Image reconstruction method with improved projection coefficient calculation

Abstract

The application provides an image reconstruction method for improving projection coefficient calculation, comprising: acquiring light rays of a measured object passing through a measured area by using a mobile detector; mapping the measured area and the light rays into a same two-dimensional coordinate system; acquiring a first total length of an optical path of the light rays passing through an i-1th pixel; acquiring a second total length of an optical path of the light rays passing through an ith pixel, a third total length of an optical path, and a discriminant value of the ith pixel; according to the discriminant value of the ith pixel, recursively calculating a projection coefficient of the ith pixel from the second total length of the optical path of the ith pixel, the third total length of the optical path, and the first total length of the optical path of the i-1th pixel, and simultaneously updating the first total length of the optical path of the ith pixel, the second total length of the optical path of the light rays passing through an i+1th pixel, the third total length of the optical path, and a discriminant value of the i+1th pixel; recursively calculating the projection coefficient of each pixel of the measured area through which the light rays pass; and acquiring a two-dimensional reconstruction image of the measured object according to multiple projection coefficients of multiple light rays at a target pixel.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of image reconstruction, and particularly relates to an image reconstruction method for improving projection coefficient calculation. BACKGROUND

[0002] Image reconstruction algorithm is widely used in medical CT, combustion diagnosis, gas distribution and other fields. In the process of image reconstruction, the projection coefficient is an important parameter for realizing image reconstruction, and therefore how to quickly and accurately calculate the projection coefficient is a key link affecting the speed and accuracy of image reconstruction. The projection coefficient refers to the weight coefficient of the current pixel to the light attenuation, that is, the length of the optical path in the pixel unit. At present, there are mainly three kinds of methods for calculating the projection coefficient at home and abroad: (1) intersection sorting method, that is, first finding the intersection points of the light and the horizontal and vertical boundaries of the pixel, then sorting the obtained intersection points, and finally obtaining the projection coefficient of the pixel by calculating the distance between the adjacent two intersection points, and obtaining the pixel index through the coordinates of the adjacent two intersection points. This method has no requirement for the position of the light start point, but the calculation amount of finding the intersection points and sorting the intersection points is large and the calculation time is long. (2) Recursive calculation method, that is, starting from the initial pixel, the projection coefficient and index of the next pixel are recursively calculated according to the discriminant value. This method has achieved certain acceleration effect compared with the intersection sorting method, but the fast recursive process is only applicable to the calculation of the projection coefficient in the case that the light penetrates the pixel. (3) Linear calculation method, that is, first determining the start point and end point of the light in the reconstruction region, and then calculating the projection coefficient and pixel index of the pixel by using the linear relationship. This method can also improve the speed of calculating the projection coefficient of the pixel compared with the intersection sorting method, but the coordinates of the light end point need to be known in advance and the algorithm is complex.

[0003] Due to the difference between the traditional reconstruction region such as medical CT, combustion diagnosis and indoor environment, the former has a feature that the gas detector is located outside or on the boundary of the reconstruction region, and the light emitted by the gas detector can penetrate the entire reconstruction region. However, in the process of reconstructing the indoor gas distribution, the emission source can only be approximately placed on the boundary of the reconstruction region, for example, the laser gas detector is fixed on the wall, and only by rotating the angle of the laser gas detector to emit laser to obtain the light on different paths in the room. However, when there is an obstruction in the room, a dead angle is easily generated, and the gas concentration in the obstructed part of the room cannot be detected.

[0004] Therefore, currently, it is increasingly popular to reconstruct indoor gas distribution by using laser lines emitted by mobile laser gas detectors. For example, light rays on different paths are obtained by using laser gas detectors placed on unmanned vehicles to reconstruct gas distribution. In the process of calculating the projection coefficient of the laser line emitted by the mobile laser detector, there are cases that the starting point of the light ray is variable relative to the reconstruction region, the starting point of the light ray is located in the reconstruction region, and the initial pixel of the light ray does not penetrate the reconstruction region. Therefore, the projection coefficient of the laser line cannot be directly calculated by using the existing recursive calculation method, and the projection coefficient of the laser line can only be calculated by using the intersection sorting method, which leads to slow reconstruction speed. In order to improve the speed of the image reconstruction algorithm based on the mobile laser gas detector, it is necessary to study a corresponding fast and effective projection coefficient recursive calculation method to reconstruct indoor gas distribution. The projection coefficient calculation of the image reconstruction method is improved to realize the calculation of the projection coefficient of the starting point of the ray distributed on the pixel boundary and in the pixel, and to achieve the purpose of no starting point constraint. SUMMARY

[0005] Therefore, the image reconstruction method for improving projection coefficient calculation is provided to at least partially solve the above technical problems.

[0006] The image reconstruction method for improving projection coefficient calculation provided by the present application comprises the following steps.

[0007] The light ray of the measured object passing through the measured region is obtained by using the mobile detector, wherein the light ray has starting point coordinates and emission angle.

[0008] The measured region and the light ray are mapped into the same two-dimensional coordinate system.

[0009] The first total length of the light path of the light ray passing through the i-1th pixel is obtained, and the first total length of the light path of the i-1th pixel represents the length of the light path from the starting point to the intersection point of the light ray penetrating the boundary of the i-1th pixel.

[0010] The second total length of the light path of the light ray passing through the i-th pixel, the third total length of the light path, and the discrimination value of the i-th pixel are obtained. The second total length of the light path of the i-th pixel represents the length of the light path from the starting point to the intersection point of the light ray penetrating the boundary line of the i-th pixel along the horizontal coordinate direction. The third total length of the light path of the i-th pixel represents the length of the light path from the starting point to the intersection point of the light ray penetrating the boundary line of the i-th pixel along the vertical coordinate direction.

[0011] According to the discriminant value of the i-th pixel, the projection coefficient of the i-th pixel is recursively calculated from the second total length of the optical path of the i-th pixel, the third total length of the optical path of the i-th pixel and the first total length of the optical path of the (i-1)-th pixel, and the first total length of the optical path of the i-th pixel, the second total length of the optical path and the third total length of the optical path of the (i+1)-th pixel through which the light ray passes, the discriminant value of the (i+1)-th pixel are updated;

[0012] The projection coefficient of each pixel of the measured region through which the light ray passes is recursively calculated until the light ray reaches the edge of the measured region.

[0013] According to the intensity values of the plurality of light rays, a plurality of path integral values of the measured object are obtained.

[0014] According to the projection coefficients of the plurality of light rays at the target pixel and the plurality of path integral values of the measured object, a two-dimensional reconstructed image of the measured object is obtained.

[0015] According to an embodiment of the present application, further comprising:

[0016] The intensity values of a plurality of light rays of different paths and angles are measured by the mobile detector.

[0017] According to an embodiment of the present application, the mobile detector comprises a mobile laser gas detector, the plurality of path integral values of the measured object comprises a plurality of path gas concentration integral values of the measured gas, and the measured object comprises a measured gas.

[0018] According to an embodiment of the present application, further comprising:

[0019] After mapping the measured region and the light ray to the same two-dimensional coordinate system, the parameters of the two-dimensional coordinate system, the parameters of the measured region and the expression parameters of the light ray are initialized; the parameters of the two-dimensional coordinate system include the coordinate origin; the parameters of the measured region include the total number of pixels along the horizontal coordinate direction, the total number of pixels along the vertical coordinate direction, the size of a single pixel along the horizontal coordinate direction, the size of a single pixel along the vertical coordinate direction and the coordinates of the lower left corner pixel of the measured region; the expression parameters of the light ray include the starting pixel coordinates of the light ray and the angle between the light ray and the horizontal coordinate of the two-dimensional coordinate system.

[0020] According to an embodiment of the present application, further comprising:

[0021] Before updating the first total length of the optical path of the i-th pixel, the second total length of the optical path of the i+1-th pixel passing through the i+1-th pixel, the third total length of the optical path of the i+1-th pixel, and the discrimination value of the i+1-th pixel, the vertical length and the horizontal length of the light ray in the measured region are obtained; the vertical length is the optical path length between the intersection points of the light ray and two boundary lines of a single pixel of the measured region along the horizontal coordinate direction; and the horizontal length is the optical path length between the intersection points of the light ray and two boundary lines of a single pixel of the measured region along the vertical coordinate direction.

[0022] According to the embodiment of the present application, when the discrimination value of the i-th pixel is greater than 0, the projection coefficient of the i-th pixel is equal to the difference between the second total length of the optical path of the i-th pixel and the first total length of the optical path of the i-1-th pixel, the second total length of the optical path of the i+1-th pixel is equal to the sum of the second total length of the optical path of the i-th pixel and the vertical length, the third total length of the optical path of the i+1-th pixel is equal to the third total length of the optical path of the i-th pixel, and the first total length of the optical path of the i-th pixel is equal to the second total length of the optical path of the i-th pixel.

[0023] According to the embodiment of the present application, when the discrimination value of the i-th pixel is less than 0, the projection coefficient of the i-th pixel is equal to the difference between the third total length of the optical path of the i-th pixel and the first total length of the optical path of the i-1-th pixel, the second total length of the optical path of the i+1-th pixel is equal to the second total length of the optical path of the i-th pixel, the third total length of the optical path of the i+1-th pixel is equal to the sum of the third total length of the optical path of the i-th pixel and the horizontal length, and the first total length of the optical path of the i-th pixel is equal to the third total length of the optical path of the i-th pixel.

[0024] According to the embodiment of the present application, when the discrimination value of the i-th pixel is equal to 0, the second total length of the optical path of the i-th pixel is equal to the third total length of the optical path of the i-th pixel, the projection coefficient of the i-th pixel is equal to the difference between the second total length of the optical path of the i-th pixel and the first total length of the optical path of the i-1-th pixel, the projection coefficient of the i-th pixel is also equal to the difference between the third total length of the optical path of the i-th pixel and the first total length of the optical path of the i-1-th pixel, the second total length of the optical path of the i+1-th pixel is equal to the sum of the second total length of the optical path of the i-th pixel and the vertical length, the third total length of the optical path of the i+1-th pixel is equal to the sum of the third total length of the optical path of the i-th pixel and the horizontal length, the first total length of the optical path of the i-th pixel is equal to the second total length of the optical path of the i-th pixel, and the first total length of the optical path of the i-th pixel is also equal to the third total length of the optical path of the i-th pixel.

[0025] According to the embodiment of the present application, the method further comprises:

[0026] Before updating the discriminant value of the i+1th pixel, a horizontal traversal direction of the light ray along the horizontal coordinate direction of the two-dimensional coordinate system and a vertical traversal direction of the light ray along the vertical coordinate direction of the two-dimensional coordinate system are obtained.

[0027] According to the embodiments of the present application, the embodiments of the present application further comprise:

[0028] When the discriminant value of the i+1th pixel is updated, the index of the i+1th pixel is also updated; the discriminant value of the i+1th pixel is calculated from the discriminant value of the ith pixel, the horizontal traversal direction, the vertical traversal direction and the slope of the light ray; the index of the i+1th pixel is calculated from the index of the ith pixel, the horizontal traversal direction and the total number of pixels in the horizontal direction of the measured region.

[0029] According to the embodiments of the present application, the embodiments of the present application provide an image reconstruction method for improving the calculation of the projection coefficient, the projection coefficient of each pixel through which the light ray emitted from any starting point of the measured region passes is recursively calculated from the discriminant value of the ith pixel, the second total length of the optical path of the ith pixel, the third total length of the optical path of the ith pixel and the first total length of the optical path of the i-1th pixel, and the first total length of the optical path of the ith pixel, the second total length of the optical path of the i+1th pixel through which the light ray passes, the third total length of the optical path of the i+1th pixel and the discriminant value of the i+1th pixel are updated simultaneously, the recursive process of the projection coefficient and the recursive formula applied in the recursive process are relatively simple, the calculation speed of the projection coefficient is improved, and the time for image reconstruction is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 A flowchart of the image reconstruction method for improving the calculation of the projection coefficient according to the embodiments of the present application is schematically shown.

[0031] Figure 2 A two-dimensional coordinate system, a measured region and a light ray after initialization are schematically shown.

[0032] Figure 3 A schematic diagram of the light ray passing through a target pixel when the discriminant value is greater than 0 is schematically shown.

[0033] Figure 4 A schematic diagram of the light ray passing through a target pixel when the discriminant value is less than 0 is schematically shown.

[0034] Figure 5 A schematic diagram of the light ray passing through a target pixel when the discriminant value is equal to 0 is schematically shown.

[0035] Figure 6 A schematic diagram of the projection coefficients of the pixels through which the light ray 1 passes in sequence is schematically shown. DETAILED DESCRIPTION

[0036] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the invention. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the invention for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0037] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0038] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0039] When using expressions such as "at least one of A, B, and C," the expression should generally be interpreted in accordance with the meaning commonly understood by a person skilled in the art (e.g., "a system having at least one of A, B, and C" should include, but is not limited to, systems having A alone, having B alone, having C alone, having A and B, having A and C, having B and C, and / or having A, B, and C, etc.). Similarly, when using expressions such as "at least one of A, B, or C," the expression should generally be interpreted in accordance with the meaning commonly understood by a person skilled in the art (e.g., "a system having at least one of A, B, or C" should include, but is not limited to, systems having A alone, having B alone, having C alone, having A and B, having A and C, having B and C, and / or having A, B, and C, etc.).

[0040] Currently, it is popular to reconstruct indoor gas distribution by using laser lines emitted by mobile laser gas detectors. For example, laser lines emitted by laser gas detectors placed on unmanned vehicles are used to reconstruct gas distribution along different paths in the room. In the process of calculating the projection coefficient of the laser line emitted by the mobile laser detector, there are cases where the starting point of the light ray is variable relative to the reconstruction region, the starting point of the light ray is located in the reconstruction region, and the initial pixel of the light ray does not penetrate the reconstruction region. Therefore, the existing recursive calculation method cannot be directly used to calculate the projection coefficient of the laser line, and a corresponding fast and effective projection coefficient recursive calculation method needs to be studied to reconstruct the indoor gas distribution. In order to achieve the projection coefficient calculation considering the distribution of the starting point of the ray on the boundary of the pixel and in the pixel, and to achieve the purpose of no starting point constraint.

[0041] Based on the problems encountered in the process of reconstructing indoor gas distribution by using laser light emitted by a mobile laser gas detector according to the prior art, the present application proposes an improved projection coefficient calculation image reconstruction method. According to the discrimination value of the i-th pixel, the projection coefficient of the i-th pixel is recursively calculated from the second total length of the light path of the i-th pixel, the third total length of the light path of the i-th pixel and the first total length of the light path of the i-1-th pixel. At the same time, the first total length of the light path of the i-th pixel, the second total length of the light path of the i+1-th pixel and the third total length of the light path of the i+1-th pixel, and the discrimination value of the i+1-th pixel are updated. The projection coefficient of each pixel through which the light ray emitted from any starting point of the measured region is recursively calculated using the latest recursive result. The recursive process of the projection coefficient of the present method and the recursive formula applied in the recursive process are relatively simple. Compared with the traditional intersection sorting method, the calculation speed of the projection coefficient is improved, the time of image reconstruction is reduced, and the recursive process has no requirement for the position of the starting point of the light ray. Compared with the traditional recursive calculation method, the present method has a wider application range.

[0042] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application is further described in detail below with reference to specific embodiments and with reference to the accompanying drawings.

[0043] Figure 1 A flowchart of the improved projection coefficient calculation image reconstruction method according to the embodiment of the present disclosure is schematically shown.

[0044] As shown in Figure 1 The image reconstruction method 100 of the improved projection coefficient calculation method of the present embodiment can include operations S101-S108.

[0045] In operation S101, the light ray passing through the measured object in the measured region is obtained by using a mobile detector.

[0046] According to the embodiment of the present application, a laser line of a predetermined intensity and waveband can be emitted indoors by using a mobile laser gas detector, and the laser line reflected back after being absorbed by the gas to be measured is measured.

[0047] According to an embodiment of the present application, the light ray has a starting point coordinate and a projection angle, which can be determined according to the position and angle of the mobile laser gas detector when emitting the laser.

[0048] In operation S102, the measured region and the light ray are mapped into the same two-dimensional coordinate system.

[0049] In operation 103, the first total length of the light path of the light ray passing through the i-1th pixel is obtained.

[0050] According to an embodiment of the present application, the first total length of the light path of the i-1th pixel represents the length of the light path from the starting point to the intersection point of the light ray and the boundary of the i-1th pixel.

[0051] In operation 104, the second total length of the light path of the light ray passing through the ith pixel, the third total length of the light path, and the discriminant value of the ith pixel are obtained.

[0052] According to an embodiment of the present application, the second total length of the light path of the ith pixel represents the length of the light path from the starting point to the intersection point of the light ray and the boundary line of the ith pixel extended along the horizontal coordinate direction, and the third total length of the light path of the ith pixel represents the length of the light path from the starting point to the intersection point of the light ray and the boundary line of the ith pixel extended along the vertical coordinate direction.

[0053] In operation 105, according to the discriminant value of the ith pixel, the projection coefficient of the ith pixel is recursively calculated from the second total length of the light path of the ith pixel, the third total length of the light path of the ith pixel, and the first total length of the light path of the i-1th pixel, and the first total length of the light path of the ith pixel, the second total length of the light path of the light ray passing through the i+1th pixel, the third total length of the light path, and the discriminant value of the i+1th pixel are updated.

[0054] In operation 106, the projection coefficient of each pixel of the measured region through which the light ray passes is recursively calculated until the light ray reaches the edge of the measured region.

[0055] In operation 107, according to the intensity values of the plurality of light rays, a plurality of path integral values of the measured object are obtained.

[0056] According to an embodiment of the present application, the intensity values of the plurality of light rays can be converted into path integral values according to the Beer-Lambert absorption law.

[0057] According to an embodiment of the present application, since different gases have different absorption intensities for different wave bands of laser, the intensity of the laser line reflected back after being absorbed by the gas to be measured can be converted into a path gas concentration integral value according to the Beer-Lambert absorption law.

[0058] In operation 108, a two-dimensional reconstructed image of the object under test is obtained based on the projection coefficients of multiple rays at the target pixel and the multiple path integral values ​​of the object under test.

[0059] According to an embodiment of the present invention, after obtaining the projection coefficients of multiple laser lines at the target pixel and the multiple path integral values ​​of the gas being measured, the gas concentration value at the target pixel can be iteratively calculated according to the ART algorithm. Each pixel in the measured area is used as a target pixel to calculate the gas concentration value at each pixel in the measured area, thereby obtaining a two-dimensional gas concentration distribution map.

[0060] According to an embodiment of the present invention, the improved image reconstruction method for calculating projection coefficients further includes: using a moving detector to measure the light intensity values ​​of multiple different paths and angles.

[0061] According to embodiments of the present invention, for example, the intensity of multiple laser lines with different paths and angles can be measured multiple times using a mobile laser gas detector.

[0062] According to an embodiment of the present invention, the moving detector includes a moving laser gas detector, the multiple path integral values ​​of the measured object include the multiple path gas concentration integral values ​​of the measured gas, and the measured object includes the measured gas.

[0063] According to an embodiment of the present invention, the improved image reconstruction method for calculating projection coefficients further includes: mapping the measured area and light rays to the same two-dimensional coordinate system, and initializing the parameters of the two-dimensional coordinate system, the parameters of the measured area, and the expression parameters of the light rays.

[0064] Figure 2 The diagram schematically illustrates the initialized two-dimensional coordinate system, the area being measured, and the light rays.

[0065] like Figure 2 As shown, during the process of mapping the measured area and ray 1 to the same two-dimensional coordinate system, the measured area is divided into a grid of m rows and n columns, with each grid representing a pixel. The center O of the measured area is the origin of the two-dimensional coordinate system. The total number of pixels in the reconstructed area is N = m × n, where n is the total number of pixels along the horizontal axis (i.e., the number of pixel columns) and m is the total number of pixels along the vertical axis (i.e., the number of pixel rows). Each pixel in the measured area is a small square with a side length of δ = 1. When the pixel side length is not a unit length of 1, the side length of the pixels in the measured area can be made to a unit length of 1 by scaling the size of the measured area. The coordinates of the pixel at the lower left corner of the reconstructed area are P. min (x min y min Pixel indices are numbered from left to right and from bottom to top.

[0066] like Figure 2As shown, the starting point coordinate of the light path represented by the light ray 1 in the two-dimensional coordinate system is P start (x start , y start ), and the angle between the light ray 1 and the positive direction of the horizontal coordinate of the two-dimensional coordinate system is θ, where θ ∈ (-π, π].

[0067] According to the embodiment of the present application, the starting point pixel coordinate of the laser light ray in the two-dimensional coordinate system and the angle between the light ray and the horizontal coordinate of the two-dimensional coordinate system can be obtained according to the position and angle of the mobile laser gas detector when emitting laser light.

[0068] According to the embodiment of the present application, the vertical length h0 is calculated by formula (1), and the horizontal length v0 is calculated by formula (2).

[0069]

[0070]

[0071] wherein k in formula (1) and formula (2) is the slope of the light ray, k = tanθ, and θ ≠ π. When θ equals , v0 equals 0 and h0 equals 1, and when θ equals ±π, v0 equals 1 and h0 equals 0.

[0072] According to the embodiment of the present application, when the discrimination value of the ith pixel is greater than 0, the projection coefficient of the ith pixel is equal to the difference between the second total length of the optical path of the ith pixel and the first total length of the optical path of the (i-1)th pixel, the second total length of the optical path of the (i+1)th pixel is equal to the sum of the second total length of the optical path of the ith pixel and the vertical length, the third total length of the optical path of the (i+1)th pixel is equal to the third total length of the optical path of the ith pixel, and the first total length of the optical path of the ith pixel is equal to the second total length of the optical path of the ith pixel.

[0073] According to the embodiment of the present application, the first total length of the optical path of the pixel corresponding to the starting point of the light ray is 0, the second total length of the optical path of the pixel is h start calculated by formula (3), and the third total length of the optical path of the pixel is v start calculated by formula (4).

[0074]

[0075]

[0076] wherein θ in formula (3) and formula (4) is the angle between the light ray and the positive direction of the horizontal coordinate of the two-dimensional coordinate system, x start and y start respectively represent the starting point horizontal coordinate value and vertical coordinate value, and These represent the x and y coordinates of the discrimination point, respectively, and the discrimination point is selected based on the value of θ. When the starting point is defined, the discrimination point is the coordinates of the upper right vertex of the pixel containing the starting point; when... When the starting point is defined, the discrimination point is the coordinates of the top-left vertex of the pixel containing the starting point; when... When the starting point is defined, the discrimination point is the coordinates of the lower right vertex of the pixel containing the starting point; when... When the point of discrimination is determined, it is the coordinate of the lower left vertex of the pixel where the starting point is located.

[0077] According to an embodiment of the present invention, when the discrimination value of the i-th pixel is greater than 0, the projection coefficient s of the i-th pixel is... i The total optical path length h of the (i+1)th pixel is calculated using formula (5). i+1 The total length of the third optical path of the (i+1)th pixel, v i+1 and the total optical path length l of the first pixel i It is calculated using formula (6).

[0078] s i =h i -l i-1 (5)

[0079]

[0080] Among them, h in formula (5) and formula (6) i Let l be the total second optical path length of the i-th pixel. i-1 v is the total optical path length of the first optical path of the (i-1)th pixel. i Let be the total length of the third optical path of the i-th pixel.

[0081] Figure 3 This diagram illustrates the passage of light through a target pixel when the discrimination value is greater than 0.

[0082] like Figure 3 As shown, the index of the target pixel is q. When the discrimination value of the target pixel is greater than 0, there are three types of light rays passing through the target pixel: ray 2, ray 3, and ray 4.

[0083] like Figure 3 As shown, ray 2 passes sequentially through the pixel with pixel index q-1, the pixel with pixel index q, and the pixel with pixel index q+n. At this point, the total length of the first optical path of the pixel with pixel index q-1 is l. 2last That is Figure 3 The length of the dashed line in the diagram, and the total lengths of the second and third optical paths of the pixel with pixel index q are h, respectively. 2q and v 2q The vertical length of ray 2 is h. 20 The horizontal length is v20 According to formula (5), the projection coefficient s of the pixel with pixel index q can be quickly derived recursively. 2q =h 2q -l 2last According to formula (6), the total length of the second optical path and the total length of the third optical path of the pixel with pixel index q+n can be quickly calculated recursively as h. 2next =h 2q +h 20 and v 2next =v 2q The first optical path length of the pixel with pixel index q is l. 2q =h 2q The same applies to light rays 3 and 4.

[0084] like Figure 3 As shown, when the discriminant value of the pixel with pixel index q is greater than 0, rays 2, 3, and 4 all pass through the pixel with pixel index q. Based on the most recent recursive result related to the pixel with pixel index q, the projection coefficients of rays 2, 3, and 4 with different starting points at the position of the pixel with pixel index q can be quickly calculated using formula (5), reducing image reconstruction time. Furthermore, the recursive result of the next pixel related to the pixel with pixel index q can be quickly calculated using formula (6), preparing for the rapid calculation of the projection coefficient of the next pixel related to the pixel with pixel index q, further shortening the image reconstruction time.

[0085] According to an embodiment of the present invention, when the discrimination value of the i-th pixel is less than 0, the projection coefficient of the i-th pixel is equal to the difference between the total third optical path length of the i-th pixel and the total first optical path length of the (i-1)-th pixel, the total second optical path length of the (i+1)-th pixel is equal to the total second optical path length of the i-th pixel, the total third optical path length of the (i+1)-th pixel is equal to the sum of the total third optical path length of the i-th pixel and the horizontal length, and the total first optical path length of the i-th pixel is equal to the total third optical path length of the i-th pixel.

[0086] According to an embodiment of the present invention, when the discrimination value of the i-th pixel is less than 0, the projection coefficient s of the i-th pixel is... i The total length h of the second optical path of the (i+1)th pixel is calculated using formula (7). i+1 The total length of the third optical path of the (i+1)th pixel, v i+1 The total optical path length li of the first optical path of the i-th pixel is calculated by formula (8).

[0087] s i =v i -l i-1 (7)

[0088]

[0089] Figure 4 A diagram is shown schematically in which the light ray passes through the target pixel in the case that the discriminant is less than 0.

[0090] As shown in Figure 4 , the index of the target pixel is q, and in the case that the discriminant of the target pixel is less than 0, the light ray passing through the target pixel has three cases: light ray 5, light ray 6 and light ray 7.

[0091] As shown in Figure 4 , light ray 5 passes through the pixel with index q-1, the pixel with index q and the pixel with index q+1 in turn. At this time, the first total length of the optical path of the pixel with index q-1 is l 5last , which is the length of the dashed line in Figure 4 , the second total length of the optical path and the third total length of the optical path of the pixel with index q are h 5q and v 5q respectively, the vertical length of light ray 5 is h 50 , and the horizontal length is v 50 . According to formula (7), the projection coefficient of the pixel with index q can be quickly recursively calculated as s 5q = v 5q -l 5last . According to formula (8), the second total length of the optical path and the third total length of the optical path of the pixel with index q+1 can be quickly recursively calculated as h 5nedt = h 5q and v 5next = v 5q +v 50 respectively, and the first total length of the optical path of the pixel with index q is l 2q = h 2q , and the same applies to light rays 6 and 7.

[0092] As shown in Figure 4 , in the case that the discriminant of the pixel with index q is less than 0, light rays 5, 6 and 7 all pass through the pixel with index q. According to the last recursive result obtained in relation to the pixel with index q, the projection coefficients of light rays 5, 6 and 7 at the position of the pixel with index q can be quickly recursively calculated by formula (7), reducing the image reconstruction time. The recursive result of the next pixel in relation to the pixel with index q can be quickly recursively calculated by formula (8), preparing for the quick recursive calculation of the projection coefficient of the next pixel in relation to the pixel with index q, further shortening the image reconstruction time.

[0093] According to the embodiment of the present application, when the discrimination value of the i-th pixel is equal to 0, the second total length of the optical path of the i-th pixel is equal to the third total length of the optical path of the i-th pixel, the projection coefficient of the i-th pixel is equal to the difference between the second total length of the optical path of the i-th pixel and the first total length of the optical path of the (i-1)-th pixel, the projection coefficient of the i-th pixel is also equal to the difference between the third total length of the optical path of the i-th pixel and the first total length of the optical path of the (i-1)-th pixel, the second total length of the optical path of the (i+1)-th pixel is equal to the sum of the second total length of the optical path of the i-th pixel and the vertical length, the third total length of the optical path of the (i+1)-th pixel is equal to the sum of the third total length of the optical path of the i-th pixel and the horizontal length, the first total length of the optical path of the i-th pixel is equal to the second total length of the optical path of the i-th pixel, and the first total length of the optical path of the i-th pixel is also equal to the third total length of the optical path of the i-th pixel.

[0094] According to the embodiment of the present application, when the discrimination value of the i-th pixel is equal to 0, the projection coefficient s i of the i-th pixel is calculated by the first formula in formula (9), the second total length h i+1 of the optical path of the (i+1)-th pixel is calculated by the second formula in formula (9), the third total length v i+1 of the optical path of the (i+1)-th pixel is calculated by the third formula in formula (9), and the first total length l i of the optical path of the i-th pixel is calculated by formula (10).

[0095]

[0096]

[0097] of the i-th pixel is equal to 0, h i is equal to v i , so the projection coefficient s i of the i-th pixel can be calculated by the first formula in formula (9) or by the second formula in formula (9), l i can be calculated by the first formula in the third formula in formula (10) or by the second formula.

[0098] Figure 5 A schematic diagram showing the light rays passing through the target pixel when the discrimination value is equal to 0 is shown.

[0099] As shown in FIG. 8, the index of the target pixel is q, and when the discrimination value of the target pixel is equal to 0, the light rays passing through the target pixel include three cases: the light ray 8, the light ray 9 and the light ray 10. Figure 5 As shown in FIG. 8, the light ray 8 passes through the pixel with the index q-1, the pixel with the index q and the pixel with the index q+n+1 in sequence. At this time, the first total length of the optical path of the pixel with the index q-1 is l

[0100] Figure 5 As shown in FIG. 8, the light ray 8 passes through the pixel with the index q-1, the pixel with the index q and the pixel with the index q+n+1 in sequence. At this time, the first total length of the optical path of the pixel with the index q-1 is l​8last That is Figure 5 The length of the dashed line in the diagram, and the total lengths of the second and third optical paths of the pixel with pixel index q are h, respectively. 8q and v 8q The vertical length of ray 8 is h. 80 The horizontal length is v 80 According to formula (9), the projection coefficient s of the pixel with pixel index q can be quickly derived recursively. 8q =v 9q -l 9last or s 8q =h 9q -l 9last According to formula (10), the total length of the second optical path and the total length of the third optical path of the pixel with pixel index q+n+1 can be quickly calculated recursively as h. 8hext =h 8q +h 80 and v 8next =v 8q +v 80 The first optical path length of the pixel with pixel index q is l. 8q =h 8q or l 8q =v 8q The same applies to light rays 9 and 10.

[0101] like Figure 5 As shown, when the discrimination value of the pixel with pixel index q is equal to 0, rays 8, 9, and 10 all pass through the pixel with pixel index q. Based on the most recent recursive result related to the pixel with pixel index q, the projection coefficients of rays 8, 9, and 10 with different starting points at the position of the pixel with pixel index q can be quickly calculated using formula (9), reducing image reconstruction time. Furthermore, the recursive result of the next pixel related to the pixel with pixel index q can be quickly calculated using formula (10), preparing for the rapid calculation of the projection coefficient of the next pixel related to the pixel with pixel index q, further shortening the image reconstruction time.

[0102] Figure 6 A schematic diagram illustrating the projection coefficients of the pixels through which ray 1 passes in sequence.

[0103] like Figure 6 As shown, ray 1 passes through pixels 0 to 11 in sequence. Figure 6 and Figure 1 The two-dimensional coordinate system and the initialization parameters of ray 1 are kept consistent. Figure 6 s in i-1is the projection coefficient of the i-1th pixel, wherein i=1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12. According to the formulas (6)-(11), the projection coefficient of the i-1th pixel is recursively calculated in turn i-1 , until the light ray reaches the boundary of the two-dimensional coordinate system. When the projection coefficient of the 5th pixel is recursively calculated, the first total length of the optical path of the 4th pixel is l4=v start +v0+v0, the second total length of the optical path of the 5th pixel is h5=h start +h0+h0, the third total length of the optical path of the 5th pixel is v5=v start +v0+v0+v0, the first total length of the optical path of the 5th pixel is h5, and the projection coefficient of the 5th pixel is s5=h5-l4.

[0104] According to the embodiment of the present application, further comprising:

[0105] Before updating the discriminant value of the i+1th pixel, the horizontal traversal direction of the light ray along the horizontal coordinate direction of the two-dimensional coordinate system and the vertical traversal direction of the light ray along the vertical coordinate direction of the two-dimensional coordinate system are obtained.

[0106] According to the embodiment of the present application, the horizontal traversal direction x dir is obtained according to the formula (11), and the vertical traversal direction y dir is obtained according to the formula (12).

[0107]

[0108]

[0109] According to the embodiment of the present application, further comprising:

[0110] When updating the discriminant value of the i+1th pixel, the index of the i+1th pixel is also updated; the discriminant value of the i+1th pixel is calculated from the discriminant value of the i-th pixel, the horizontal traversal direction, the vertical traversal direction and the slope of the light ray; and the index of the i+1th pixel is calculated from the index of the i-th pixel, the horizontal traversal direction and the total number of pixels along the horizontal direction of the two-dimensional coordinate system.

[0111] According to the embodiment of the present application, the discriminant value Δ0 of the starting pixel is calculated according to the formula (13).

[0112]

[0113] According to the embodiment of the present application, the discriminant value of the pixel other than the starting pixel is calculated according to the formula (14).

[0114]

[0115] wherein Δ i+1 represents the discriminant value of the i+1th pixel, Δ i represents the discriminant value of the ith pixel.

[0116] According to an embodiment of the present application, the index q0 of the starting pixel is calculated by formula (15).

[0117]

[0118] wherein Δ represents the upward rounding, represents the downward rounding, x min represents the horizontal coordinate value of the leftmost boundary of the reconstruction region in the two-dimensional coordinate system, y min represents the vertical coordinate value of the lowermost boundary of the reconstruction region in the two-dimensional coordinate system.

[0119] According to an embodiment of the present application, the index of the pixel other than the starting pixel is calculated by formula (16).

[0120]

[0121] According to an embodiment of the present application, after the projection coefficients of each of the plurality of laser light rays at the target pixel and the plurality of path gas concentration integral values of the measured gas are obtained, the gas concentration value at the target pixel can be iteratively calculated according to the ART algorithm. Formula (17) is a specific formula for calculating the gas concentration value at the target pixel using the ART algorithm.

[0122]

[0123] wherein f a is the discrete gas concentration after the gas concentration f(x, y) of the entire measured region is discretized into N pixels, and the corresponding gas concentration value at each pixel position is denoted as a constant f a (1≤a≤N), p b (1≤b≤M) is the M path gas concentration integral values, w ab is the projection coefficient of the bth light ray at the ath pixel, representing the contribution weight coefficient of the ath pixel to the bth light ray gas concentration integral value.

[0124] Formula (17) can be represented by the matrix in formula (18).

[0125] WF=P (18)

[0126] wherein W in formula (18) is an M×N-dimensional projection coefficient matrix, F is an N-dimensional gas concentration vector, and P is an M-dimensional path gas concentration integral value vector.

[0127] The formula (17) is expressed by the formula (18), that is, the reconstruction problem of the gas concentration distribution is converted into the problem of solving the high-dimensional linear equations. However, in the process of solving the high-dimensional linear equations, the linear equations are often overdetermined or underdetermined, and various noises are contained in the actually obtained multiple projection coefficients and multiple path gas concentration integral values, so that the linear equations have no solution or have infinite solutions. Therefore, the linear equations cannot be directly solved by an analytical method, but can only be solved by an iterative algorithm. The formula (19) is the formula for iterative calculation of f a .

[0128]

[0129] In the formula (19), j is the iteration number, and λ (0 < λ < 2) is a relaxation factor. The greater the λ is, the faster the convergence speed is. After a given initial value f0 of the gas concentration is given, the M path gas concentration integral values and the MxN projection coefficients are brought into the formula (19), and the next gas concentration value f1 is calculated by using the formula (19), so that one complete iteration is completed. The above iteration is repeated until the error of the results of two adjacent iterations is less than a threshold value or the iteration number exceeds a threshold value. The gas concentration value calculated in the last iteration is taken as the gas concentration value at the target pixel, and the gas concentration value at each pixel in the measured region is calculated by taking each pixel in the measured region as the target pixel, so that a two-dimensional gas concentration distribution map is obtained.

[0130] According to the formula (19), the projection coefficient is repeatedly used in the process of reconstructing the two-dimensional gas concentration distribution by using the ART algorithm, so that the fast and accurate calculation of the projection coefficient is a key factor for determining whether the algorithm can be quickly reconstructed.

[0131] According to the embodiments of the present application, the projection coefficients recursively obtained in the embodiments of the present application are mainly used for reconstructing the two-dimensional gas concentration distribution in a room, but can also be used for reconstructing the two-dimensional image of other measured objects.

[0132] The embodiments of the present application are described above. However, these embodiments are only for illustrative purposes, and are not intended to limit the scope of the present application. Although each embodiment is described above, this does not mean that the measures in each embodiment cannot be advantageously combined. The scope of the present application is defined by the appended claims and their equivalents. Without departing from the scope of the present application, various alternatives and modifications can be made by those skilled in the art, and all of these alternatives and modifications should fall within the scope of the present application.

Claims

1. An improved image reconstruction method for calculating projection coefficients, comprising: A moving detector is used to acquire light rays passing through the measured area of ​​the object, wherein the light rays have origin coordinates and emission angle; The measured area and the light rays are mapped onto the same two-dimensional coordinate system; Obtain the first total optical path length of the light ray passing through the (i-1)th pixel, where the first total optical path length of the (i-1)th pixel represents the optical path length of the light ray from its starting point to the point where the light ray intersects the boundary of the (i-1)th pixel. Obtain the second total optical path length, the third total optical path length, and the discrimination value of the i-th pixel; the second total optical path length of the i-th pixel represents the optical path length from the starting point of the ray to the point where the ray intersects with the boundary line extending along the horizontal axis of the i-th pixel; the third total optical path length of the i-th pixel represents the optical path length from the starting point of the ray to the point where the ray intersects with the boundary line extending along the vertical axis of the i-th pixel. Based on the discrimination value of the i-th pixel, the projection coefficient of the i-th pixel is recursively calculated from the second total optical path length of the i-th pixel, the third total optical path length of the i-th pixel, and the first total optical path length of the (i-1)-th pixel. At the same time, the first total optical path length of the i-th pixel, the second total optical path length and the third total optical path length of the light passing through the (i+1)-th pixel, and the discrimination value of the (i+1)-th pixel are updated. The projection coefficient of each pixel in the measured area through which the light passes is calculated recursively until the light reaches the edge of the measured area; Based on the intensity values ​​of each of the multiple light rays, obtain multiple path integral values ​​of the object under test; A two-dimensional reconstructed image of the object under test is obtained based on the projection coefficients of each of the multiple rays at the target pixel and the multiple path integral values ​​of the object under test.

2. The image reconstruction method according to claim 1 further includes: The moving detector is used to measure the light intensity values ​​along multiple different paths and at different angles.

3. The image reconstruction method according to claim 1, wherein the moving detector includes a moving laser gas detector, the multiple path integral values ​​of the object under test include multiple path gas concentration integral values ​​of the gas under test, and the object under test includes the gas under test.

4. The image reconstruction method according to claim 1 further includes: After mapping the measured area and the ray to the same two-dimensional coordinate system, the parameters of the two-dimensional coordinate system, the parameters of the measured area, and the expression parameters of the ray are initialized. The parameters of the two-dimensional coordinate system include the origin. The parameters of the measured area include the total number of pixels along the horizontal axis, the total number of pixels along the vertical axis, the size of a single pixel along the horizontal axis, the size of a single pixel along the vertical axis, and the coordinates of the pixel at the lower left corner of the measured area. The expression parameters of the ray include the starting pixel coordinates of the ray and the angle between the ray and the horizontal axis of the two-dimensional coordinate system.

5. The image reconstruction method according to claim 1, further comprising: Before updating the first total optical path length of the i-th pixel, the second total optical path length and the third total optical path length of the ray passing through the (i+1)-th pixel, and the discrimination value of the (i+1)-th pixel, the vertical length and horizontal length of the ray in the measured area are obtained; the vertical length is the optical path length between the intersection of the ray and the two boundary lines along the horizontal axis of a single pixel in the measured area; the horizontal length is the optical path length between the intersection of the ray and the two boundary lines along the vertical axis of a single pixel in the measured area.

6. In the image reconstruction method according to claim 5, when the discrimination value of the i-th pixel is greater than 0, the projection coefficient of the i-th pixel is equal to the difference between the total second optical path length of the i-th pixel and the total first optical path length of the (i-1)-th pixel, the total second optical path length of the (i+1)-th pixel is equal to the sum of the total second optical path length of the i-th pixel and the vertical length, the total third optical path length of the (i+1)-th pixel is equal to the total third optical path length of the i-th pixel, and the total first optical path length of the i-th pixel is equal to the total second optical path length of the i-th pixel.

7. The image reconstruction method according to claim 5, wherein when the discrimination value of the i-th pixel is less than 0, the projection coefficient of the i-th pixel is equal to the difference between the total third optical path length of the i-th pixel and the total first optical path length of the (i-1)-th pixel, the total second optical path length of the (i+1)-th pixel is equal to the total second optical path length of the i-th pixel, the total third optical path length of the (i+1)-th pixel is equal to the sum of the total third optical path length of the i-th pixel and the horizontal length, and the total first optical path length of the i-th pixel is equal to the total third optical path length of the i-th pixel.

8. The image reconstruction method according to claim 5, wherein when the discrimination value of the i-th pixel is equal to 0, the total second optical path length of the i-th pixel is equal to the total third optical path length of the i-th pixel, the projection coefficient of the i-th pixel is equal to the difference between the total second optical path length of the i-th pixel and the total first optical path length of the (i-1)-th pixel, the projection coefficient of the i-th pixel is also equal to the difference between the total third optical path length of the i-th pixel and the total first optical path length of the (i-1)-th pixel, the total second optical path length of the (i+1)-th pixel is equal to the sum of the total second optical path length of the i-th pixel and the vertical length, the total third optical path length of the (i+1)-th pixel is equal to the sum of the total third optical path length of the i-th pixel and the horizontal length, the total first optical path length of the i-th pixel is equal to the total second optical path length of the i-th pixel, and the total first optical path length of the i-th pixel is also equal to the total third optical path length of the i-th pixel.

9. The image reconstruction method according to claim 1, further comprising: Before updating the discrimination value of the (i+1)th pixel, obtain the horizontal traversal direction of the light along the x-coordinate direction of the two-dimensional coordinate system and the vertical traversal direction along the y-coordinate direction of the two-dimensional coordinate system.

10. The image reconstruction method according to claim 9, further comprising: When updating the discrimination value of the (i+1)th pixel, the index of the (i+1)th pixel is also updated simultaneously; The discrimination value of the (i+1)th pixel is calculated from the discrimination value of the i-th pixel, the horizontal traversal direction, the vertical traversal direction, and the slope of the light ray. The index of the (i+1)th pixel is calculated from the index of the i-th pixel, the horizontal traversal direction, and the total number of pixels in the measured area along the horizontal direction.

Images