JP2011002306A - Iterative image reconstruction method for pet system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To solve the problem wherein sensitivity correction has been insufficient in conventional iterative image reconstruction methods with a PSF model incorporated.SOLUTION: A point radiation source is arranged in a detector ring, and radiation is measured by a plurality of PET detectors positioned in the direction of one tangent of the detector ring 1 to acquire projection data (S1). The projection data is approximated by the Gaussian function separately on the right and left of its peak position to determine a left-side standard deviation σand a right-side standard deviation σ(S2), and t values of σand σare plotted at radial positions of corresponding PET detectors to model σand σ, as functions of radial positions (S3). A normalization coefficient of the Gaussian function is modeled as a function of a radial position through the use of σand σ(S4), and modelled σand σand the Gaussian function having the normalization coefficient are incorporated to a system matrix to improve an iterative image reconstruction method (S5). A reconstructed image is generated through the use of a successive approximation image reconstruction method (S6).

Description

  The present invention relates to a successive approximation image reconstruction method used in a PET (Positron Emission Tomography) apparatus.

  A PET apparatus is known as one of medical image diagnostic apparatuses. The PET device is a device for measuring a subject to which a medicine containing an RI radiation source (positron emitting nuclide) is administered, imaging a body distribution of the RI radiation source, and viewing a biological function. It is applied to research and clinical tests.

  The PET apparatus includes a detector ring row in which a plurality of detector rings in which a large number of PET detectors are arranged on the circumference are stacked, and a medicine containing an RI radiation source in an inner opening of the detector ring row The subject who received the administration of is placed. Then, the positrons emitted from the RI source in the subject are immediately combined with nearby electrons, whereby γ ray pairs are emitted in directions opposite to each other by 180 °. The emitted γ-ray pairs are simultaneously counted by the detector ring array, and the RI line that radiates γ-rays on a line segment (referred to as a coincidence line (LOR)) connecting the two PET detectors simultaneously counted. A source is considered to exist. The PET apparatus collects such coincidence data, reconstructs a distribution image (PET image) of the RI radiation source in the subject based on the collected coincidence data, and displays it on the display.

  As a conventional PET image reconstruction method, a successive approximation image reconstruction method has been proposed so far. The successive approximation image reconstruction method is a reconstruction method that reduces statistical noise in consideration of the statistical properties of noise, and is an effective image for a PET apparatus that has a small amount of data and noise is conspicuous and a sharp image is difficult to obtain. It is a reconstruction method.

また、ａ_ｉｊはＰＥＴ装置の検出特性を表すもので、システムマトリックスと呼ばれる。 In the successive approximation image reconstruction method, estimated projection data is created by calculation from the estimated image, and this is directly compared with measured projection data, the difference is evaluated by some method, and the image is corrected. It is common.
Hereinafter, the algorithm of the successive approximation image reconstruction method will be briefly described. Now, as shown in FIG. 7, the target area is in one circle, this area is composed of J pixels, and the image vector is represented by x ↑ (when the symbol “↑” is appended to the letter. Represents a vector display, and so on.) Let each pixel value of that component be x _j . Further, it is assumed that there are I projection data in total, the projection data vector is y ↑, and each projection value of the component is y _i . Furthermore, the probability that the source of the pixel x _j is detected in the projection y _i is represented by a _ij . a _ij represents a detection characteristic of the PET apparatus and is called a system matrix.
At this time, the component of the estimated projection data z ⁽ⁿ⁾ obtained from the image x ⁽ⁿ⁾ obtained by the n-th approximation is given by the following equation.

A _ij represents the detection characteristic of the PET apparatus and is called a system matrix.

Then, as an algorithm for determining the n-th successive approximation image ^{x (n)} and (n + 1) th successive approximation image ^{x (n + 1),} for example, ML-EM (maximum likelihood expectation maximization) method, OSEM (ordered subset ML -EM) method, RAMLA (row-action maximization-likelihood) method and DRAMA (dynamic RAMLA) method.

ここで、Ｓ_ｍは１つのサブセットに属する投影の集合、ｍ（＝０，１，・・・、Ｍ−１）はサブセットの番号、Ｍはサブセット数である。例えば、投影データの測定方向が２５６である場合、全体をＭ＝１６個のサブセットに分割すると、各サブセットには、１６（＝２５６／１６）方向の投影データが含まれる。各サブセット内の投影方向はなるべく広い範囲に分布するように選択され、画像修正の順序は、前回のサブセットからなるべく離れた方向のサブセットが順次選ばれるように選択される。そして、この反復式から最適解ｘ_ｉを求めることによって再構成画像が得られる。 For example, the OSEM method divides projection data in a number of directions into several subsets, corrects the image for each subset, and makes an approximation once when the correction is completed for all subsets. The algorithm of this method is given by

Here, S _m is a set of projections belonging to one subset, m (= 0, 1,..., M−1) is a subset number, and M is the number of subsets. For example, when the measurement direction of projection data is 256, when the whole is divided into M = 16 subsets, each subset includes projection data in 16 (= 256/16) directions. The projection direction in each subset is selected so as to be distributed in as wide a range as possible, and the order of image correction is selected so that subsets in directions as far away as possible from the previous subset are sequentially selected. Then, a reconstructed image is obtained by obtaining the optimal solution x _i from this iterative formula.

  By the way, each detector ring is composed of a large number of PET detectors arranged in a circle, and each PET detector is composed of a combination of a scintillator crystal and a photomultiplier tube. The incident position is detected by identifying the scintillator crystals that have emitted light by the interaction with γ-rays, so that the number of scintillator crystals that emit light is the smallest at the center of the field of view and the spatial resolution is the best, but the edge of the field of view In this section, γ rays are incident obliquely on the detection surface of the PET detector and light is emitted in the deep part of the scintillator crystal, and the number of scintillator crystals that emit light increases and the spatial resolution decreases.

  For this reason, in the successive approximation image reconstruction method, it has been proposed so far to incorporate the projection data of the point source as a point spread function (PSF) into the reconstruction operation and thereby perform spatial resolution correction. (For example, refer nonpatent literature 1).

  In this method, although it is considered that the spatial resolution is lowered at the peripheral edge of the field of view, it is not considered that the sensitivity changes in the peripheral part of the field of view, so that sufficient sensitivity correction cannot be performed. Therefore, according to this method, the blur in the reconstructed image can be corrected and artifacts can be removed, but a reconstructed image that quantitatively reflects the degree of activity in the body of the subject can be obtained. As a result, there is a problem in that a highly accurate quantitative diagnosis using the reconstructed image cannot be performed.

Vladimir Y. Panin, Frank Kehren, Christian Michel and Michael Casey, "Fully 3-D PET Reconstruction With System Matrix Derived From Point Source Measurements", IEEE TRANSACTIONS ON MEDICAL IMAGING, Vol.25, NO.7, July 2006.

  Therefore, an object of the present invention is to solve the problem of insufficient sensitivity correction in the conventional sequential image reconstruction method in which PSF is incorporated in a system matrix.

  In order to solve the above-mentioned problem, the first invention is a successive approximation image reconstruction method of a PET apparatus, and (1) a point-like reference radiation source is arranged in an inner opening of a detector ring of the PET apparatus, Measuring radiation emitted from the reference radiation source with a plurality of PET detectors located in one linear direction of the detector ring, and obtaining projection data for each PET detector; (2) Approximating each of the projection data with a Gaussian function to obtain a standard deviation σ; and (3) a coordinate axis having the projection of the reference radiation source on the one straight line as an origin along the one straight line. A step of modeling the standard deviation as a function of the position on the coordinate axis by setting and plotting the value of the standard deviation σ against the position on the coordinate axis of the corresponding PET detector. And (4) using the value of the standard deviation σ and plotting the value of the normalization coefficient of the Gaussian function against the corresponding position on the coordinate axis of the PET detector, And (5) incorporating the Gaussian function having the modeled standard deviation and the modeled normalization coefficient into a system matrix of the successive approximation image reconstruction method. (6) applying the improved successive approximation image reconstruction method to the projection data acquired by the detector ring of the PET apparatus, and reconstructing And a step of generating an image, and a successive approximation image reconstruction method characterized by sequentially executing.

In order to solve the above-mentioned problems, the second invention is a successive approximation image reconstruction method of a PET apparatus, and (1) a point-like reference radiation source is arranged in an inner opening of a detector ring of the PET apparatus. Measuring radiation emitted from the reference radiation source by a plurality of PET detectors located in one linear direction of the detector ring, and obtaining projection data for each PET detector; 2) approximating each of the projection data with a Gaussian function separately on the left and right with respect to the peak position to obtain a left standard deviation σ _L and a right standard deviation σ _R , and (3) along the one straight line, set the coordinate axes with the origin of the projection of the reference radiation source to the straight line, the coordinates of the PET detectors a value of the left standard deviation sigma _L and the right the standard deviation sigma _R, respectively, the corresponding By plotting with respect to the position of the upper, the steps of each of the left standard deviation sigma _L and the right the standard deviation sigma _R, modeled as a function of position on the coordinate axes, (4) the left standard deviation sigma Using the values of _L and the right side standard deviation σ _R and plotting the value of the normalization coefficient of the Gaussian function against the corresponding position on the coordinate axis of the PET detector, the normalization coefficient is expressed as the coordinate axis. Modeling as a function of the upper position; and (5) sequentially approximating the Gaussian function having the modeled left standard deviation σ _L and the right standard deviation σ _R , and the modeled normalization coefficient. Improving the successive approximation image reconstruction method by incorporating it into the system matrix of the construction method; and (6) the improved successive approximation image reconstruction. Is applied to the projection data acquired by the detector ring of the PET apparatus, and a step of generating a reconstructed image is sequentially performed, and a successive approximation image reconstruction method is constructed. .

  In the configurations of the first and second inventions, it is preferable that the successive approximation image reconstruction method is an OSEM method or a DRAMA method.

  According to the first invention, radiation from a point-like reference radiation source is collected at a plurality of positions of the detector ring to obtain projection data, and the obtained projection data is approximated by a Gaussian function, thereby obtaining a standard deviation. In addition, this standard deviation and the normalization coefficient of the Gaussian function are modeled as a function of the radial position, and they are incorporated into the system matrix of the successive approximation reconstruction method, thereby correcting the resolution and sensitivity of the PET apparatus. Can be done sufficiently.

  According to the second invention, when the projection data obtained by collecting the radiation from the point-like reference radiation source at a plurality of positions of the detector ring is asymmetrical with respect to the peak position, approximation is performed with the left and right Gaussian functions. To calculate the left and right standard deviations as well as the left and right standard deviations and the Gaussian function normalization factor as a function of radial position and incorporate them into the system matrix of the successive approximation image reconstruction method Therefore, resolution correction and sensitivity correction can be sufficiently performed.

FIG. 1 is a flowchart of the successive approximation image reconstruction method of the PET apparatus according to the present invention. It is a graph of an example of the projection data acquired by the some PET detector located in the 1 tangent direction of a detector ring. It is a graph of a Gaussian function approximating projection data. It is the graph which plotted the value of the left side standard deviation (sigma) _L and the right side standard deviation (sigma) _R with respect to the radial direction position of a corresponding PET detector, respectively. It is the graph which plotted the normalization coefficient of the Gaussian function with respect to the radial direction position of a corresponding PET detector. It is the figure which showed the reconstructed image at the time of applying the successive approximation image reconstruction method of this invention, and the conventional successive approximation image reconstruction method, respectively. It is a figure explaining the algorithm of a successive approximation image reconstruction method.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. FIG. 1 is a flowchart of a successive approximation image reconstruction method according to the present invention. Referring to FIG. 1, according to the present invention, a point-like reference radiation source (consisting of nuclides that emit gamma rays in this embodiment) is first placed in the inner opening of the detector ring of the PET apparatus. Then, the radiation emitted from the reference radiation source is measured by a plurality of PET detectors positioned in one tangential direction of the detector ring, and two-dimensional projection data is obtained for each PET detector (S1 in FIG. 1). ).
FIG. 2 shows a graph of an example of projection data. In the graph of FIG. 2, the horizontal axis is a position on the coordinate axis (hereinafter referred to as “radial position”) set along the one tangent direction and having a projection onto the one tangent of the γ-ray source as an origin. The vertical axis represents the count of γ rays after a predetermined time has elapsed.

によって近似し、左側標準偏差σ_Ｌおよび右側標準偏差σ_Ｒを求める（図１のＳ２）。 Next, as shown in FIG. 3, each of the projection data is separately divided into the left and right with respect to the peak position.

To obtain the left side standard deviation σ _L and the right side standard deviation σ _R (S2 in FIG. 1).

Also, as shown in FIG. 4, by plotting the values of the left standard deviation σ _L and the right standard deviation σ _R against the radial position of the corresponding PET detector, respectively, the left standard deviation σ _L and the right standard deviation σ _L Each of the standard deviations σ _R is modeled as a function (polynomial function) of the radial position r (S3 in FIG. 1).

Then, using the modeled left side standard deviation σ _L (r) and right side standard deviation σ _R (r), as shown in FIG. 5, the value of the normalization coefficient of the Gaussian function is set in the radial direction of the corresponding PET detector. By plotting against the position, the normalization coefficient is modeled as a function (polynomial function) of the radial position r (S4 in FIG. 1). The modeled normalization coefficient A (r) is expressed as the following equation.

と変形し、この変形した式を用いて逐次近似画像再構成法を改良する（図１のＳ５）。これにより、半径方向外向きに小さくなる係数がシステムマトリックスａ_ｉｊに掛け合わされ、逐次近似画像再構成法による演算において実測データに対して除算されることで、半径方向外向きに小さくなるデータの修正がなされる。この場合、逐次近似画像再構成法は、ＯＳＥＭ法およびＤＲＡＭＡ法であることが好ましいが、それら以外の逐次近似画像再構成法であってもよい。 Further, a Gaussian function having a modeled left standard deviation σ _L (r) and a right standard deviation σ _R (r) and a modeled normalization coefficient A (r) is used as a system matrix a _{ij of the} successive approximation image reconstruction method. Specifically, by multiplying aij in equation (1) by the normalized coefficient A (r) modeled,

And the successive approximation image reconstruction method is improved using this modified expression (S5 in FIG. 1). As a result, a coefficient that decreases outward in the radial direction is multiplied by the system matrix a _ij , and the data that decreases outward in the radial direction is corrected by dividing the measured data in the calculation by the successive approximation image reconstruction method. Is made. In this case, the successive approximation image reconstruction method is preferably the OSEM method and the DRAMA method, but other successive approximation image reconstruction methods may be used.

  Then, the improved successive approximation image reconstruction method is applied to the measured projection data acquired by the detector ring of the PET apparatus, and a reconstructed image is acquired (S6 in FIG. 1). According to the present invention, since not only the standard deviation of the Gaussian function but also the normalization coefficient is incorporated as a function of the γ-ray incident position for the system matrix, the resolution correction and the sensitivity correction are improved, In addition to correcting the blur, the artifact can be removed, and a reconstructed image that quantitatively reflects the degree of activity in the body of the subject can be obtained. Then, quantitative diagnosis with high accuracy using the reconstructed image can be performed.

  Next, a Derenzo phantom is arranged in the inner opening of the detector ring of the PET apparatus, and the successive approximation image reconstruction according to the present invention is applied to the projection data acquired by the detector ring, and the PSF is incorporated into the conventional system matrix. The approximate image reconstruction method and the conventional successive approximation image reconstruction method were applied, respectively, to generate a reconstructed image. In this case, the DRAMA method is adopted as the successive approximation image reconstruction method.

図６に、それぞれの画像再構成法で得られた再構成画像を示した。図６から、本発明の逐次近似画像再構成法によれば、より鮮明な画像が得られることがわかる。 The algorithm for image reconstruction in the DRAMA method is given by the following equation.

FIG. 6 shows reconstructed images obtained by the respective image reconstruction methods. From FIG. 6, it can be seen that a sharper image can be obtained by the successive approximation image reconstruction method of the present invention.

As mentioned above, although the preferable Example of this invention was described, the structure of this invention is not limited to this Example. For example, in the above embodiment, the radiation emitted from the reference radiation source is measured by a PET detector located in one tangential direction of the detector ring, and the standard deviation σ _{L of the} Gaussian function and the obtained projection data are used. Although σ _R and the normalization factor are modeled as a function of the one tangential position (radial position), instead of modeling in the detector ring's one tangential direction, for example, the coincidence line (LOR) direction May be modeled. That is, according to the present invention, projection data acquired in any one linear direction of the detector ring is used, and a coordinate axis with the projection of the reference radiation source on the straight line as an origin is set along the straight line. , Standard deviations σ _L and σ _R , and normalization factors may be modeled as a function of position on this coordinate axis and incorporated into the system matrix.

In the above-described embodiment, two-dimensional projection data is used. However, according to the present invention, the standard deviations σ _L and σ _R and the normalization coefficient are expressed as a function of the γ-ray incident position using the three-dimensional projection data. Can also be modeled as

Furthermore, in the above-described embodiment, the acquired projection data is approximated by a Gaussian function separately on the left and right with respect to the peak position. However, when the projection data is substantially symmetric with respect to the peak position, the projection data is converted into one Gaussian function. , The standard deviation σ and the normalized coefficient A are modeled, and the modeled standard deviation σ and the normalized coefficient A are incorporated into the system matrix a _ij in the same manner as in the above-described embodiment. The same effect as in the embodiment can be obtained. In this case, the modeled normalization coefficient is expressed by the following equation.

  In the above-described embodiments, the present invention is applied to a general PET apparatus. However, by applying the present invention to a TOF-PET apparatus, the time response on the coincidence line (LOR) and the sensitivity correction are improved. You can also.

Claims (3)

A successive approximation image reconstruction method for a PET apparatus,
(1) A plurality of point-shaped reference radiation sources are arranged in the inner opening of the detector ring of the PET apparatus, and the radiation emitted from the reference radiation source is positioned in one linear direction of the detector ring. Measuring with a PET detector and obtaining projection data for each PET detector;
(2) approximating each of the projection data with a Gaussian function to obtain a standard deviation σ;
(3) A coordinate axis whose origin is the projection of the reference radiation source onto the one straight line is set along the one straight line, and the value of the standard deviation σ is set as the coordinate axis of the corresponding PET detector. Modeling the standard deviation as a function of position on the coordinate axes by plotting against the position above;
(4) Using the value of the standard deviation σ and plotting the value of the normalization coefficient of the Gaussian function against the position on the coordinate axis of the corresponding PET detector, Modeling as a function of the position above,
(5) improving the successive approximation image reconstruction method by incorporating the Gaussian function having the modeled standard deviation and the modeled normalization coefficient into a system matrix of the successive approximation image reconstruction method; ,
(6) The improved successive approximation image reconstruction method is applied to the projection data acquired by the detector ring of the PET apparatus, and a step of generating a reconstruction image is sequentially performed. Iterative image reconstruction method. A successive approximation image reconstruction method for a PET apparatus,
(1) A plurality of point-shaped reference radiation sources are arranged in the inner opening of the detector ring of the PET apparatus, and the radiation emitted from the reference radiation source is positioned in one linear direction of the detector ring. Measuring with a PET detector and obtaining projection data for each PET detector;
(2) approximating each of the projection data with a Gaussian function separately on the left and right with respect to the peak position to obtain a left standard deviation σ _L and a right standard deviation σ _R ;
(3) Along the one straight line, a coordinate axis having the projection of the reference radiation source on the one straight line as an origin is set, and the values of the left standard deviation σ _L and the right standard deviation σ _R are set as follows: Each of the left side standard deviation σ _L and the right side standard deviation σ _R is modeled as a function of the position on the coordinate axis by plotting against the position on the coordinate axis of the corresponding PET detector, respectively. Steps,
(4) By using the values of the left standard deviation σ _L and the right standard deviation σ _R and plotting the value of the normalization coefficient of the Gaussian function against the corresponding position on the coordinate axis of the PET detector. Modeling the normalization factor as a function of position on the coordinate axis;
(5) By incorporating the Gaussian function having the modeled left standard deviation σ _L and the modeled right standard deviation σ _R and the modeled normalization coefficient into the system matrix of the successive approximation image reconstruction method, Improving the approximate image reconstruction method;
(6) The improved successive approximation image reconstruction method is applied to the projection data acquired by the detector ring of the PET apparatus, and a step of generating a reconstruction image is sequentially performed. Iterative image reconstruction method.   3. The successive approximation image reconstruction method according to claim 1, wherein the successive approximation image reconstruction method is an OSEM method or a DRAMA method.

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