WO2012022171A1

WO2012022171A1 - Method and device for selecting and sampling pi lines, and method and device for reconstructing computed tomography (ct) image

Info

Publication number: WO2012022171A1
Application number: PCT/CN2011/073654
Authority: WO
Inventors: 邢宇翔; 张丽; 陈志强; 张文宇; 赵自然; 肖永顺; 李亮; 黄志峰
Original assignee: 清华大学; 同方威视技术股份有限公司
Priority date: 2010-08-18
Filing date: 2011-05-04
Publication date: 2012-02-23
Also published as: CN102376096B; CN102376096A

Abstract

A method and a device for selecting and sampling PI lines, and a method and a device for reconstructing a computed tomography (CT) image are provided, wherein the method for selecting and sampling PI lines includes: selecting the PI lines whose projections are parallel each other and distribute equidistantly in the X-Y plane in a spiral track, and selecting sampling points equidistantly in the PI lines. The method for reconstructing the computed tomography image reconstructs the selected sampling points according to projection data related to the PI lines selected using the method for selecting and sampling PI lines, and samples the reconstruction result into uniform pixels in a rectangular coordinate system. In addition, the device for selecting and sampling PI lines and the device for reconstructing the computed tomography image are respectively corresponding to the method for selecting and sampling PI lines and the method for reconstructing the computed tomography image. Using the present solution, the sampling points with global consistency can be acquired.

Description

PI线选取和采样方法和装置以及 CT图像重建方法和装置技术领域本发明总体上涉及计算机断层成像技术，尤其涉及一种 PI 线选取和采样方法和装置以及 CT图像重建方法和装置。背景技术 BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention generally relates to computed tomography techniques, and more particularly to a PI line selection and sampling method and apparatus, and a CT image reconstruction method and apparatus. Background technique

计算机断层成像技术（CT， Computed tomography) 是指从扫描三维物体的一系列一维或二维图像得到反映此物体内部的物理或化学特性的数据集合，通过运算得到物体一个截面上或一个容积内部的任意位置的参数值，并由此得到一个断层或一个体的图像。目前计算机断层成像技术被广泛应用于医学诊断和无损检测中。其中，锥束螺旋 CT在近年来得到越来越广泛的关注，其重建方法是当前 CT 领域的一个研究热点。就目前来说，主要的 CT 图像重建方法有两类：近似重建方法和精确重建方法。精确重建是大家追求的目标。 Tuy-Smith 数据完备性条件证明螺旋锥束 CT 可被精确重建。近似重建方法中主要有 PI 线重建方法，包括 Katsevich方法禾口微分反投！ ^滤波（DBPF， Derivative backpro jection fi ltering algorithm) 方法。其中，所述 PI线是指在扫描螺旋轨道上间隔小于 2 π 的点之间的连线。 Computed tomography (CT) is a collection of data that reflects the physical or chemical properties of an object from a series of one-dimensional or two-dimensional images of a three-dimensional object. The calculation results in a cross section or a volume inside the object. The parameter value of any position, and thus the image of a fault or a body. Currently, computed tomography is widely used in medical diagnosis and non-destructive testing. Among them, cone-beam spiral CT has received more and more attention in recent years, and its reconstruction method is a research hotspot in the field of CT. For the time being, there are two main methods of CT image reconstruction: the approximate reconstruction method and the exact reconstruction method. Accurate reconstruction is the goal that everyone pursues. Tuy-Smith Data Completeness Conditions Prove that the helical cone beam CT can be accurately reconstructed. There are mainly PI line reconstruction methods in the approximate reconstruction method, including Katsevich method and differential injection! ^Filter (DBPF, Derivative backpro jection fi ltering algorithm) method. Wherein, the PI line refers to a line between points spaced apart by less than 2π on the scanning spiral track.

在这类 ΡΙ线重建方法中， ΡΙ线的选取和离散化方式在其实现过程中影响图像质量和重建速度，对于 ΡΙ 线的选择而言在满足一定空间分辨率的要求下可以是任意的。目前，通常使用的 ΡΙ线选取方式，诸如： Zheng, Η.， Kang， Y.和 Dai， Y. 在 proceedings of the 10th International Meeting on Ful ly Three—Dimensional Image Reconstruction in Radiology and Nuclear Medicine, 45-48 (2009)发表的 " Implementation of Hel ical Cone-Beam Back-Projection Fi ltered Reconstruction Algorithm on GPU"禾口 Han Zheng, Yanyan Yu, Yan Kang Jiren Liu, 在 Proc. Of SPIE ( the international society for optics and photonics，国际光学工程学会）卷. 7622， 7622G, 2009年发表的" Investigation on PI-l ine Selecting Method Base on GPU Accelerated Back-projection Fi ltered V0I Reconstruction", 这些都是以光源位置为基点，选取从该基点到扫描螺旋轨道上的点之间连线上的点。这样所选取的 PI线构成了一个扇形曲面，如图 lc所示。 In this type of squall line reconstruction method, the selection and discretization of the squall line affects the image quality and reconstruction speed during its implementation, and can be arbitrary for the selection of the squall line to meet certain spatial resolution requirements. At present, the commonly used squall line selection methods, such as: Zheng, Η., Kang, Y. and Dai, Y. in the proceedings of the 10th International Meeting on Ful ly Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, 45-48 (2009) " Implementation of Helical Cone-Beam Back-Projection Fi ltered Reconstruction Algorithm on GPU" and Han Zheng, Yanyan Yu, Yan Kang Jiren Liu, in Proc. Of SPIE (the international society for optics and photonics, International Society of Optical Engineering, Vol. 7622, 7622G, "Research on PI-l ine Selecting Method Base on GPU Accelerated Back-projection Fi ltered V0I Reconstruction", which is based on the position of the light source and is selected from the base point. To the point on the line connecting the points on the spiral track. The selected PI lines form a fan-shaped surface. As shown in Figure lc.

在图 la中，图示了 CT扫描轨道和常规 PI线选取和采样示意图。其中， X光源和探测器位于被扫描物体区域的两边， X光源和探测器绕旋转轴旋转（或者被扫描物体旋转中心反方向旋转），并且沿轴向运动， In Figure la, a schematic diagram of the CT scan track and conventional PI line selection and sampling is shown. Wherein, the X light source and the detector are located on both sides of the scanned object region, and the X light source and the detector rotate around the rotation axis (or rotate in the opposite direction of the rotation center of the scanned object) and move in the axial direction.

u h , 、 r_n (λ) = (R cos , R sin ,—— λ) 射线源的位置 (^X， ^Z)在直角坐标***中表示为 2 r ，这里 R为射线源旋转的半径，是旋转角度， A是螺距，也就是射线源旋转一周后相对于置物台的轴向移动距离，重建图像区域（也即被扫描物体区域）是半径为的一个圆柱体。图 lb和图 lc分别是图 la的侧视图和俯视图。 Uh , , r _n (λ) = (R cos , R sin , λ ) The position of the ray source ( ^X , ^Z ) is expressed as 2 r in the Cartesian coordinate system, where R is the radius of rotation of the ray source, which is the rotation Angle, A is the pitch, that is, the axial movement distance relative to the stage after the ray source rotates one revolution. The reconstructed image area (that is, the scanned object area) is a cylinder with a radius of one. Figure lb and Figure lc are side and top views, respectively, of Figure la.

图 lc示出了 PI线在 XY平面上的投影，其中，实线表示 PI线，实心点是 PI 线上的采样点，虚线表示另一个 PI曲面的 PI线。从该图可以看出， PI线形成了一个扇形形状，且距光源位置越近采样点越密集，远离光源位置则采样稀疏。 Figure lc shows the projection of the PI line on the XY plane, where the solid line represents the PI line, the solid point is the sample point on the PI line, and the dashed line represents the PI line of the other PI surface. As can be seen from the figure, the PI line forms a fan shape, and the closer the position is to the light source, the denser the sampling point is, and the sampling is sparse away from the position of the light source.

综上所述，现有技术存在下列缺点： In summary, the prior art has the following disadvantages:

首先，现有技术所选取的 PI线采样点不能达到全局一致性。 First, the PI line sampling points selected by the prior art cannot achieve global consistency.

其次，为了在稀疏处也能够达到一定的分辨率效果，必然需要大量增加 PI 线的密度，从而增加了计算量。 Secondly, in order to achieve a certain resolution effect in a sparse place, it is necessary to increase the density of the PI line in a large amount, thereby increasing the amount of calculation.

再者，其重建点采样很难与图像重建所需的像素分辨率建立直接关联，无法作出优化的离散策略，给选择采样参数造成一定困难。发明内容 Furthermore, the reconstruction point sampling is difficult to directly relate to the pixel resolution required for image reconstruction, and the optimized discrete strategy cannot be made, which makes it difficult to select sampling parameters. Summary of the invention

本发明要解决的主要技术问题是提供一种具有全局一致性的 PI 线采样点的 PI线选取和采样方法和装置以及 CT图像重建方法和装置。 The main technical problem to be solved by the present invention is to provide a PI line selection and sampling method and apparatus with globally consistent PI line sampling points and a CT image reconstruction method and apparatus.

为了解决上述问题，本发明 PI线选取和采样方法的技术方案包括步骤：在螺旋轨道上选取在 XY平面上投影互相平行且等间距分布的 PI线；在所述 PI线上等距离选取采样点。 In order to solve the above problem, the technical solution of the PI line selection and sampling method of the present invention includes the steps of: selecting PI lines that are parallel to each other and equally spaced on the XY plane on a spiral track; and selecting sampling points at equal distances on the PI line .

优选地，所述步骤在螺旋轨道上选取在 XY 平面上投影互相且等间距分布的 PI线进一步包括：选取与重建区域相切的 PI线，其中， = + 2^_2c )_S— /R)， Λ^Β表示该 Preferably, the step of selecting PI lines projected on the XY plane and spaced apart from each other on the spiral track further comprises: selecting a PI line tangent to the reconstruction area, wherein, = + 2^_2c ) _S — /R) , Λ ^Β indicates that

PI线起始点的光源角度，表示该 PI线终止点的光源角度， R表示射线源旋转半径， r表示重建区域在 XY平面上投影的半径; 选取下一条 PI线使其在 χ-γ平面的投影与前面所选 PI线在 χ-γ平面的投影平行且相距一距离，直到这些 PI线所形成的 PI 曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线的投影间距离相等； The angle of the light source at the starting point of the PI line, the angle of the light source indicating the end point of the PI line, R represents the radius of rotation of the source, and r represents the radius of the projected area on the XY plane; Select the next PI line so that the projection of the χ-γ plane is parallel to the projection of the previously selected PI line in the χ-γ plane, and the distance from the PI surface formed by these PI lines in the XY plane covers the reconstruction area. Projection in the XY plane and the distance between projections of adjacent PI lines is equal;

按照上述步骤选取下一 PI 曲面上的 PI线直到这些 PI 曲面覆盖了需重建的物体高度，其中， ^{+1 _} h ，是该 PI曲面的第一条 PI线起始点的光源角度，表示两个相邻 PI曲面与 ζ轴交点的距离之差。在本发明的另一方面，本发明 CT图像重建方法的技术方案包括步骤：在螺旋轨道上选取在 ΧΥ平面上投影相互平行且等间距分布的 Ρ Ι线；在所述 ΡΙ线上等距离选取采样点； Follow the steps above to select the PI lines on the next PI surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _} h is the angle of the light source at the beginning of the first PI line of the PI surface, indicating two The difference between the distance between the adjacent PI surface and the 交 axis intersection. In another aspect of the present invention, the technical solution of the CT image reconstruction method of the present invention includes the steps of: selecting a Ρ Ι line that is parallel to each other and equally spaced on the ΧΥ plane on the spiral trajectory; Sampling point;

根据 P I线所相关的投影数据重建所述采样点； Reconstructing the sampling point according to projection data related to the P I line;

把上述重建结果采样成直角坐标系下的均匀像素。 The above reconstruction result is sampled into uniform pixels in a Cartesian coordinate system.

优选地，所述步骤在螺旋轨道上选取在 ΧΥ 平面上投影互相平行且等间距分布的 Ρ Ι线进一步包括： Preferably, the step of selecting the Ρ line projected on the ΧΥ plane parallel to each other and equally spaced on the spiral track further comprises:

选取与重建区域相切的 ΡΙ 线，其中， = + 2^ _ 2c )_S— /R)， A 表示 PI线起始点的光源角度，表示 PI线终止点的光源角度， R为射线源旋转半径， r表示重建区域在 XY平面投影的半径； Select the tangential line tangent to the reconstruction area, where = + 2^ _ 2c ) _S — /R), A represents the angle of the light source at the starting point of the PI line, the angle of the light source at the end point of the PI line, and R is the radius of rotation of the ray source. , r represents the radius of the reconstruction area projected on the XY plane;

选取下一条 PI线使其在 χ-γ平面的投影与前面所选 PI线在 χ-γ平面的投影平行且相距一距离，直到这些 PI线所形成的 PI 曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线的投影间距离相等； Select the next PI line so that the projection of the χ-γ plane is parallel to the projection of the previously selected PI line in the χ-γ plane, and the distance from the PI surface formed by these PI lines in the XY plane covers the reconstruction area. Projection in the XY plane and the distance between projections of adjacent PI lines is equal;

按照上述步骤选取下一 PI 曲面上的 PI线直到这些 PI 曲面覆盖了需重建的物体高度，其中， ^{+1 _ h} ，表示该 PI 曲面的第一条 PI线起始点的光源角度， ^Δζ表示两个相邻 PI曲面与 ζ轴交点的距离之差。优选地，所述步骤根据 Ρ Ι线所相关的投影数据重建所述采样点进一步包括: 对 ΡΙ线所相关的投影数据进行微分加权反投影； Follow the steps above to select the PI lines on the next PI surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _ h} represents the angle of the light source at the starting point of the first PI line of the PI surface, ^Δ ζ The difference between the distances between two adjacent PI surfaces and the intersection of the ζ axes. Preferably, the step of reconstructing the sampling point according to the projection data related to the Ι line further comprises: performing differential weighted back projection on the projection data related to the ΡΙ line;

对加权反投影后的结果进行有限希尔伯特滤波。 A finite Hilbert filter is performed on the results of the weighted back projection.

相应地，本发明 ΡΙ线选取和采样装置的技术方案包括： Accordingly, the technical solution of the twist line selection and sampling device of the present invention includes:

ΡΙ线选取单元，用于在螺旋轨道上选取在 ΧΥ平面上投影互相平行且等间距分布的 PI线； ΡΙ line selection unit for selecting projections on the spiral plane parallel to each other and equally spaced on the ΧΥ plane Distributed PI line;

采样点选取单元，用于在所述 PI线上等距离选取采样点。 A sampling point selecting unit is configured to select sampling points at equal distances on the PI line.

优选地，所述 PI线选取单元还包括： Preferably, the PI line selection unit further includes:

第一单元，用于选取与重建区域相切的 PI 线，其中， =Λ^Β + 2 - 2eos— /R)， Λ^Β表示该？₁线起始点的光源角度，表示该 Pi线终止点的光源角度， R表示射线源旋转半径， r表示重建区域在 ΧΥ平面上投影的半径； The first unit is used to select the PI line tangent to the reconstruction area, where =Λ ^Β + 2 - 2eos_ /R), Λ ^Β indicates this? _The angle of the light source at the starting point of the line ₁ indicates the angle of the light source at the end point of the Pi line, R indicates the radius of rotation of the source, and r indicates the radius of the projected area on the pupil plane;

第二单元，用于选取下一条 PI线使其在 X-Y平面的投影与前面所选 PI线在 X-Y平面的投影平行且相距一距离，直到这些 PI线所形成的 PI曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线的投影间距离相等； The second unit is configured to select the next PI line so that the projection in the XY plane is parallel to and parallel to the projection of the previously selected PI line in the XY plane until the projection of the PI surface formed by the PI lines in the XY plane Projection of the reconstructed region in the XY plane and the distance between projections of adjacent PI lines is equal;

第三单元，用于使所述第一单元和第二单元选取下一 PI曲面上的 PI线直到这些 PI曲面覆盖了需重建的物体高度，其中， ^{+1 _ h} ，是该 PI曲面的第一条 PI线起始点的光源角度，表示两个相邻 PI 曲面与 Ζ轴交点的距离 a third unit, configured to: the first unit and the second unit select PI lines on the next PI surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _ h} is the first of the PI surfaces The angle of the light source at the starting point of a PI line, indicating the distance between two adjacent PI surfaces and the intersection of the Ζ axis

此外，本发明 CT图像重建装置的技术方案包括： In addition, the technical solution of the CT image reconstruction device of the present invention includes:

ΡΙ线选取单元，用于在螺旋轨道上选取在 ΧΥ平面上投影相互平行且等间距分布的 ΡΙ线； a 选取 line selecting unit for selecting a ΡΙ line that is parallel to each other and equally spaced on the ΧΥ plane on the spiral track;

采样点选取单元，用于在所述 PI线上等距离选取采样点； a sampling point selecting unit, configured to select sampling points equidistantly on the PI line;

重建单元，用于根据 PI线所相关的投影数据重建所述采样点； a reconstruction unit, configured to reconstruct the sampling point according to projection data related to the PI line;

转换单元，用于把上述重建结果采样成直角坐标系下的均匀像素。 And a converting unit, configured to sample the above reconstruction result into uniform pixels in a Cartesian coordinate system.

优选地，所述 ΡΙ线选取单元进一步包括： Preferably, the squall line selection unit further comprises:

第一单元，用于选取与重建区域相切的 ΡΙ 线，其中， ^=^^B + 2^-2cos-¹(r/R)_; ^B 表示 _PI线起始点的光源角度，表示 PI线终止点的光源角度， R为射线源旋转半径， r表示重建区域在 XY平面投影的半径；第二单元，用于选取下一条 PI线使其在 X-Y平面的投影与前面所选 PI线在 X-Y平面的投影平行且相距一距离，直到这些 PI线所形成的 PI曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线的投影间距离相等； A first means for selecting the reconstruction region ΡΙ tangent line, ^{where, ^ = ^ B + 2 ^} -2cos- 1 (r / R); B represents the starting point of the line light source angle _PI, PI represents a line end point The angle of the light source, R is the radius of rotation of the source, r is the radius of the reconstruction area projected on the XY plane; the second unit is used to select the next PI line to make its projection in the XY plane and the previously selected PI line in the XY plane The projections are parallel and at a distance, until the projection of the PI surface formed by the PI lines in the XY plane covers the projection of the reconstruction region in the XY plane and the distance between projections of adjacent PI lines is equal;

第三单元，用于使所述第一单元和所述第二单元选取下一 PI曲面上的 PI线直到这些 PI 曲面覆盖了需重建的物体高度，其中， ^{+1 _}

表示该 PI 曲面的第一条 PI线起始点的光源角度， ^Δζ表示两个相邻 PI 曲面与 Ζ轴交点的距离之差。 a third unit, configured to: the first unit and the second unit select a PI line on a next PI surface Until these PI surfaces cover the height of the object to be reconstructed, where ^{+1 _}

The angle of the light source representing the starting point of the first PI line of the PI surface, and ^Δ ζ indicates the difference between the distances of the intersections of two adjacent PI surfaces and the Ζ axis.

其中，所述重建单元还包括： The reconstruction unit further includes:

投影单元，用于对 ΡΙ线所相关的投影数据进行微分加权反投影； a projection unit, configured to perform differential weighted back projection on projection data related to the squall line;

滤波单元，用于对加权反投影后的结果进行有限希尔伯特滤波。 A filtering unit is configured to perform finite Hilbert filtering on the weighted back projection result.

与现有技术相比，本发明 ΡΙ线采样点的 ΡΙ线选取和采样方法和装置以及 CT 图像重建方法和装置的有益效果为： Compared with the prior art, the method and apparatus for selecting and sampling the squall line sampling point of the present invention and the CT image reconstruction method and apparatus have the following beneficial effects:

由于本发明所选取的 ΡΙ线在 ΧΥ平面上的投影互相平行且等间距分布，另外在 ΡΙ线上所选取的相邻采样点间的距离也相等，所以一个 ΡΙ 曲面上的采样点在 Since the projections of the ridge lines selected by the present invention on the pupil plane are parallel and equally spaced, and the distances between adjacent sampling points selected on the ΡΙ line are also equal, so the sampling points on one 曲面 surface are

ΧΥ 平面上的投影呈均匀分布，间距通过，控制。在旋转轴方向上相邻的 ΡΙ 曲面的 ΡΙ线在 ΧΥ平面上的投影成角度 ^Δ 在旋转轴方向的距离为 ^Δζ，从而可以通过 '^Δ ' 控制采样点间距，可以通过 '^Δ 令 ΡΙ 线的平面内采样均匀，可以通过选择 ^Δ ί ζ方向上的采样与平面内一致，来达到全局均匀。因此，在整个重建区域达到全局均匀可控的 ΡΙ线采样点。附图说明下面参考结合附图所进行的下列描述以便更透彻地理解本公开内容，在附图中： The projections on the ΧΥ plane are evenly distributed, with the spacing passed and controlled. The projection of the ΡΙ line adjacent to the 曲面 surface in the direction of the rotation axis on the ΧΥ plane is at an angle ^{Δ Δ} ^{在 in the} direction of the rotation axis, so that the sampling point spacing can be controlled by ' ^Δ ', which can be passed through the ' ^Δ ΡΙ line The sampling in the plane is uniform, and the global uniformity can be achieved by selecting the sampling in the direction of ^Δ ζ 与 to be consistent with the plane. Therefore, a globally controllable squall line sampling point is achieved throughout the reconstruction area. BRIEF DESCRIPTION OF THE DRAWINGS The following description, taken in conjunction with the drawings

图 la图示了 CT扫描轨道及常规 PI线选取和采样示意图； Figure la shows a schematic diagram of the CT scan track and conventional PI line selection and sampling;

图 lb图示了图 la的侧视图； Figure lb illustrates a side view of Figure la;

图 lc图示了图 la的俯视图； Figure lc illustrates a top view of the diagram la;

图 2a图示了依据本发明 PI线选取和采样方法所选取的 PI线的示意图；图 2b图示了图 2a的侧视图； Figure 2a is a schematic illustration of a PI line selected in accordance with the PI line selection and sampling method of the present invention; Figure 2b illustrates a side view of Figure 2a;

图 2c图示了图 2a的俯视图； Figure 2c illustrates a top view of Figure 2a;

图 3图示了螺旋锥束 CT扫描示意图； Figure 3 is a schematic view showing a CT scan of a spiral cone beam;

图 4图示了采用本发明 PI线选取和采样方法所选取的 PI线在 XY平面内投影的角度关系示意图； Figure 4 illustrates the PI line selected by the PI line selection and sampling method of the present invention cast in the XY plane. Schematic diagram of the angular relationship of the shadow;

图 5图示了依据本发明 CT图像重建方法把 P I线上像素采样成直角坐标系下均匀网格的空间关系示意图； 5 is a schematic diagram showing the spatial relationship of a pixel on a P I line to a uniform grid in a Cartesian coordinate system according to the CT image reconstruction method of the present invention;

图 6图示了本发明 P I线选取和采样方法的流程图； Figure 6 is a flow chart showing the P I line selection and sampling method of the present invention;

图 7图示了本发明 CT图像重建方法的流程图。具体实施方式 Fig. 7 is a flow chart showing the CT image reconstruction method of the present invention. detailed description

下面将详细描述本发明的具体实施例，但本发明并不限于下述具体实施例。如图 6所示，本发明 PI线选取和采样方法包括步骤： Specific embodiments of the present invention will be described in detail below, but the present invention is not limited to the specific embodiments described below. As shown in FIG. 6, the PI line selection and sampling method of the present invention includes the steps of:

1 ) 在螺旋轨道上选取在 XY平面上投影互相平行且等间距分布的 PI线； 2 ) 在所述 PI线上等距离选取采样点。 1) Selecting PI lines that are parallel to each other and equally spaced on the XY plane are selected on the spiral track; 2) sampling points are equally spaced on the PI line.

由上述可知，本发明 PI 线选取和采样方法的技术方案所选取的 PI 线在 XY 平面上的投影互相平行且等间距分布，另外在 PI 线上所选取的相邻采样点间的距离也相等，假设相邻 P I线在 XY平面的投影间距离为且相邻采样点投影间距离为 , 所以一个 P I曲面上的采样点在 XY平面上的投影呈均匀分布，间距通过，控制。在旋转轴方向上相邻的 PI 曲面的 P I 线在 XY平面上的投影成角度 It can be seen from the above that the projections of the PI lines selected by the PI line selection and sampling method of the present invention on the XY plane are parallel and equally spaced, and the distances between adjacent sampling points selected on the PI line are also equal. Assuming that the distance between the projections of adjacent PI lines in the XY plane is and the distance between projections of adjacent sampling points is, the projection of the sampling points on one PI surface on the XY plane is evenly distributed, and the spacing is passed and controlled. The projection of the P I line of the adjacent PI surface in the direction of the rotation axis is angled on the XY plane

^θ , 在旋转轴方向的距离为，从而可以通过 ^Δ"^Δ ' 控制采样点间距，可以通过，而令 ΡΙ线的平面内采样均匀，又可以通过选择使 Ζ方向上的采样与平面内一致，来达到全局均匀。因此，在整个重建区域达到全局均匀可控的 ΡΙ 线采样点。 ^θ , the distance in the direction of the rotation axis is , so that the sampling point spacing can be controlled by ^Δ " ^Δ ', which can be passed, and the in-plane sampling of the ΡΙ line is uniform, and the sampling in the Ζ direction can be selected to be in-plane. To achieve global uniformity, therefore, globally controllable sigma sampling points are achieved throughout the reconstruction area.

优选地，所述步骤在螺旋轨道上选取在 ΧΥ 平面上投影互相平行且等间距分布的 ΡΙ线进一步包括：选取与重建区域相切的 ΡΙ线，如图 4所示，其中， = + 2^_2c )s— /R)， Preferably, the step of selecting a parallel line and equally spaced lines on the pupil plane on the spiral track further comprises: selecting a line tangent to the reconstruction area, as shown in FIG. 4, wherein, = + 2^ _2c )s — /R),

^ 是该 PI线起始点的光源角度，是该 PI线终止点的光源角度， R为射线源旋转半径， r是重建区域在 XY平面投影的半径； ^ is the angle of the light source at the starting point of the PI line, is the angle of the light source at the end point of the PI line, R is the radius of rotation of the source, and r is the radius of the projected area projected on the XY plane;

如图 4所示，选取下一条 PI线使其在 X-Y平面的投影与前面所选 PI线在 X-Y 平面的投影平行且相距一距离，直到这些 PI线所形成的 PI 曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线的投影间距离相等； As shown in Figure 4, select the next PI line to make its projection in the XY plane and the previously selected PI line in XY. The projections of the plane are parallel and at a distance, until the projection of the PI surface formed by the PI lines in the XY plane covers the projection of the reconstruction region in the XY plane and the distance between projections of adjacent PI lines is equal;

按照上述步骤选取下一 PI 曲面上的 PI线直到这些 PI 曲面覆盖了需重建的物体高度，其中， ^{+1 _ h} ，是该 PI 曲面的第一条 PI线起始点的光源角度，是两个相邻 PI 曲面与 Z轴交点的距离之差，如图 2b所示，其中， ^Z" 表示第 n个 PI 曲面与 z轴的交点， ^Ζ"+ι表示第 n+1个 PI曲面与 z轴的交点。由于所选取的 PI线在 XY平面上的投影互相平行且距离相等（例如，该距离为），以及在一条 PI线上所选取的相邻采样点投影之间的距离相等（例如，该距离为^ ，如图 2c所示。在这样选取的 PI线所构成的各 PI曲面中，在旋转轴方向上相邻的 PI 曲面的 PI 线在 XY 平面上的投影成角度 ^Δ (该角度为 Follow the steps above to select the PI lines on the next PI surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _ h} is the source angle of the first PI line starting point of the PI surface, which is two The difference between the distance between the adjacent PI surface and the Z-axis intersection, as shown in Figure 2b, where ^Z " represents the intersection of the n-th PI surface and the z-axis, ^Ζ "+ι denotes the n+ ^1th PI surface and the z-axis The intersection. Since the projections of the selected PI lines on the XY plane are parallel and equidistant (eg, the distance is), and the distance between adjacent sample points selected on one PI line is equal (eg, the distance is ^, as shown in Fig. 2c. In each PI surface formed by the PI line thus selected, the PI line of the adjacent PI surface in the direction of the rotation axis is projected at an angle ^Δ on the XY plane (the angle is

2 Λ 2 Λ

ΑΘ = λ_Ν+ι - =■ ΑΘ = λ _Ν+ι - =■

h )。因此，这些 PI 曲面在 X和 Y轴方向上的采样率全局- 致可控， PI曲面间的距离也可根据层间分辨率要求任意控制，从而在整个重建区域达到全局均匀可控的 PI线采样点，因此使用本方法选取 PI线和对其采样不影响后续的 PI线上的重建。 h). Therefore, the sampling rates of these PI surfaces in the X and Y directions are globally controllable, and the distance between the PI surfaces can be arbitrarily controlled according to the inter-layer resolution requirements, thereby achieving a globally uniform controllable PI line throughout the reconstruction area. Sampling points, so using this method to select PI lines and sampling them does not affect the reconstruction of subsequent PI lines.

相应地，本发明还公开了一种 CT图像重建方法，如图 7所示，其包括步骤： Correspondingly, the present invention also discloses a CT image reconstruction method, as shown in FIG. 7, which includes the steps of:

10 ) 在螺旋轨道上选取在 XY平面上投影相互平行且等间距分布的 PI线；10) selecting PI lines that are parallel to each other and equally spaced on the XY plane on the spiral track;

11 ) 在所述 PI线上等距离选取采样点； 11) selecting sampling points equidistantly on the PI line;

12 ) 根据 PI线所相关的投影数据重建所述采样点； 12) reconstructing the sampling point according to projection data related to the PI line;

13 ) 把上述重建结果采样成直角坐标系下的均匀像素。 13) Sampling the above reconstruction result into uniform pixels in a Cartesian coordinate system.

从上述可知，本发明 CT图像重建方法是基于本发明 PI线选取和采样方法的技术方案的。也即选取的是 PI 线所相关的投影数据，然后根据这些投影数据重建所选取的采样点，最后再把重建结果采样成直角坐标系下的均匀像素。 As apparent from the above, the CT image reconstruction method of the present invention is based on the technical scheme of the PI line selection and sampling method of the present invention. That is, the projection data related to the PI line is selected, and then the selected sampling points are reconstructed based on the projection data, and finally the reconstruction result is sampled into uniform pixels in a Cartesian coordinate system.

对于图像重建而言，可以通过下述来实现： For image reconstruction, it can be achieved by:

对 PI线所相关的投影数据进行微分加权反投影； Perform differential weighted back projection on the projection data related to the PI line;

当然，这只是实现图像重建的一种方法，还可以采用本领域技术人员已知或者将来已知的任何方法。 Of course, this is just one way to achieve image reconstruction, and can also be known to those skilled in the art or Any method known to the future.

优选地，所述步骤在螺旋轨道上选取在 XY 平面上投影互相平行且等间距分布的 PI线： Preferably, the step selects PI lines that are projected parallel to each other and equally spaced on the XY plane on the spiral track:

选取与重建区域相切的 PI 线，其中， = + 2^_2c )_S— /R)， A 是该 PI线起始点的光源角度，是该 PI线终止点的光源角度， R为射线源旋转半径， r是重建区域在 XY平面投影的半径； Select the PI line tangent to the reconstruction area, where = + 2^_2c ) _S — /R), A is the angle of the light source at the starting point of the PI line, is the angle of the light source at the end point of the PI line, and R is the rotation of the ray source. Radius, r is the radius of the reconstructed area projected on the XY plane;

按照上述步骤选取下一 PI 曲面上的 PI线直到这些 PI 曲面覆盖了需重建的物体高度，其中， ^{+1 _ h} ，是该 PI 曲面的第一条 PI线起始点的光源角度，是两个相邻 PI曲面与 z轴交点的距离之差。如图 3所示的螺旋锥束 CT扫描示意图， X光源和探测器位于被扫描物体区域的两边， X光源和探测器绕旋转轴旋转（或者被扫描物体旋转中心反方向旋转），并且沿轴向运动，射线源的位置（^χ，·^^ζ) 在直角坐标***中表示为 r_n (λ) = (R cos , R sin ,—— λ) Follow the steps above to select the PI lines on the next PI surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _ h} is the source angle of the first PI line starting point of the PI surface, which is two The difference between the distance between the adjacent PI surface and the z-axis intersection. As shown in Fig. 3, the CT scan of the spiral cone beam, the X-ray source and the detector are located on both sides of the scanned object region, and the X-ray source and the detector rotate around the rotation axis (or rotate in the opposite direction of the rotation center of the scanned object), and along the axis To the motion, the position of the ray source ( ^χ ,·^ ^ζ ) is expressed in the Cartesian coordinate system as r _n (λ) = (R cos , R sin , —— λ)

^ ，这里 R为射线源旋转的半径，是旋转角度， A是螺距，也就是射线源旋转一周后相对于置物台的轴向移动距离，设重建图像区域是半径为的一个圆柱体。当然，重建图像区域还可以是其他任何形状，这里仅仅是一个示例，而不应被理解为是对本发明的限制。下面我们以其为例来详细描述本发明的技术方案。 ^ , where R is the radius of rotation of the source, is the angle of rotation, and A is the pitch, which is the axial movement distance relative to the stage after one rotation of the source. Let the reconstructed image area be a cylinder with a radius of one. Of course, the reconstructed image area can also be any other shape, and is merely an example, and should not be construed as limiting the invention. The technical solution of the present invention will be described in detail below by taking as an example thereof.

如图 2a、图 2b和 2c所示，其中，螺旋线表示扫描轨道。首先选取第一条 As shown in Figures 2a, 2b and 2c, wherein the spiral represents the scanning track. First select the first one

(R cos I^s, R sin I^s,— I^s) (R cos I ^s , R sin I ^s , — I ^s )

PI线，该 PI线与重建区域相切，并且起始点位于 ^ ，终止点为 (Rcc W '^ 这里 = _{+ 2 r}__{2cos /} 。在该 _?1线上选取各采样点且各相邻采样点在 XY平面投影之间的距离为 ^Δ 。选取第二条 PI线使其在 XY平面内的投影与第一条 PI线的投影平行并且相PI line, the PI line is tangent to the reconstruction area, and the starting point is at ^, and the ending point is (Rcc W '^ where = _{+ 2 r} _ _{2cos /} . Select each sampling point on the _?1 line and each adjacent sampling The distance between the points on the XY plane projection is ^Δ . Select the second PI line so that its projection in the XY plane is parallel to the projection of the first PI line and

_Λ (Rcos L^B,Rsin L^B,— L^B) 距，从而第二条 PI 起始点位于 2r _Λ (Rcos L ^B , Rsin L ^B , - L ^B ), so that the second PI starting point is at 2r

-ι ^Rτ〕Υ^Λ ) _L Ro -ι ^R τ〕Υ^Λ ) _L Ro

，终止点位于， 2 ），

在该 PI线上选取各采样点且各相邻采样点在 XY平面投影之间的距离为 ^Δ 。按照上述选取第 i (1<⁷'≤N)条 ΡΙ线，该 PI线在 XY平面内的投影与第 i-1 条 PI线在 XY平面内的投影平行且相距，直到选取了第 N条 PI线。这时，这些 PI线在 XY平面内的投影覆盖半径为 r的圆形区域，也即覆盖了图像重建区域。如图 2a-c所示，所有这些 PI线构成一个 PI曲面。 , the termination point is located, 2)

Each sampling point is selected on the PI line and the distance between adjacent sampling points in the XY plane projection is ^Δ . Select the i-th (1< ⁷ '≤N) line as described above, and the projection of the PI line in the XY plane is parallel and spaced from the projection of the i-1th PI line in the XY plane until the Nth line is selected. PI line. At this time, the projection of these PI lines in the XY plane covers a circular area of radius r, that is, covers the image reconstruction area. As shown in Figures 2a-c, all of these PI lines form a PI surface.

_W f ^,.^ ^ ^₊„ ^^(^cos^₊₁,Rsin^₊₁ ) 取下一个 PI 曲面的第一条 PI线起始点为 ^ ，该 _W f ^,.^ ^ ^ ₊ „ ^^(^cos^ ₊₁ ,Rsin^ ₊₁ ) Take the first PI line starting point of the PI surface as ^,

？工线的终止点是^^^^^^^， ^：^+^— ^^^ 然后，在该 PI 曲面上按照上述方式依次选取 PI线直到该 PI 曲面上的这些 PI线在 XY 平面内的投影覆盖半径为 r的圆形区域。如图 2a、 2b和 2c所示，其中，实线所构成的面表示一个 PI曲面，虚线所构成的面表示另一 PI 曲面。 ? The termination point of the line is ^^^^^^^, ^:^+^—^^^ Then, the PI line is sequentially selected on the PI surface in the above manner until the PI lines on the PI surface are in the XY plane. The projection covers a circular area of radius r. As shown in Figures 2a, 2b and 2c, where the solid line forms a PI surface and the dashed line represents another PI surface.

接着选取再下一个 PI 曲面，设为第 j个 PI 曲面，其第一条 PI线起始点为 (R cos λ^_Ν+ , R sin λ^_Ν+ ,― λ^_Ν+ ) d =— ^ΒB + \ 2^J'A_Z Then select the next PI surface and set it as the jth PI surface. The starting point of the first PI line is (R cos λ^ _Ν+ , R sin λ^ _Ν+ , ― λ^ _Ν+ ) d =— ^ΒB + \ 2^J'A _Z

''2^ ^+l ~ h ~~ ''2^ ^+l ~ h ~~

(Rcos¾₊₁,Rsin¾₊₁ -¾₊₁)^ ^₊ =^_{+ +}2π-2^- ΠΚ)^ 共选取 _N条 _PI线且这 N条 PI线组成的该 PI 曲面在 XY平面的投影覆盖以 r为半径的圆形区域。这样一直选取直到选取的所有 PI 曲面在 z方向上覆盖了所需重建的物体高度为止。 (Rcos3⁄4 ₊₁ , Rsin3⁄4 ₊₁ -3⁄4 ₊₁ )^ ^ ₊ =^ _{+ +} 2π-2^- ΠΚ)^ A total of _N _PI lines and the projection of the PI surface composed of the N PI lines in the XY plane are selected. Covers a circular area with a radius of r. This is selected until all of the selected PI surfaces cover the height of the object to be reconstructed in the z direction.

下面以这些 PI线上的采样点所相关的投影数据为基础，重建 CT图像。 The CT image is reconstructed based on the projection data associated with the sample points on these PI lines.

可以采用任何常规方式来完成，本例使用平板探测器下的微分反投影滤波 This can be done in any conventional way. This example uses differential back projection filtering under a flat panel detector.

(DBPF Derivative backpro jection filtering algorithm) 方法进行说明。首先定义探测器旋转坐标系为： e_u (λ) = (- sin λ, cos λ, 0)(DBPF Derivative backpro jection filtering algorithm) method is explained. First define the detector rotation coordinate system as: e _u (λ) = (- sin λ, cos λ, 0)

νμ) = (0,0,1) Νμ) = (0,0,1)

w X) - (cos Λ， sin Λ， 0) 其中，和表示定义的探测器旋转坐标系的三个坐标轴方向; w X) - (cos Λ, sin Λ, 0) where , and represent the three coordinate axes of the defined detector rotation coordinate system;

S为光源到探测器平面的距离；所采集的投影数据为 g^^v), 其中， u禾 P v表不采集的数据所对应的探测器单元的索引； λ表示光源的旋转角度。 S is the distance from the light source to the detector plane; the acquired projection data is g^^v), where u and P v represent the index of the detector unit corresponding to the data collected; λ represents the rotation angle of the light source.

按如下公式对投影数据：

Project the data as follows:

这里是 PI线的索引号， ^Λ' 分别是所选择的各条 ΡΙ线的起始点和终止点所对应的投影角度。表示 PI线上采样点的坐标，表示光源的坐标。 ^是 Here is the index number of the PI line, and ^Λ ' is the projection angle corresponding to the start point and the end point of each selected line. Indicates the coordinates of the sample points on the PI line, indicating the coordinates of the light source. ^Yes

PI线上采样点在 PI线上的位置， ^"二^^^-^ + ^^^^， c[0，l]。 The position of the sample point on the PI line on the PI line, ^"二^^^-^ + ^^^^, c[0,l].

hv Hv

Ru + Ru +

2π 2π

u +v +S du

接着对经过加权反投影处特变换:

u +v +S du

Then the weighted back projection is transformed:

1 1 BP_n g( *,V*,A ) τ _ί_Β)(1_ί_Α) , 1 1 BP _n g( *,V*,A ) τ _ί _Β )(1_ί _Α ) ,

+ - r₀{ )-r f 0< <L + - r ₀ { )-rf 0<<L

这里其中，。 ^s)表示 PI线的起始点的坐标向量，。 ^s)表示 PI线的终点的坐标向量， / ^^ ，^)表示加权反投影后的结果， ( , ）表示 PI线上的某一点的重建结果。这里使用^[/^， ^3]定义 PI线上的一个区间，要求覆盖被重建区域； g(_M*，v*，）_{¾ PI}线的积分值，也就是从对应的光源点出发沿着这条？₁线发出的射线的投影值，它也可以用从对应的光源点出发沿着这条 PI线发出的射线投影值即 g(^M*'^v*' ）代替，两者等效。 Here, . ^s) indicates the coordinate vector of the starting point of the PI line. ^s) indicates the coordinate vector of the end point of the PI line, / ^^ , ^) indicates the result of the weighted back projection, and ( , ) indicates the reconstruction result of a certain point on the PI line. Here ^[/ ^, ^{3] is used to} define an interval on the PI line, and it is required to cover the reconstructed area; g( _M *, v*, ) _3⁄4 The integral value of the _PI line, that is, from the corresponding light source point along this line ? The projection value of the ray emitted by the ₁ line, which can also be replaced by the ray projection value (g* ^M *' ^v *') emitted from the corresponding light source point along the PI line, and the two are equivalent.

最后使用三线性插值把上述结果采样成直角坐标系的均匀像素： Finally, the above results are sampled into uniform pixels in a Cartesian coordinate system using trilinear interpolation:

对某一条 PI线上的某一个采样点在固定物体坐标系中的坐标为 The coordinates of a sampling point on a PI line in the fixed object coordinate system are

的三个元素写出来定义为 ¾ (½，Λι，^ζπ) ，即可得到上式, 定义其邻域为 8 个直角坐标系下像素， (^{i + l} ^^k , ( + )， (i + lj + ^k)^ (i,j,k + X) , ( + 1, A + l)，（, + 1,4 + 1)， (/ + 1, + 1,Λ + 1)_ο 这里像素索引 ζ'， '，Α 分别代表 Χ，Υ和 Ζ (层）方向。如图 5所示， ^:½ _^xi ⁼yu -yj "_z=¾_¾。使用三线性插值得到:

The three elements are written as 3⁄4 (1⁄2, Λι, ^ζ π), and the above equation is obtained, and the neighborhood is defined as pixels in 8 Cartesian coordinates, ( ^{i + l} ^ ^k , ( + ), (i + lj + ^k)^ (i,j,k + X) , ( + 1, A + l), (, + 1,4 + 1), (/ + 1, + 1,Λ + 1) _οhere The pixel index ζ', ', Α represents the Χ, Υ and Ζ (layer) directions respectively. As shown in Figure 5, ^: 1⁄2 _ ^x i ⁼ yu -yj " _z =3⁄4_3⁄4. Use trilinear interpolation to get:

这里 Δ为均匀网格重建所要求的平面内像素离散间距，为均匀网格重建所要求的层厚。

Here Δ is the in-plane pixel discrete spacing required for uniform mesh reconstruction, which is the layer thickness required for uniform mesh reconstruction.

如图 5所示，依据本发明 CT图像重建方法把 ΡΙ线上像素采样成直角坐标系下均匀网格的空间关系示意图。图 5展示了 ΡΙ线上的一个点所对应的 As shown in Fig. 5, according to the CT image reconstruction method of the present invention, the pixel on the ΡΙ line is sampled into a spatial relationship of a uniform grid in a Cartesian coordinate system. Figure 5 shows a point on the ΡΙ line.

₈个邻域点 + 1, '^), , + 1^), ('' + W + 1,A)， , ^ + 1), (' + W, 1)， ₈ neighborhood points + 1, '^), , + 1^), ('' + W + 1,A), , ^ + 1), (' + W, 1),

( + i，t+i)，（ +ij + i +i)的立体图，表示的距离， ^表示 _ 的距离， ^表示 ^_ 的距离。由于在大多数情况下，三维重建像素的 ^≡Δ，因此可以取 = = = o^(G，l]。 "越小，图像质量越好，但计算量增加。鉴于"≤0·8情况下，重建质量在肉眼看来已无显著区别，所以通常取 "⁼⁽⁾·⁸可得到最佳的速度而不影响重建质量。 ( + i, t + i), ( + ij + i + i) stereogram, the distance represented, ^ indicates the distance of _, ^ represents the distance of ^_ . Since in most cases, the ^{≡Δ of the} pixel is reconstructed in three dimensions, it is possible to take ⁼⁼⁼ o^(G,l]. "The smaller the image quality, the better the calculation, but the amount of calculation increases." In the case of "≤0·8" The quality of reconstruction has no significant difference from the naked eye, so usually take " ^{= ()} · ^{8 to} get the best speed without affecting the quality of reconstruction.

相应地，本发明还公开了一种 ΡΙ线选取和采样装置，包括： Correspondingly, the present invention also discloses a twist line selection and sampling device, including:

ΡΙ线选取单元，用于在螺旋轨道上选取在 ΧΥ平面上投影互相平行且等间距分布的 ΡΙ线； a 选取 line selecting unit, configured to select a ΡΙ line that is parallel to each other and equally spaced on the ΧΥ plane on the spiral track;

采样点选取单元，用于在所述 ΡΙ线上等距离选取采样点。 A sampling point selecting unit is configured to select sampling points at equal distances on the ΡΙ line.

优选地，所述 ΡΙ线选取单元还包括： Preferably, the line selection unit further includes:

第一单元，用于选取与重建区域相切的 ΡΙ 线，其中， =Λ^Β + 2 - 2eos— /R)， Λ^Β表示该？₁线起始点的光源角度，表示该 Pi线终止点的光源角度， R表示射线源旋转半径， r表示重建区域在 ΧΥ平面上投影的半径； The first unit is used to select a tangential line tangent to the reconstruction area, where =Λ ^Β + 2 - 2eos_ /R), Λ ^Β indicates this? _The angle of the light source at the starting point of the line ₁ indicates the angle of the light source at the end point of the Pi line, R indicates the radius of rotation of the source, and r indicates the radius of the projected area on the pupil plane;

第二单元，用于选取下一条 PI线使其在 X-Y平面的投影与前面所选 PI线在 X-Y平面的投影平行且相距一距离，直到这些 ΡΙ线所形成的 ΡΙ曲面在 ΧΥ平面的投影覆盖重建区域在 ΧΥ平面的投影且各相邻 ΡΙ线在 ΧΥ平面上的投影间距离相等. The second unit is used to select the next PI line to make its projection in the XY plane and the previously selected PI line The projections of the XY plane are parallel and at a distance, until the projection of the meandering surface formed by the meandering lines covers the reconstruction of the reconstructed region in the pupil plane and the distance between the projections of the adjacent tangent lines on the pupil plane is equal.

第三单元，用于使所述第一单元和第二单元选取下一 ΡΙ曲面上的 ΡΙ线直到这些 PI曲面覆盖了需重建的物体高度，其中， ^{+1 _ h} ，是该 PI曲面的第一条 PI线起始点的光源角度， ^Δζ表示两个相邻 PI 曲面与 ζ轴交点的距离 a third unit, configured to: the first unit and the second unit select a squall line on the next ΡΙ surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _ h} is the first of the PI surface The angle of the light source at the starting point of a PI line, ^Δ ζ indicates the distance between two adjacent PI surfaces and the intersection of the ζ axis

由于本发明 PI线选取和采样装置的技术方案与本发明 PI线选取和采样方法的技术方案相对应，因此，在此不对本发明 ΡΙ 线选取和采样装置的技术方案进行详细描述。 Since the technical solution of the PI line selecting and sampling device of the present invention corresponds to the technical solution of the PI line selecting and sampling method of the present invention, the technical solution of the wire selecting and sampling device of the present invention will not be described in detail herein.

另外，本发明还公开了一种 CT图像重建装置，包括： In addition, the present invention also discloses a CT image reconstruction apparatus, including:

第三单元，用于使所述第一单元和所述第二单元选取下一 PI曲面上的 PI线直到这些 PI 曲面覆盖了需重建的物体高度，其中， ^{+1 _} h ，表示该 PI 曲面的第一条 PI线起始点的光源角度，表示两个相邻 PI 曲面与 Ζ轴交点的距离之差。其中，所述重建单元还包括： a third unit, configured to: the first unit and the second unit select PI lines on a next PI surface until the PI surfaces cover an object height to be reconstructed, where ^{+1 _} h represents the PI surface The angle of the light source at the starting point of the first PI line, indicating the difference between the distance between two adjacent PI surfaces and the intersection of the Ζ axis. The reconstruction unit further includes:

投影单元，用于对各 PI 线上的采样点所相关的投影数据进行微分加权反投影； a projection unit, configured to perform differential weighted anti-projection on projection data related to sampling points on each PI line;

由于本发明 CT图像重建装置的技术方案与本发明 CT图像重建方法的技术方案相对应，因此，在此不对本发明 CT图像重建装置的技术方案进行详细描述。 Since the technical solution of the CT image reconstruction device of the present invention corresponds to the technical solution of the CT image reconstruction method of the present invention, the technical solution of the CT image reconstruction device of the present invention will not be described in detail herein.

虽然上述已经结合附图描述了本发明的具体实施例，但是本领域技术人员在不脱离本发明的精神和范围的情况下，可以对本发明进行各种改变、修改和等效替代。这些改变、修改和等效替代都意为落入随附的权利要求所限定的精神和范围之内。 While the invention has been described with respect to the embodiments of the present invention, various modifications, modifications and equivalents of the invention may be made without departing from the spirit and scope of the invention. Such changes, modifications, and equivalents are intended to be within the spirit and scope of the appended claims.

Claims

权利要求 Rights request

1. 一种 PI线选取和采样方法，其特征在于，包括步骤： A PI line selection and sampling method, comprising the steps of:

在螺旋轨道上选取在 XY平面上投影互相平行且等间距分布的 PI线；在所述 PI线上等距离选取采样点。 Selecting PI lines that are parallel to each other and equally spaced on the XY plane are selected on the spiral track; sampling points are equally spaced on the PI line.

2. 如权利要求 1所述的 PI线选取和采样方法，其特征在于，所述步骤在螺旋轨道上选取在 XY平面上投影互相平行且等间距分布的 PI线进一步包括：选取与重建区域相切的 PI 线，其中， = + 2^_2c )_S— /R)，表示该 PI线起始点的光源角度，表示该 PI线终止点的光源角度， R表示射线源旋转半径， r表示重建区域在 XY平面上投影的半径； 2. The PI line selection and sampling method according to claim 1, wherein the step of selecting PI lines that are parallel to each other and equally spaced on the XY plane on the spiral track further comprises: selecting and reconstructing the area The cut PI line, where = + 2^_2c ) _S — /R), the angle of the light source representing the starting point of the PI line, the angle of the light source indicating the end point of the PI line, R representing the radius of rotation of the source, and r representing the reconstruction area The radius projected on the XY plane;

选取下一条 PI线使其在 χ-γ平面的投影与前面所选 PI线在 χ-γ平面的投影平行且相距一距离，直到这些 PI线所形成的 PI 曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线间距离相等； Select the next PI line so that the projection of the χ-γ plane is parallel to the projection of the previously selected PI line in the χ-γ plane, and the distance from the PI surface formed by these PI lines in the XY plane covers the reconstruction area. Projection in the XY plane and the distance between adjacent PI lines is equal;

按照上述步骤选取下一 PI曲面上的 PI线直到这些 PI曲面覆盖了需重建的物体高度，其中， ^{+1 _} h ，是该 PI 曲面的第一条 PI线起始点的光源角度，表示两个相邻 PI 曲面与 ζ轴交点的距离之差。 Follow the above steps to select the PI lines on the next PI surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _} h is the angle of the light source at the starting point of the first PI line of the PI surface, indicating two The difference between the distance between the adjacent PI surface and the 交 axis intersection.

3. 一种 CT图像重建方法，其特征在于，包括步骤： A CT image reconstruction method, comprising the steps of:

在螺旋轨道上选取在 ΧΥ平面上投影相互平行且等间距分布的 ΡΙ线；在所述 ΡΙ线上等距离选取采样点； Selecting on the spiral track, projecting parallel lines and equally spaced lines on the pupil plane; selecting sampling points equidistantly on the line;

根据 ΡΙ线所相关的投影数据重建所述采样点； Reconstructing the sampling point according to projection data related to the squall line;

4. 如权利要求 3所述的 CT图像重建方法，其特征在于，所述步骤在螺旋轨道上选取在 ΧΥ平面上投影互相平行且等间距分布的 ΡΙ线进一步包括：选取与重建区域相切的 ΡΙ线，其中， = + 2^r_2c )_S— /R)， A 表示 PI线起始点的光源角度，表示 PI线终止点的光源角度， R为射线源旋转半径， r表示重建区域在 XY平面投影的半径; 选取下一条 P I线使其在 χ-γ平面的投影与前面所选 P I线在 χ-γ平面的投影平行且相距一距离，直到这些 PI线所形成的 PI 曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线间距离相等； The CT image reconstruction method according to claim 3, wherein the step of selecting a parallel line and equally spaced lines on the pupil plane on the spiral track further comprises: selecting a tangent to the reconstruction area ΡΙ line, where, = + 2^r_2c ) _S — /R), A represents the angle of the source at the starting point of the PI line, the angle of the source representing the end point of the PI line, R is the radius of rotation of the source, and r is the area of reconstruction in the XY plane The radius of the projection; Select the next PI line so that the projection of the χ-γ plane is parallel to the projection of the previously selected PI line in the χ-γ plane, and the distance from the PI surface formed by these PI lines in the XY plane covers the reconstruction area. Projection in the XY plane and the distance between adjacent PI lines is equal;

按照上述步骤选取下一 PI曲面上的 PI线直到这些 PI曲面覆盖了需重建的物体高度，其中， ^{+1 _} h ，表示该 PI 曲面的第一条 PI线起始点的光源角度，表示两个相邻 PI 曲面与 ζ轴交点的距离之差。 According to the above steps, select the PI lines on the next PI surface until the PI surfaces cover the height of the object to be reconstructed, where ^{+1 _} h represents the angle of the light source at the starting point of the first PI line of the PI surface, indicating two The difference between the distance between the adjacent PI surface and the 交 axis intersection.

5. 如权利要求 3或者 4所述的 CT图像重建方法，其特征在于，所述步骤根据 PI线所相关的投影数据重建所述采样点进一步包括： The CT image reconstruction method according to claim 3 or 4, wherein the step of reconstructing the sampling point according to the projection data related to the PI line further comprises:

对 ΡΙ线所相关的投影数据进行微分加权反投影； Perform differential weighted back projection on the projection data related to the squall line;

6. 一种 ΡΙ线选取和采样装置，其特征在于，包括： 6. A twist line selection and sampling device, comprising:

7. 如权利要求 6所述的 ΡΙ 线选取和采样装置，其特征在于，所述 ΡΙ 线选取单元还包括： The squall line selection and sampling device according to claim 6, wherein the squall line selection unit further comprises:

第一单元，用于选取与重建区域相切的 ΡΙ 线，其中， a first unit for selecting a tangential line tangent to the reconstruction area, wherein

^ ₌ ^ _{+ 2}^ - 2 cos-¹ (r /R) _j 表示该？₁线起始点的光源角度，表示该 ^ ₌ ^ _{+ 2} ^ - 2 cos- ¹ (r /R) _j means this? _The angle of the light source at the starting point of the ₁ line, indicating the

PI线终止点的光源角度， R表示射线源旋转半径， r表示重建区域在 XY平面上投影的半径； The angle of the light source at the end point of the PI line, R represents the radius of rotation of the source, and r represents the radius of the projected area on the XY plane;

第二单元，用于选取下一条 PI线使其在 χ-γ平面的投影与前面所选 PI 线在 X-Y平面的投影平行且相距一距离，直到这些 PI线所形成的 PI 曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线间距离相等；第三单元，用于使所述第一单元和第二单元选取下一 PI 曲面上的 PI线直到这些 PI 曲面覆盖了需重建的物体高度，其中， + A ，是该 The second unit is used to select the next PI line so that the projection of the χ-γ plane is parallel to and parallel to the projection of the previously selected PI line in the XY plane until the PI surface formed by the PI lines is in the XY plane Projection covers the projection of the reconstruction region in the XY plane and the distance between adjacent PI lines is equal; the third unit is configured to cause the first unit and the second unit to select PI lines on the next PI surface until the PI surfaces are covered The height of the object to be rebuilt, where + A is the

PI 曲面的第一条 PI线起始点的光源角度， ^Δζ表示两个相邻 ΡΙ 曲面与 Ζ轴交点的距离之差。 The angle of the light source at the starting point of the first PI line of the PI surface, ^Δ ζ represents the difference between the distances of the intersections of two adjacent ΡΙ surfaces and the Ζ axis.

8. —种 CT图像重建装置，其特征在于，包括： PI线选取单元，用于在螺旋轨道上选取在 XY平面上投影互相平行且等间距分布的 PI线； 8. A CT image reconstruction device, comprising: a PI line selecting unit, configured to select, on the spiral track, PI lines that are parallel to each other and equally spaced on the XY plane;

重建单元，用于根据 PI线所相关的投影数据重建所述采样点；转换单元，用于把上述重建结果采样成直角坐标系下的均匀像素。 And a reconstruction unit, configured to reconstruct the sampling point according to the projection data related to the PI line; and a conversion unit, configured to sample the reconstruction result into a uniform pixel in a Cartesian coordinate system.

9. 如权利要求 8所述的 CT图像重建方法，其特征在于，所述 PI线选取单元进一步包括： The CT image reconstruction method according to claim 8, wherein the PI line selection unit further comprises:

第一单元，用于选取与重建区域相切的 PI 线，其中， ^=^ + 2^- cos-¹(r/R)_j ^Β 表示 _ΡΙ 线起始点的光源角度，表示 ΡΙ 线终止点的光源角度， R为射线源旋转半径， r表示重建区域在 ΧΥ平面投影的半径； A first means for selecting and reconstruction area PI tangent line, where, ^ = ^ + 2 ^ - cos- 1 (r / R) j Β angle _ΡΙ source line represents a starting point, the end point of the line represents ΡΙ The angle of the light source, R is the radius of rotation of the source, and r is the radius of the projected area projected on the pupil plane;

第二单元，用于选取下一条 PI线使其在 χ-γ平面的投影与前面所选 PI 线在 X-Y平面的投影平行且相距一距离，直到这些 PI线所形成的 PI 曲面在 XY平面的投影覆盖重建区域在 XY平面的投影且各相邻 PI线间距离相等；第三单元，用于使所述第一单元和所述第二单元选取下一 PI 曲面上的 The second unit is used to select the next PI line so that the projection of the χ-γ plane is parallel to and parallel to the projection of the previously selected PI line in the XY plane until the PI surface formed by the PI lines is in the XY plane The projection covers the projection of the reconstruction region in the XY plane and the distance between adjacent PI lines is equal; the third unit is configured to select the first unit and the second unit to be selected on the next PI surface

PI线直到这些 PI曲面覆盖了需重建的物体高度，其中， ^{+1 _} h ，^₊₁ 表示该 PI 曲面的第一条 PI线起始点的光源角度，表示两个相邻 PI 曲面与 Ζ轴交点的距离之差。 The PI line up to these PI surfaces covers the height of the object to be reconstructed, where ^{+1 _} h , ^ ₊₁ represents the angle of the source of the first PI line of the PI surface, representing two adjacent PI surfaces and axes The difference in the distance of the intersection.

10. 如权利要求 8或者 9所述的 CT图像重建方法，其特征在于，所述重建单元还包括： The CT image reconstruction method according to claim 8 or 9, wherein the rebuilding unit further comprises:

投影单元，用于对 ΡΙ线所相关的投影数据进行微分加权反投影；滤波单元，用于对加权反投影后的结果进行有限希尔伯特滤波。 a projection unit, configured to perform differential weighted back projection on the projection data related to the squall line; and a filtering unit configured to perform finite Hilbert filtering on the weighted back projection result.