Patent Publication Number: US-10319118-B2

Title: Reconstructing PET image

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to Chinese Patent Application No. 201610940112.4 entitled “Method and Apparatus for Reconstructing PET Image” filed on Oct. 25, 2016, the entire content of which is incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to medical image processing technologies, and more particularly, to reconstructing a PET image. 
     BACKGROUND 
     At present, Positron Emission Computed Tomography (PET) technologies have been widely applied to biomedical research fields, e.g., early tumor detection research and drug screening research. Based on the PET technologies, a radioactive tracer is injected into a subject, a photon signal generated by an annihilation event is detected in vitro, and spatial distribution of the tracer in vivo is reconstructed according to the detected data. Thus, physiological metabolism information about the subject can be indirectly obtained. 
     NEUSOFT MEDICAL SYSTEMS CO., LTD. (NMS), founded in 1998 with its world headquarters in China, is a leading supplier of medical equipment, medical IT solutions, and healthcare services. NMS supplies medical equipment with a wide portfolio, including CT, Magnetic Resonance Imaging (MRI), digital X-ray machine, ultrasound, Positron Emission Tomography (PET), Linear Accelerator (LINAC), and biochemistry analyser. Currently, NMS&#39; products are exported to over 60 countries and regions around the globe, serving more than 5,000 renowned customers. NMS&#39;s latest successful developments, such as 128 Multi-Slice CT Scanner System, Superconducting MRI, LINAC, and PET products, have led China to become a global high-end medical equipment producer. As an integrated supplier with extensive experience in large medical equipment, NMS has been committed to the study of avoiding secondary potential harm caused by excessive X-ray irradiation to the subject during the CT scanning process. 
     SUMMARY 
     The present disclosure provides methods, systems, and machine-readable storage mediums for reconstructing a PET image by allocating multiple-coincidence data to each of LORs, which can effectively improve PET sensitivity and an image quality of the reconstructed PET image. 
     One innovative aspect of the subject matter described in the present disclosure can be embodied in methods that include the actions of determining a plurality of Lines of Response (LORs) associated with multiple-coincidence data in coincidence data detected by a PET device through scanning, the coincidence data including double-coincidence data indicating that two single events satisfy a coincidence condition and the multiple-coincidence data indicating that three or more single events satisfy the coincidence condition, and each of the LORs being a line between crystals corresponding to every two of the three or more single events corresponding to the multiple-coincidence data; obtaining, for each of the LORs, a respective line integral value along the LOR according to a time difference between two single events corresponding to the LOR; allocating the multiple-coincidence data to the LORs according to the obtained respective line integral values of the LORs associated with the multiple-coincidence data, a respective part of the multiple-coincidence data allocated to each of the LORs being respective multiple allocation data on the LOR; correcting, for each of the LORs, respective double-coincidence data in the coincidence data corresponding to the LOR based on the respective multiple allocation data on the LOR to obtain respective data of the LOR; and reconstructing an image according to the respective data of each of the LORs. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, obtaining the respective line integral value along the LOR includes: determining a Time-of-Flight (TOF) kernel function according to the time difference between the two single events corresponding to the LOR; and integrating the TOF kernel function and pixel values of a second image in a corresponding range along the LOR to obtain the line integral value of the LOR associated with the multiple-coincidence data, where the second image is reconstructed according to the double-coincidence data in the coincidence data. The corresponding range can be determined based on the TOF kernel function and can have a width larger than a width of an event occurrence region on the LOR that is determined based on the time difference between the two single events. 
     In some cases, determining the TOF kernel function according to the time difference between the two single events includes: obtaining a function center of the TOF kernel function according to the time difference between the two single events; and determining the TOF kernel function according to the function center. In some cases, determining the TOF kernel function according to the time difference between the two single events includes: obtaining a midpoint of a time difference region corresponding to the time difference between the two single events; obtaining a function center of the TOF function according to the midpoint; and determining the TOF kernel function according to the function center. 
     In some implementations, obtaining the respective line integral value along the LOR includes: dividing the LOR into a plurality of event occurrence regions based on time difference regions; performing TOF orthographic projection for a second image to obtain a respective line integral value corresponding to each of the plurality of event occurrence regions on the LOR, where the second image is reconstructed according to the double-coincidence data in the coincidence data; generating correspondences between the time difference regions and the respective line integral values corresponding to the plurality of event occurrence regions on the LOR; and obtaining the line integral value along the LOR according to the time difference between the two single events corresponding to the LOR and the correspondences. 
     Allocating the multiple-coincidence data to the LORs can include: allocating a respective proportion of a count value of the multiple-coincidence data to each of the LORs according to the respective line integral values of the LORs associated with the multiple-coincidence data. Correcting the respective double-coincidence data in the coincidence data corresponding to the LOR based on the respective multiple allocation data on the LOR can include: adding a count value of the multiple allocation data on the LOR and a count value of the double-coincidence data corresponding to the LOR together to obtain a corrected count value; and taking the corrected count value as a count value of the data of the LOR. 
     In some cases, reconstructing the image according to the respective data of each of the LORs includes: generating a scatter correction factor and an attenuation correction factor according to the respective data of each of the LORs; and reconstructing the image according to the scatter correction factor, the attenuation correction factor and the respective data of each of the LORs. 
     Another aspect of the subject matter described in the present disclosure can be embodied in methods that include the actions of reconstructing a first PET image according to double coincidence data in coincidence data detected by a PET device through scanning; determining a plurality of lines of response (LOR) associated with multiple-coincidence data in the coincidence data, each of the LORs being a line between crystals corresponding to every two of three or more single events corresponding to the multiple-coincidence data; determining a respective weight for each of the LORs based on a time difference between two single events corresponding to the LOR and an overlapping region between the first PET image and the LOR; allocating the multiple-coincidence data to the LORs based on the determined respective weights to obtain respective multiple allocation data on the LORs; correcting, for each of the LORs, respective double-coincidence data in the coincidence data corresponding to the LOR based on the respective multiple allocation data on the LOR to obtain respective data of the LOR; and reconstructing a second PET image according to the respective data of the LORs. 
     Determining a respective weight for each of the LORs can include: determining a Time-of-Flight (TOF) kernel function according to the time difference between the two single events corresponding to the LOR; and integrating the TOF kernel function and pixel values of the first PET image in an integral range along the LOR to obtain a line integral value of the LOR associated with the multiple-coincidence data, wherein the line integral value is determined to be the respective weight for the LOR. The integral range can be determined based on the TOF kernel function and have a width larger than a width of an event occurrence region on the LOR that is determined based on the time difference between the two single events. 
     Other embodiments of these aspects include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. For a system of one or more computers to be configured to perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation cause the system to perform the operations or actions. For one or more computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by data processing apparatus, cause the apparatus to perform the operations or actions. 
     The details of one or more examples of the subject matter described in the present disclosure are set forth in the accompanying drawings and description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims. Features of the present disclosure are illustrated by way of example and not limited in the following figures, in which like numerals indicate like elements. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a flowchart illustrating a method of reconstructing a PET image according to an example of the present disclosure. 
         FIG. 2  is a schematic diagram illustrating a multiple-allocation process according to an example of the present disclosure. 
         FIG. 3  is a flowchart illustrating a method of reconstructing a PET image according to an example of the present disclosure. 
         FIG. 4  is a schematic diagram of a structure of a PET device according to an example of the present disclosure. 
         FIG. 5  is a schematic diagram of a structure of logic for reconstructing a PET image according to an example of the present disclosure. 
         FIG. 6  is a schematic diagram of a structure of logic for reconstructing a PET image according to an example of the present disclosure. 
         FIG. 7  is a schematic diagram of a structure of logic for reconstructing a PET image according to an example of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Example embodiments will be described in detail herein with the examples thereof expressed in the drawings. When the following descriptions involve the drawings, like numerals in different drawings represent like or similar elements unless stated otherwise. The implementations described in the following example embodiments do not represent all implementations consistent with the present disclosure. On the contrary, they are examples of an apparatus and a method consistent with some aspects of the present disclosure described in detail in the appended claims. 
     After a radionuclide is injected into a subject, annihilation events occur in vivo, and a γ-photon generated by an annihilation event may be detected by a crystal on a PET device. When detecting a γ-photon with energy higher than a predetermined energy threshold, the crystal may record that a single event is detected. When two single events satisfy time coincidence, e.g., detected in a time window, the two single events constitute a coincidence event, e.g., it is indicated that two γ-photons corresponding to the two single events are photons which are generated by a same annihilation event and have same energy and opposite directions. A line between two crystals corresponding to the detected coincidence event is a Line of Response (LOR) (or response line). The detected coincidence event may be a double-coincidence event or a multiple-coincidence event. When the number of single events which are detected in a time window and satisfy a coincidence condition is equal to 2, the detected coincidence event is a double-coincidence event. When the number of single events which are detected in a time window and satisfy the coincidence condition is more than 2, the detected coincidence event is a multiple-coincidence event. 
     In some cases, it is hard to determine which LOR associated with a multiple-coincidence event is true, and the PET device may discard corresponding multiple-coincidence data. In some cases, the PET device may use the multiple-coincidence data to improve sensitivity of the PET device. For example, the double-coincidence data and the multiple-coincidence data are separately determined, and the multiple-coincidence data is allocated to various LORs associated with the multiple-coincidence data based on a proportion of count values in the double-coincidence data on the LORs. However, when the count values of the double-coincidence data are small, the amount of the determined coincidence data above is not sufficient. When the allocation above is still in accordance with the proportion of the count values in the double-coincidence data, an allocation result cannot be accurate, and a quality of a PET image reconstructed according to the coincidence data on the LORs is bad. 
     In an example of the present disclosure, coincidence data is information of a coincidence event. For example, the coincidence data includes γ-photon energy information, reception time information, reception position information and a count value of γ-photon corresponding to each single event in a coincidence event. The number of single events in the coincidence event may be equal to 2. For example, a crystal J 1  detects a single event, and a crystal J 2  detects another single event. When each of γ-photons corresponding to the two single events satisfies an energy threshold and a difference between reception times of the γ-photons corresponding to the two single events satisfies a time coincidence, the two single events constitute a double-coincidence event, and data of the two single events constitute double-coincidence data. Further, a multiple-coincidence event may occur. The multiple-coincidence event may be a triple-coincidence event, a quadruple-coincidence event, or a coincidence event including even more single events satisfying a coincidence condition. In an example, a crystal J 1  detects a single event, a crystal J 2  detects another single event, and a crystal J 3  detects yet another single event. When each of γ-photons corresponding to the three single events satisfies an energy threshold and reception time of each of the γ-photons corresponding to the three single events is within a same time window, e.g., satisfying the time coincidence, the three single events constitute a triple-coincidence event, and corresponding triple-coincidence data includes data of the three single events. 
     The coincidence data detected by the PET device may include the double-coincidence data or the multiple-coincidence data. For each of LORs corresponding to the coincidence data, the coincidence data on the LOR may include double-coincidence data and multiple-coincidence data. An LOR between the crystal J 1  and the crystal J 2  is taken as an example. A plurality of coincidence events are detected on the LOR. The coincidence events includes a double-coincidence “D 1  (a single event detected by the crystal J 1 ) and D 2  (a single event detected by the crystal J 2 )”, and a triple-coincidence event “D 3  (a single event detected by the crystal J 1 ), D 4  (a single event detected by the crystal J 2 ) and D 5  (a single event detected by a crystal J 3 )”. In the example, information of the single events for the two crystals (J 1  and J 2 ) on the LOR is a part of the triple-coincidence data. 
     Two photons which are generated by an annihilation event and have equal energy and opposite directions correspond to two single events. The multiple-coincidence event includes more than two single events. It is hard to accurately determine which two single events correspond to the true coincidence event, e.g., which two single events corresponds to two γ-photons which are generated by a same annihilation event and have equal energy and opposite directions. Thus, the multiple-coincidence data may be discarded when the PET image is reconstructed according to the coincidence data obtained by the PET device. For example, in the triple-coincidence event “D 3 , D 4  and D 5 ”, the true coincidence event may include D 3  and D 4 , D 3  and D 5 , or D 4  and D 5 , which is hard to be accurately determined. According to methods of reconstructing a PET image in examples of the present disclosure, the multiple-coincidence data is used to reconstruct a PET image in a way that a sensitivity of a PET device is improved. 
     The multiple-coincidence data can be effectively used, e.g., the multiple-coincidence data can be accurately allocated to various LORs in a way that a quality of an image reconstructed according to the coincidence data on the LORs is good. For example, the triple-coincidence data includes three single events each of which satisfies a coincidence condition, e.g., D 3  detected by the crystal J 1 , D 4  detected by the crystal J 2 , and D 5  detected by the crystal J 3 . Three LORs corresponding to the triple-coincidence data are LOR 12  (a line between the crystal J 1  and the crystal J 2 ), LOR 13  (a line between the crystal J 1  and the crystal J 3 ) and LOR 23  (a line between the crystal J 2  and the crystal J 3 ). The triple-coincidence data may be allocated for LOR 12 , LOR 13  and LOR 23 , which can indicate probabilities that the true coincidence event is on each of the LORs. For example, it is assumed that in the triple-coincidence data, a count value 0.5 is allocated for LOR 12 , a count value 0.25 is respectively allocated for LOR 13  and LOR 23 . It is indicated that a probability that the true coincidence event is on LOR 12  is largest, i.e., it is most possible that the true coincidence event is on LOR 12 , a probability that the true coincidence event includes D 3  and D 4  is large, a probability that the true coincidence event includes D 3  and D 4  and a probability that the true coincidence event includes D 4  and D 5  are small. 
       FIG. 1  is a flow chart of a process illustrating a method of reconstructing a PET image according to an example of the present disclosure. An image is reconstructed according to coincidence data detected by a PET device. The coincidence data includes double-coincidence data and multiple-coincidence data. In this example, a triple-coincidence data is taken as an example of the multiple-coincidence data. A method for another multiple-coincidence data is the same as that for the triple-coincidence data, which is not repeatedly described herein. In  FIG. 1 , it is described how the multiple-coincidence data is allocated to different LORs and how the allocated data is used to reconstructing an image. 
     At step  101 , a plurality of LORs corresponding to each piece of multiple-coincidence data is determined. 
     Each of the LORs corresponding to the multiple-coincidence data is a line between crystals corresponding to every two of single events in the multiple-coincidence data. For example, in  FIG. 2 , it is assumed that a triple-coincidence event “D 3 , D 4  and D 5 ” are detected by crystals J 1 , J 2  and J 3 , which respectively correspond to three LORs: LOR 12 , LOR 13  and LOR 23 . The LOR 12  is a line between the two crystals J 1  and J 2  corresponding to the single events D 3  and D 4 . The LOR 13  is a line between the two crystals J 1  and J 3  corresponding to the single events D 3  and D 5 . The LOR 23  is a line between the two crystals J 2  and J 3  corresponding to the single events D 4  and D 5 . In the example, triple-coincidence data is taken as an example of allocating the multiple-coincidence data. Another multiple-coincidence data can be allocated to LORs according to the same method as that for the triple-coincidence data. 
     At step  102 , a line integral value corresponding to each of the LORs is determined according to a time difference between two single events corresponding to the LOR. 
     In the example, Time-of-Flight Positron Emission Tomography (TOF-PET) is used. In the PET, an exact position of a detected annihilation event on an LOR is not obtained. In image reconstruction, an annihilation event detected on each LOR is distributed to all paths of the LOR based on equal weights. In the example, according to TOF-PET, a position of the annihilation event which occurs on the LOR is determined based on a difference between times when the two γ-photons respectively arrive at two crystals. 
     When the time difference between the two single events in the coincidence event is obtained, an occurrence region of the coincidence event is positioned on an LOR. In an example, an LOR may be segmented based on a time difference region. In some examples, the LOR, e.g., a path between two crystal, is segmented into a number of event occurrence regions. The time difference region can be used to determine a length of an event occurrence region. In a particular example, each event occurrence region has a same length identical to a product of a time interval of the time difference region and a speed of light. The time difference region can include a region between a time difference t 1  and a time difference t 2 . The time difference region can correspond to a path region on the LOR, which may be an event occurrence region. For example, it is assumed that a double-coincidence event is detected, a difference between reception times of two γ-photons corresponding to two single events in the coincidence event is t, where t 1 &lt;t&lt;t 2 . It is determined that an occurrence position of the coincidence event is within an event occurrence region corresponding to the time difference region [t 1 , t 2 ] on the LOR. For another example, another time difference region is between a time difference t 3  and a time different t 4 . The another time difference region corresponds to another path region on the LOR, which may be another event occurrence region. In  FIG. 2 , LOR 12  is taken as an example. The LOR is divided into a plurality of segments. Each of the segments corresponds to a time difference region. When a time difference between two single events in a coincidence event is within a time difference region, it is determined that the coincidence event occurs in the event occurrence region corresponding to the time difference region. 
     In the step, according to a time difference between two single events corresponding to each of LORs associated with the multiple-coincidence data, an event occurrence region corresponding to the time difference on the LOR may be determined. The triple coincidence data “D 3 , D 4  and D 5 ” is taken as an example. In  FIG. 2 , an event occurrence region A on the LOR 12  associated with the coincidence data may be determined according to a time difference between D 3  and D 4 . An event occurrence region B corresponding to the coincidence data on the LOR 13  may be determined according to a time difference between D 3  and D 5 . An event occurrence region C corresponding to the coincidence data on the LOR 23  may be determined according to a time difference between D 4  and D 5 . 
     A line integral value corresponding to each of the LORs associated with the multiple-coincidence data may be obtained by performing a line integral for a TOF kernel function and pixel values of an image along the LOR, where the image is a reconstruction image obtained according to the double-coincidence data. Calculation for a line integral value relates to two factors, e.g., the TOF kernel function and the the pixel values of the image. 
     In an example, the TOF kernel function may be determined according to the time difference between two single events corresponding to the LOR. 
     For example, the TOF kernel function may be a function that a center is not lower than an edge, such as a Gaussian function, an exponential function, or a window function. The Gaussian function is taken as an example. A function center and a standard deviation of the Gaussian function are determined. 
     The function center μ of the Gaussian function is μ=c·(t 2 −t 1 )/2. The function center μ is determined based on the time difference t 2 −t 1 . For example, LOR 12  is taken as an example, t 2  and t 1  in the formula are times when two photons respectively arrive at the crystals J 1  and J 2 , and c represents a velocity of light. In another example, the time difference t 2 −t 1  used for determining the center of the Gaussian function is a midpoint of a time difference region including the time difference between two single events corresponding to the LOR. For example, the time difference between two single events corresponding to the LOR is t 0 , where t 0  is within a time difference region [6,10]. The midpoint value 8 of the region is used as t 2 −t 1  in the formula above. That is, the function center of the TOF kernel function can be obtained according to the time difference region corresponding to the time difference. 
     The standard deviation σ of the Gaussian function is σ=timeRes/(2√{square root over (2 ln 2)}), where timeRes represents a system time resolution. 
     The Gaussian function can be expressed as 
                 g   ⁡     (   x   )       =       1       2   ⁢   πσ         ⁢     e     -         (     x   -   μ     )     2       2   ⁢     σ   2                 ,         
which is determined according to the function center and the standard deviation above, where x in the function represents a radial position corresponding to projection data.
 
     In an example, the image is reconstructed according to the double-coincidence data in the coincidence data to obtain pixel values of the reconstruction image. In  FIG. 2 , the reconstruction image is obtained based on the double-coincidence data in the coincidence data. The line integral corresponds to an integral interval. The line integral is performed on the pixel values of the image in the corresponding integral interval along the LOR. The integral interval may be determined based on the TOF kernel function. For example, the integral interval satisfies 
                   S   1     S     &gt;   Thre     ,         
where S 1  represents an area between a TOF kernel function curve and the LOR in the interval; S represents a total area between the TOF kernel function curve and the LOR, and Thre represents an area proportion threshold, for example, 99%.
 
     The integral interval corresponding to the TOF kernel function may be larger than width of an event occurrence region, e.g., three or four times as large as the width of the event occurrence region. The Gaussian function is taken as an example. To cover most of the area between the TOF kernel function curve and the LOR in the integral interval, the function center may be taken as a midpoint, and a length range including minus and plus three standard deviations is selected, i.e., [−3σ,+3σ]. Line integral is performed along the LOR in the range, e.g., multiplying a pixel value of each pixel point of the image on the LOR by the TOF kernel function and accumulating products to obtain a line integral value. The above selected integral range [−3σ,+3σ] is just as an example, the integral interval is not limited herein. When the above range on the LOR does not go through the reconstructed image, the pixel value is equal to 0. For example, in  FIG. 2 , the pixel values of the image on the path of the LOR 23  is equal to 0. 
     According to the method above, for each of the LORs associated with the multiple-coincidence data, the TOF kernel function is determined according to the time difference between the two single events corresponding to the LOR. The line integral is performed for the TOF kernel function and the pixel values of the image along the LOR in the integral interval to obtain the line integral value corresponding to the LOR. 
     For example, the above-mentioned triple coincidence data “D 3 , D 4  and D 5 ” is taken as an example. 
     The line integral along the LOR 12  may be calculated by a formula as follows:
 
Prob( LOR   12 )=∫ L     12     g   12   I   12   dl  
 
     In the formula above, the integral interval L 12  in the integral formula above may be obtained by the TOF kernel function determined according to the time difference between the two single events D 3  and D 4 . The integral interval may be larger than the width of the event occurrence region in a way that the integral interval can include most of the area between the TOF kernel function and the LOR. The Gaussian function g 12  is determined according to the time difference between D 3  and D 4 , or is determined according to according to the midpoint of the time difference region including the time difference between D 3  and D 4 . I 12  is the pixel value of a pixel point of the reconstruction image in the integral interval L 12 . 
     The line integral along the LOR 13  is calculated by a formula as follows:
 
Prob( LOR   13 )=∫ L     13     g   13   I   13   dl  
 
     In the formula above, the integral interval L 13  is determined according to the TOF kernel function corresponding to the LOR 13  in  FIG. 2 . The Gaussian function g 13  is determined according to the time difference between the two single events D 3  and D 5  in  FIG. 2 , or is determined according to the midpoint of the time difference region including the time difference between D 3  and D 5 . The pixel value I 13  of the image is a pixel value of a pixel point of the reconstruction image in the integral interval L 13  determined according to the kernel function corresponding to the LOR 13 . 
     The line integral along the LOR 23  is calculated by a formula as follows:
 
Prob( LOR   23 )=∫ L     23     g   23   I   23   dl  
 
     In the formula above, the integral interval L 23  is determined according to the TOF kernel function corresponding to the LOR 23  in  FIG. 2 . The Gaussian function g 23  is determined according to the time difference between the two single events D 4  and D 5  in  FIG. 2 , or is determined according to the midpoint of the time difference region including the time difference between D 4  and D 5 . The image pixel value I 23  is a pixel value of a pixel point of the reconstruction image in the integral interval L 23 . 
     A plurality of methods can be used for calculating a line integral, e.g., transforming a line integral into parametric equations corresponding to a line. The line integral corresponding to the LOR 12  is taken as an example. A midpoint between two crystals is expressed by a point M (x c , y c , z c ). The line may be expressed as the parametric equations with k∈[−1, +1]: 
     
       
         
           
               
             
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     For any k∈[−1, +1], a distance to the center of the line (e.g., a location where the time difference is equal to 0) is: 
     
       
         
           
             
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     In this case, the line integral may be expressed in a form of a single integral:
 
Prob( LOR   12 )=∫ −1   +1   g ( Dis ( k )) l ( x,y,z ) dk  
 
     In an example, the parameter σ of a Gaussian function is small relative to the integral range, thus, the integral range is narrowed. The integral value of the Gaussian function outside 6σ is generally equal to 1% of the integral value of the Gaussian function, which can be neglected. 
     In another example, for a PET image reconstructed according to the double-coincidence data, TOF orthographic projection is performed for the image in each event occurrence region on each LOR to obtain a line integral value corresponding to the event occurrence region on the LOR. The process of performing the TOF orthographic projection for the image in the event occurrence region on the LOR is equivalent to performing line integration for a TOF kernel function and the image along the LOR, where a function center of the TOF kernel function is determined according to the midpoint of the event occurrence region. According to the method, a line integral value corresponding to each event occurrence region on each of the LORs is pre-obtained. When the multiple-coincidence data is allocated, the line integral value corresponding to the event occurrence region is directly obtained according to a pre-obtained correspondence. In particular, different LORs corresponding to the multiple-coincidence data is determined. According to a time difference between two single events corresponding to each of the LORs, the event occurrence region corresponding to the time difference is determined; and the line integral value corresponding to the event occurrence region is directly obtained according to the pre-obtained correspondence. 
     Further, the TOF orthographic projection for the reconstruction image may be performed on all LORs, or may be performed on each of the LORs associated with the multiple-coincidence data. 
     At step  103 , according to a proportion of the line integral values corresponding to the LORs, the multiple-coincidence data is allocated to the LORs to obtain multiple allocation data on the LORs. 
     For example, the triple coincidence data “D 3 , D 4  and D 5 ” is taken as an example. The triple-coincidence data may be allocated according to the proportion of the line integral values corresponding to LOR 12 , LOR 13  and LOR 23  calculated in step  103 . In  FIG. 2 , the LOR 23  is not overlapped with the reconstruction image, the pixel values in the event occurrence region is equal to zero, thus, the line integral value along the LOR 23  is equal to zero. The LOR 12  and the LOR 13  are respectively overlapped with the reconstruction image, thus, the line integral values along the LOR 12  and the LOR 13  are not equal to zero. For example, the line integral value of the LOR 12  is large, the line integral value of the LOR 13  is small, and the line integral value of the LOR 23  is zero, where a ratio of the line integral value of the LOR 12  to the line integral value of the LOR 13  is 7/3. 70% of the triple-coincidence data is allocated to the LOR 12 , and 30% of the triple-coincidence data is allocated to LOR 13 . For example, it is assumed that a count value in the double-coincidence data on the LOR 12  is X, a count value in the double-coincidence data on the LOR 13  is Y, and a count value in the double-coincidence data on the LOR 23  is Z. A count value of the multi-coincidence data is M, e.g., M=1. When the multiple-coincidence data is allocated to the LOR 12 , the LOR 13  and the LOR 23 , the count value in the double-coincidence data on the LOR 12  is updated to be X+0.7M, the count value in the double-coincidence data on the LOR 13  is updated to be Y+0.3M, and the count value in the double-coincidence data on the LOR 23  is not changed and remains to be Z. 
     In the example, when the the multiple-coincidence data is allocated to the LORs, data allocated to the LORs may be multiple allocation data. 
     According to the multiple-coincidence data allocating method above, an event allocation proportion corresponding to an LOR is associated with pixel values of an image in an integral interval corresponding to the event on the LOR. In the example above, in a multiple-coincidence event, an LOR is not overlapped with the reconstruction image (e.g., the pixel values for which the line integral is performed is equal to zero). Thus, the line integral value is equal to zero, and an occurrence position of an annihilation event is not on the LOR. That is, even though a count of the double-coincidence data on the LOR is not zero, the LOR is not involved in the multiple-coincidence data allocation. i.e., the multiple-coincidence data is not allocated for the LOR. When no line integral values respectively along three LORs is equal to zero, i.e., the three LORs are respectively overlapped with the reconstruction image, an allocation proportion is estimated according to the line integral values corresponding to the pixel values of the image on the three LORs. When a line integral value for an LOR is large, it is possible that the pixel values in the integral interval on the LOR is large, and a probability that an annihilation event occurs is large, therefore, a probability that the coincidence event occurs on the LOR is large. Thus, according to the data allocating method, the multiple-coincidence data can be accurately allocated. 
     At step  104 , the double-coincidence data and the multiple allocation data on each of the LORs associated with the coincidence data are added together to obtain data of the LOR. 
     For each of the LORs, the coincidence data corresponding to annihilation events which occur on the LOR includes double-coincidence data and multiple-coincidence data. In the example, the multiple-coincidence data allocated to the LOR in the step above and the double-coincidence data on the LOR are added together to obtain the data of the LOR. 
     At step  105 , a PET image is reconstructed according to data of each of the LORs. 
     In the step, the PET image is reconstructed according to an image reconstruction algorithm, which will not be described herein. 
     In examples of the method of reconstructing a PET image, multiple-coincidence data is allocated to each of LORs according to a proportion of line integral values of the LORs in a way that a PET sensitivity is effectively improved, and a quality of the image reconstructed according to the coincidence data of the LOR is good. Further, the method is associated with the pixel values of the image and the time difference, which is not affected when the data is not sufficient. 
     In an example, the PET image reconstruction includes a plurality of corrections, so that reconstruction data is accurate, e.g., random correction, normalization correction, scatter correction and attenuation correction. The corrections can be performed according to various methods, which is be not repeatedly described. In an example of a method of reconstructing a PET image in  FIG. 3 , normalization corrections  305 ,  306  are respectively performed for double-coincidence data  301  and allocated multiple-coincidence data  302 . Random correction  303  is performed based on a random correction factor, which is an addition factor and related with a single-event count rate. In a process in  FIG. 3 , the random correction  303  is performed on a left path of processing the double-coincidence data, and is not performed on a right path of processing the multiple-coincidence data. Thus, it is avoided to repeating random corrections. 
     Scatter correction  308  and attenuation correction  309  are performed after the double-coincidence data and the multiple allocation data are added ( 307 ) together. That is, the scatter correction  308  and the attenuation correction  309  are combined with a subsequent iterative reconstruction algorithm  310  performed after the coincidence data is added together. Thus, Poisson distribution characteristics of data can be maintained, and iterative reconstruction quality of an image is good. 
     Further, in  FIG. 3 , the multiple-coincidence data is allocated to on each of the LORs according to the method in the examples above, which is not repeatedly described herein. In an example, the double-coincidence data detected by a PET device may be replicated to be a copy of the double-coincidence data. One of the original double-coincidence data and the copy double-coincidence data is used for reconstructing a PET image, and line integral is performed for the reconstructed PET image along the LOR. The other is processed based on the process in  FIG. 3 , which is added with the multiple allocation data to obtain the coincidence data. 
     Referring to  FIG. 4 , a PET device is further provided according to examples of the present disclosure. In the PET device, after a γ-photon generated by an annihilation event is detected by a PET detector, data such as a collection time, energy and a position of the photon, is obtained. Coincidence data such as double-coincidence data and multiple-coincidences data is obtained by performing coincidence determination according to the obtained data. The coincidence data may be sent to an image reconstructing device to reconstruct a PET image according to the coincidence data. 
       FIG. 4  schematically illustrates a hardware structure diagram of a PET device, which is provided by an example of the present disclosure. The PET device may include a processor  401  and a machine-readable storage medium  402  storing machine executable instructions. The processor  401  may communicate with the machine-readable storage medium  402  via an internal bus  403 , and execute the method described above by reading and executing the machine executable instructions corresponding to control logic in the machine-readable storage medium  402 . The PET device may further include an external interface  404  to communicate with another device or component. 
     As used herein, the machine-readable storage medium  402  may be any electronic, magnetic, optical, or other physical storage apparatus to contain or store information such as executable instructions, data, and the like. For example, any machine-readable storage medium described herein may be any of Random Access Memory (RAM), volatile memory, non-volatile memory, flash memory, a storage drive (e.g., a hard drive), a solid state drive, any type of storage disc (e.g., a compact disc, a DVD, etc.), and the like, or a combination thereof. 
     As shown in  FIG. 5 , functionally divided, the logic for reconstructing a PET image above may include modules as follows. 
     An LOR determining module  51  is configured to determine a plurality of Lines of Response (LORs) associated with multiple-coincidence data in coincidence data detected by a PET device through scanning, where the coincidence data includes double-coincidence data indicating that two single events satisfy a coincidence condition and the multiple-coincidence data indicating that three or more single events satisfy the coincidence condition, and each of the LORs is a line between crystals corresponding to every two of three or more single events corresponding to the multiple-coincidence data. 
     A multiple-allocating module  52  is configured to obtain a line integral value along each of the LORs associated with the multiple-coincidence data according to a time difference between two single events corresponding to the LOR associated with the multiple-coincidence data; allocate the multiple-coincidence data to the LORs according to respective line integral values of the LORs associated with the multiple-coincidence data, where a part of the multiple-coincidence data allocated to each of the LORs is multiple allocation data on the LOR. 
     A data adding module  53  is configured to correct the respective double-coincidence data in the coincidence data corresponding to each of the LORs based on the multiple allocation data on the LOR to obtain data of the LOR. 
     A reconstructing module  54  is configured to reconstruct a first image according to the data of each of the LORs. 
     In an example, as shown in  FIG. 6 , the multiple-allocating module  52  includes sub-modules as follows. 
     A function determining sub-module  521  is configured to determine a Time-of-Flight (TOF) kernel function according to the time difference between the two single events corresponding to the LOR associated with the multiple-coincidence. 
     An integrating sub-module  522  is configured to integrate the TOF kernel function and pixel values of a second image in a pre-determined range along the LOR to obtain the line integral value of the LOR associated with the multiple-coincidence data, where the second image is reconstructed according to the double-coincidence data in the coincidence data. 
     In an example, the function determining sub-module  521  is configured to obtain a function center of the TOF kernel function according to the time difference between the two single events and determine the TOF kernel function according to the function center. 
     In an example, the function determining sub-module  521  is configured to obtain a midpoint of a time difference region corresponding to the time difference between the two single events, obtain a function center of the TOF function according to the midpoint, and determine the TOF kernel function according to the function center. 
     In an example, as shown in  FIG. 7 , the logic further includes a projecting module  55 . The projecting module  55  is configured to divide the LOR into a plurality of event occurrence regions based on time difference regions, perform TOF orthographic projection for a second image to obtain a line integral value corresponding to each of event occurrence regions on the LOR, where the second image is reconstructed according to the double-coincidence data in the coincidence data, build a correspondence between time difference region and line integral value corresponding to event occurrence region on the LOR, and obtain the line integral value along the LOR associated with the multiple-coincidence data according to the time difference between the two single events corresponding to the LOR associated with the multiple-coincidence data and the correspondence between time difference region and line integral value on the LOR. 
     In an example, the multiple-allocating module  52  includes sub-modules as follows. 
     A time-difference determining sub-module  523  is configured to determine a Time-of-Flight (TOF) kernel function according to the time difference between the two single events corresponding to the LOR associated with the multiple-coincidence. 
     An integral searching sub-module  524  is configured to obtain the line integral value along the LOR associated with the multiple-coincidence data according to the time difference between the two single events corresponding to the LOR associated with the multiple-coincidence data and the correspondence between time difference region and line integral value on the LOR. 
     In an example, the reconstructing module  54  is configured to generate a scatter correction factor and an attenuation correction factor according to the data of each of the LORs, reconstruct the first image according to the scatter correction factor, the attenuation correction factor and the data of each of the LORs. 
     In different examples, the machine readable storage medium  402  may be: a Read-Only Memory (ROM), a volatile memory, a non-volatile memory, a flash memory, a storage drive (e.g. hard disk drive), a solid state hard disk, any type of storage disk (e.g., optical disk, Digital Video Disk (DVD)), or a similar storage medium, or a combination thereof. 
     The foregoing disclosure is merely illustrative of preferred embodiments of the present disclosure but not intended to limit the present disclosure, and any modifications, equivalent substitutions, adaptations thereof made within the spirit and principles of the disclosure shall be encompassed in the scope of protection of the present disclosure.