensation | |
| CN114943784A (en) | Correction method and system of scanning equipment | |
| WO2020118828A1 (en) | Gradient domain-based low-dose pet image reconstruction method and apparatus, device, and medium | |
| US10102650B2 (en) | Model-based scatter correction for non-parallel-hole collimators | |
| US20060065838A1 (en) | Re-binning method for nuclear medicine imaging devices | |
| US20230058112A1 (en) | Machine learning-based scintillator resonse modelling for increased spatial resolution in nuclear imaging | |
| CN114677455A (en) | Method for acquiring normalization correction factor for PET image reconstruction | |
| JP7302737B2 (en) | List Mode Image Reconstruction Method and Nuclear Medicine Diagnostic Apparatus | |
| US11961164B2 (en) | Continuous bed motion acquisition with axially short phantom for PET imaging system setup and quality control | |
| CN110706175B (en) | Method, system, readable storage medium and device for generating PET correction coefficient | |
| Manglos et al. | Attenuation compensation of cone beam SPECT images using maximum likelihood reconstruction | |
| WO2023241722A1 (en) | Methods and systems for image reconstruction | |
| US20230237638A1 (en) | Apparatus and methods for unsupervised image denoising using double over-parameterization | |
| Brown et al. | Iterative concurrent reconstruction algorithms for emission computed tomography |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |