CN111369638B - Laser reflection tomography undersampled reconstruction method, storage medium and system - Google Patents

Laser reflection tomography undersampled reconstruction method, storage medium and system Download PDF

Info

Publication number
CN111369638B
CN111369638B CN202010459498.3A CN202010459498A CN111369638B CN 111369638 B CN111369638 B CN 111369638B CN 202010459498 A CN202010459498 A CN 202010459498A CN 111369638 B CN111369638 B CN 111369638B
Authority
CN
China
Prior art keywords
projection
image
laser
reconstructed
projection data
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010459498.3A
Other languages
Chinese (zh)
Other versions
CN111369638A (en
Inventor
胡以华
石亮
赵楠翔
徐世龙
张鑫源
王磊
杨星
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
National University of Defense Technology
Original Assignee
National University of Defense Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by National University of Defense Technology filed Critical National University of Defense Technology
Priority to CN202010459498.3A priority Critical patent/CN111369638B/en
Publication of CN111369638A publication Critical patent/CN111369638A/en
Application granted granted Critical
Publication of CN111369638B publication Critical patent/CN111369638B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography

Abstract

The invention discloses a laser reflection tomography undersampling reconstruction method, which comprises the following steps: the method comprises the following steps that firstly, a laser emits narrow laser pulses to irradiate a target, laser scanning is carried out around the target at equal projection angle intervals, and original projection data of the multi-view target under-sampled projection angles at complete angles are obtained; step two, carrying out back projection center alignment processing on the multi-view target original projection data under the projection angle under the complete angle; thirdly, sparse observation sampling is carried out on the projection data subjected to the back projection center alignment processing by utilizing a local Hadamard matrix; and step four, carrying out iterative processing of joint algebraic reconstruction and total variation minimization adjustment on the projection data after sparse observation sampling in sequence. The invention also discloses a storage medium and a system. The invention realizes reconstruction of a high-quality laser image by sampling projection data at a few angles, accelerates the convergence of image iterative reconstruction and ensures the quality of the reconstructed image.

Description

Laser reflection tomography undersampled reconstruction method, storage medium and system
Technical Field
The invention belongs to the technical field of laser reflection tomography processing, and particularly relates to a laser reflection tomography undersampling reconstruction method, a storage medium and a system.
Background
Laser reflection Tomography (J) is a remote high-precision imaging method (r.m. marino, r.n. caps, w.e. Keicher et al. Tomographic image reception from laser radar reflection Tomography) formed by combining Computer Tomography (CT for short) with laser radar]SPIE Laser Radar III, 1988, Vol.999: 248-263). The difference between the two is that laser reflection tomography is based on the reflection characteristic coefficient of the object surface, and generally needs to acquire the projection number within the 360-degree projection angle rangeClear target images can be reconstructed; CT imaging is based on the transmission characteristic coefficient inside an object, and a target image can be reconstructed only by acquiring projection data within a 180-degree projection angle range. More importantly, laser reflection tomography mainly images non-cooperative targets, and is difficult to acquire fully sampled projection data within the range of 360-degree projection angles generally and even difficult to acquire projection data within the range of 360-degree projection angles under special conditions; in contrast, in CT imaging, it is relatively easy to acquire fully sampled reflected projection data at angles within the 180 ° or 360 ° projection angle range for imaging of a cooperative target. Theoretically, according to the Nyquist sampling theorem, the maximum projection angle sampling interval required by completely reconstructing a detection target laser image within a complete angle range of 360 DEG is satisfied
Figure 726796DEST_PATH_IMAGE001
Then the number of projection angle sampling points is required to satisfy
Figure 63230DEST_PATH_IMAGE002
，
Figure 555392DEST_PATH_IMAGE003
The system range resolution, which depends on the corresponding lower range resolution in both the detector and the laser pulse,
Figure 344487DEST_PATH_IMAGE004
to detect the maximum size of the object. For example, if the detector bandwidth is 4GHz, the laser pulse width is 100
Figure 947507DEST_PATH_IMAGE005
The distance resolution of the system is 3.75cm, if the maximum size of the detected target is
Figure 401097DEST_PATH_IMAGE006
60cm, the number of sampling points of projection data on the angle must satisfy
Figure 798581DEST_PATH_IMAGE007
I.e. projection angle sampling interval
Figure 340552DEST_PATH_IMAGE008
(ii) a If the maximum size of the detected target
Figure 481683DEST_PATH_IMAGE009
120cm, the number of sampling points of the projection data on the angle must satisfy
Figure 792710DEST_PATH_IMAGE010
I.e. projection angle sampling interval
Figure 361094DEST_PATH_IMAGE011
. The above is the maximum value of the projection angle sampling interval, and the smaller the projection angle sampling interval is in actual selection, the larger the projection data volume is, and the better the quality of the reconstructed target image is. When the laser reflection tomography is actually applied, due to the unique scanning imaging mechanism, the relative rotation between an imaging target and an imaging system is fast, the scanning irradiation interval angle of the laser to the target object is relatively large, even if the complete projection angle, namely 360 degrees, is reached, the projection angle is undersampled due to the fact that the projection interval angle is too large due to the fast relative rotation, the Nyquist sampling theorem is not satisfied, if the target image can not be completely reconstructed according to the calculation reconstruction, and the practicability of the laser reflection tomography is seriously restricted.
Chinese patent specification CN106646511B discloses a reconstruction processing method of laser reflection tomography projection data, in which the projection angle interval is selected to be 0.5 °, 720 sets of projection data are acquired, and a filtered back-projection algorithm is used to reconstruct a laser image of a target object. The document "contrast of techniques for image reconstruction using tomographics" also describes laser reflection tomography image reconstruction methods such as iterative algorithms (conjugate gradients, gradients) and interpolation algorithms. The image reconstruction algorithm can reconstruct a high-quality target laser image only under the condition of relatively sufficient projection data, and has the problem of relatively long imaging time consumption, so that the practicability of laser reflection tomography is influenced. When the angle under-sampling projection data is acquired, if the reconstructed image algorithm is reused to reconstruct an image, the reconstructed image has artifacts due to incomplete projection data, and the quality of the reconstructed laser image is reduced.
Disclosure of Invention
One of the objectives of the present invention is to provide a laser reflection tomography undersampling reconstruction method, which overcomes the technical problem of relatively low laser image quality caused by incomplete projection data in the prior art.
It is a second object of the present invention to provide a storage medium.
It is a further object of the present invention to provide a laser reflectance tomography undersampled reconstruction system.
In order to achieve one of the purposes, the invention adopts the following technical scheme:
a reconstruction method for laser reflectance tomography undersampling, the reconstruction method comprising the steps of:
the method comprises the following steps that firstly, a laser emits narrow laser pulses to irradiate a target, laser scanning is carried out around the target at equal projection angle intervals, and original projection data of the multi-view target under-sampled projection angles at complete angles are obtained;
step two, carrying out back projection center alignment processing on the multi-view target original projection data under the projection angle under the complete angle;
thirdly, sparse observation sampling is carried out on the projection data subjected to the back projection center alignment processing by utilizing a local Hadamard matrix;
and step four, carrying out iterative processing of joint algebraic reconstruction and total variation minimization adjustment on the projection data after sparse observation sampling in sequence.
Further, the specific implementation process of the step one is as follows:
step 11, emitting narrow laser pulses by a laser to irradiate a target, and carrying out one-step one-stop laser scanning within a 360-degree range around the target object at equal projection angle intervals;
and step 12, detecting and receiving laser echo pulse signals reflected by the target, and performing discrete sampling on the echo signals to obtain target original projection data under the projection angle undersampled at the complete angle.
Further, the narrow laser pulse width is 100 ps; the detection receiving bandwidth is 4GHz, and the discrete sampling rate is 20 GS/s.
Further, in the step one, the value range of the projection angle interval is
Figure 390361DEST_PATH_IMAGE012
。
Further, the specific implementation process of the step four is as follows:
step 401, setting an initial value of a laser reflection tomography image to be reconstructed
Figure 335184DEST_PATH_IMAGE013
，kIs the iteration number;
step 402, assigning the projection data after the projection center alignment processing to a projection matrix
Figure 497787DEST_PATH_IMAGE014
(ii) a And solving the system matrix by using a fast grid traversal method
Figure 502652DEST_PATH_IMAGE015
；
Step 403, according to the initial value and projection matrix of the laser reflection tomography image to be reconstructed
Figure 753636DEST_PATH_IMAGE014
And a system matrix
Figure 236570DEST_PATH_IMAGE016
Calculated according to the following formula
Figure 522189DEST_PATH_IMAGE017
Figure 432376DEST_PATH_IMAGE018
；
Wherein the content of the first and second substances,
Figure 170656DEST_PATH_IMAGE019
is as follows
Figure 457281DEST_PATH_IMAGE020
In sub-SART reconstruction
Figure 594477DEST_PATH_IMAGE014
Middle projection data of
Figure 941145DEST_PATH_IMAGE021
Obtaining a pixel value of an image to be reconstructed by the projection values of the sampling points;
Figure 166721DEST_PATH_IMAGE022
is as follows
Figure 991457DEST_PATH_IMAGE023
sub-SART reconstructed peptides
Figure 986089DEST_PATH_IMAGE024
Middle projection data of
Figure 175762DEST_PATH_IMAGE025
Obtaining a pixel value of an image to be reconstructed by the projection values of the sampling points;
Figure 216530DEST_PATH_IMAGE026
is a projection matrix
Figure 844958DEST_PATH_IMAGE027
Middle projection data of
Figure 714604DEST_PATH_IMAGE025
Projection values of sampling points;
Figure 403074DEST_PATH_IMAGE028
is a system matrix
Figure 603243DEST_PATH_IMAGE015
To (1) a
Figure 769782DEST_PATH_IMAGE025
A row-row vector;
Figure 739006DEST_PATH_IMAGE029
is composed of
Figure 598378DEST_PATH_IMAGE028
The transposed vector of (1);
Figure 20263DEST_PATH_IMAGE030
，
Figure 256072DEST_PATH_IMAGE031
the number of points of discrete sampling of target original projection data;
Figure 76873DEST_PATH_IMAGE032
is a relaxation factor;
step 404, judge
Figure 107146DEST_PATH_IMAGE022
Whether it is greater than or equal to 0, if yes, then order
Figure 16327DEST_PATH_IMAGE033
Go to step 405; if not, then order
Figure 524669DEST_PATH_IMAGE034
Go to step 405;
step 405, initialization
Figure 468485DEST_PATH_IMAGE035
Get it
Figure 669659DEST_PATH_IMAGE036
；
Step 406, calculating the incremental factor
Figure 66137DEST_PATH_IMAGE037
：
Figure 378170DEST_PATH_IMAGE038
Wherein the content of the first and second substances,
Figure 173563DEST_PATH_IMAGE039
the method comprises the steps of obtaining an initial pixel value of a laser reflection tomography image to be reconstructed;
step 407, calculate Total variation gradient
Figure 545638DEST_PATH_IMAGE040
And direction of negative gradient
Figure 429412DEST_PATH_IMAGE041
；
Wherein the content of the first and second substances,
Figure 545135DEST_PATH_IMAGE042
，
Figure 197965DEST_PATH_IMAGE043
for an image to be reconstructed
Figure 740941DEST_PATH_IMAGE044
Go to the first
Figure 846432DEST_PATH_IMAGE045
The values of the pixels of the column are,
Figure 765846DEST_PATH_IMAGE046
for an image to be reconstructed
Figure 270252DEST_PATH_IMAGE047
Go to the first
Figure 984131DEST_PATH_IMAGE045
The values of the pixels of the column are,
Figure 842496DEST_PATH_IMAGE048
for the image to be reconstructed
Figure 300022DEST_PATH_IMAGE044
Go to the first
Figure 661865DEST_PATH_IMAGE049
The values of the pixels of the column are,
Figure 812223DEST_PATH_IMAGE050
，
Figure 892306DEST_PATH_IMAGE051
，
Figure 887944DEST_PATH_IMAGE052
and
Figure 291243DEST_PATH_IMAGE053
respectively representing the line number and the example number of the image to be reconstructed;
Figure 688202DEST_PATH_IMAGE054
is as follows
Figure 911373DEST_PATH_IMAGE055
The pixel values of the image to be reconstructed resulting from the sub-TV minimization,
Figure 727013DEST_PATH_IMAGE056
，
Figure 391344DEST_PATH_IMAGE057
minimizing a maximum number of iterations of the process for the TV;
step 408, iteratively correcting the image along the negative gradient of the TV according to the following formula:
Figure 290030DEST_PATH_IMAGE058
；
wherein the content of the first and second substances,
Figure 672601DEST_PATH_IMAGE059
is as follows
Figure 275620DEST_PATH_IMAGE055
Pixel values of the image to be reconstructed obtained when the secondary TV is minimized;
Figure 463632DEST_PATH_IMAGE060
is as follows
Figure 126694DEST_PATH_IMAGE061
Second in TV
Figure 324457DEST_PATH_IMAGE023
Iterative SART of sub-SART
Figure 481900DEST_PATH_IMAGE062
Middle projection data of
Figure 42195DEST_PATH_IMAGE063
Obtaining a pixel value of an image to be reconstructed by the projection values of the sampling points;
Figure 361312DEST_PATH_IMAGE064
is a regulatory factor;
step 409, judgment
Figure 639846DEST_PATH_IMAGE055
Whether or not less than
Figure 335401DEST_PATH_IMAGE057
If yes, then order
Figure 750202DEST_PATH_IMAGE065
Returning to step 408; if not, then go to step 410;
step 410, judge
Figure 237291DEST_PATH_IMAGE066
Whether less than or equal to the threshold value, if yes, order
Figure 737542DEST_PATH_IMAGE067
And ending; if not, go to step 411;
step 411, calculate
Figure 236788DEST_PATH_IMAGE068
And
Figure 506095DEST_PATH_IMAGE069
；
step 412, when
Figure 432594DEST_PATH_IMAGE070
Then give an order
Figure 420141DEST_PATH_IMAGE071
Proceed to step 403; otherwise, it gives
Figure 457499DEST_PATH_IMAGE072
Step 408 is entered.
In order to achieve the second purpose, the invention adopts the following technical scheme:
a storage medium storing computer-executable instructions; when the computer executes the instructions, the reconstruction method is realized.
In order to achieve the third purpose, the invention adopts the following technical scheme:
a laser reflectance tomography undersampled reconstruction system, said reconstruction system comprising a storage medium as described above.
The invention has the beneficial effects that:
the invention carries out the iterative processing of the back projection center alignment processing, the sparse observation sampling, the combined algebra reconstruction and the total variation minimum adjustment on the angle under-sampled projection data in sequence, effectively inhibits the influence of noise in the projection data, realizes the reconstruction of a higher-quality laser image by less angle sampled projection data, accelerates the convergence of the iterative reconstruction of the image, ensures the quality of the reconstructed image, breaks through the Nyquist sampling theorem limit, reduces the laser scanning time, improves the speed and the efficiency of the image reconstruction and promotes the practicability of the laser reflection tomography.
Drawings
FIG. 1 is a schematic flow chart of a laser reflection tomography undersampling reconstruction method of the present invention;
FIG. 2 is a schematic diagram of laser irradiation of a target spot area and acquisition of multi-view laser reflection projection data of a target object;
FIG. 3 is a schematic diagram illustrating an interval between an initial angle and a projection angle of a detected target;
FIG. 4 is a flow chart of a phase recovery algorithm;
FIG. 5 is a flowchart of an image reconstruction algorithm based on conjugate gradient optimization Total Variation (TV) minimization combined with a joint algebraic reconstruction algorithm (SART);
in the figure: 1-a laser; 2-a beam expander; 3-laser irradiation area; 4-detecting the target; 5-a receiving telescope; 6-laser echo; 7-a detector; 8-an optical fiber; 9-a data acquisition system; 10-a probe beam; 11-target object motion trajectory.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
The embodiment provides a laser reflection tomography undersampling reconstruction method, which is characterized by comprising the following steps:
step one, a laser emits narrow laser pulses to irradiate a target, laser scanning is carried out around the target at equal projection angle intervals, and multi-view target original projection data of projection angle undersampling under a complete angle are obtained.
The principle of irradiating a target spot area with laser and collecting multi-view laser reflection projection data of a target object in the embodiment is as follows:
1. the laser 1 emits laser pulses, the width of the laser pulses is 100ps, the attenuation coefficient of the gradual attenuation lens is adjusted, the size of a laser spot is adjusted by adjusting the focal length of the beam expanding lens 2, and the outer contour of the laser spot reaching the target object 4 can completely cover the whole target object 4 through the laser irradiation area 3, as shown in fig. 2.
2. Establishing a two-dimensional coordinate system by using the planes of the laser 1, the target object 4 and the detector 7, and defining the initial angle of the laser pulse irradiating the target object 4 at the moment as
Figure 846892DEST_PATH_IMAGE073
As shown in fig. 3. The laser 1 emits a single pulse to irradiate the target object 4, and the receiving telescope 5 collects the laser irradiated by the reflection of the target objectA laser echo 6 formed by the light pulse, a detector 7 detects the laser echo 6 received by the receiving telescope 5, converts an optical signal into an electric signal and sends the electric signal to a data acquisition system 9 through an optical fiber 8, and the data acquisition system 9 acquires and records the angle
Figure 941362DEST_PATH_IMAGE073
Laser reflection echo data after target profile modulation
Figure 150626DEST_PATH_IMAGE074
. Here, the detector 7 is a Si-APD photoelectric detector, the bandwidth is 4GHz, the bandwidth of the data acquisition system 9 is 4GHz, and the sampling rate is 20 Gs/s;
3. the centroid of the target object 4 is taken as the origin of the coordinate axis, the target object 4 rotates around the centroid in a one-step one-stop manner at equal angular intervals, and the rotation trajectory of the target object is like the motion trajectory 11 of the target object. Rotating the target object 4 by an angular interval
Figure 991675DEST_PATH_IMAGE075
When the detection angle becomes
Figure 235574DEST_PATH_IMAGE076
The laser 1 emits laser pulses again to irradiate the target object 4, and the data acquisition system 9 acquires the reflection projection echo data at the angle
Figure 503876DEST_PATH_IMAGE077
(ii) a Re-rotation angle interval of the target object 4
Figure 466015DEST_PATH_IMAGE078
When the detection angle becomes
Figure 845175DEST_PATH_IMAGE079
The laser 1 emits a pulse to the target object 4, and the data acquisition system 9 records the reflection projection echo data at the angle
Figure 678002DEST_PATH_IMAGE080
(ii) a Repeating the above stepsUntil the relative rotation of 360 degrees around the target object 4, the target object is obtained by co-acquisition
Figure 137713DEST_PATH_IMAGE081
Group laser reflection echo data set
Figure 321569DEST_PATH_IMAGE082
Wherein
Figure 504420DEST_PATH_IMAGE083
And is
Figure 722912DEST_PATH_IMAGE084
Is a positive integer. Based on the principle, the process for acquiring the original projection data of the multi-view target under-sampled by the projection angle under the complete angle is as follows:
and step 11, emitting narrow laser pulses by a laser to irradiate the target, and carrying out one-step one-stop laser scanning within 360 degrees around the target object at equal projection angle intervals.
And step 12, detecting and receiving laser echo pulse signals reflected by the target, and performing discrete sampling on the echo signals to obtain target original projection data under the projection angle undersampled at the complete angle.
The narrow laser pulse width of the present embodiment is 100 ps; the detection receiving bandwidth is 4GHz, and the discrete sampling rate is 20 GS/s. The projection angle interval has a value range of
Figure 333016DEST_PATH_IMAGE085
。
And step two, carrying out back projection center alignment treatment on the multi-view target original projection data under the projection angle undersampled at the complete angle.
When a moving target, particularly a spatial target, is detected, random motion in other directions, such as vibration in the vertical direction of a target body, may exist in the relative rotation process of the target, so that the positions of the target rotation center at different projection angles are no longer aligned with the same straight line, and image reconstruction is performed directly by using projection data with misaligned back projection center, which leads to thatCausing misalignment and geometric distortion. Sampling interval when projection angle
Figure 4169DEST_PATH_IMAGE086
When the sampling interval is short, the random motion effect is small, and the influence on image reconstruction is small and even possibly neglected. However, when the sampling interval of the projection angle is large, the problem of the misalignment of the back projection center must be emphasized, and the back projection center alignment process is performed by using the phase recovery method. Phase recovery (Phase recovery) is to recover target Phase information from the fourier transform amplitude of the signal and further recover the image, as shown in fig. 4, the specific process is as follows:
step 21, projecting according to Fourier slice theorem
Figure 725131DEST_PATH_IMAGE087
One-dimensional Fourier transform is carried out, and a target Fourier spectrum model value image is obtained by angle inversion
Figure 798129DEST_PATH_IMAGE088
；
Step 22, calculating a target Fourier spectrum model value graph
Figure 576205DEST_PATH_IMAGE088
Power spectrum function of
Figure 734654DEST_PATH_IMAGE089
Performing inverse Fourier transform to obtain autocorrelation function image
Figure 259307DEST_PATH_IMAGE090
According to its scope
Figure 452391DEST_PATH_IMAGE091
Determining a support domain of the target iteration;
step 23, with range
Figure 404298DEST_PATH_IMAGE091
The original image of
Figure 784463DEST_PATH_IMAGE092
As an initial estimate, a spectral matrix is obtained after fourier transformation
Figure 112808DEST_PATH_IMAGE093
Extracting an initial phase matrix therefrom
Figure 160398DEST_PATH_IMAGE094
Combining the frequency spectrum modulus value graph obtained in step 21
Figure 280276DEST_PATH_IMAGE088
Forming a new spectral matrix
Figure 147738DEST_PATH_IMAGE095
Then, inverse Fourier transform is carried out to generate a new target image, and self limiting conditions such as real number non-negative and the like are added to be used as initial estimation of next iteration
Figure 14194DEST_PATH_IMAGE091
；
And 24, repeating the steps 21, 22 and 23 until the ideal recovery effect is achieved.
Thus, the aligned projection drawing is obtained through the processing of the phase recovery algorithm
Figure 916291DEST_PATH_IMAGE096
Wherein
Figure 210000DEST_PATH_IMAGE097
Drawing by projection
Figure 830338DEST_PATH_IMAGE096
Is a pattern of information about the angle and intensity distribution.
And thirdly, sparse observation sampling is carried out on the projection data subjected to the back projection center alignment processing by utilizing a local Hadamard matrix.
The compressed sensing comprises three links of sparse representation, observation matrix design and signal reconstruction. For laser reflection tomography, the difference of external reflection characteristics of the same target is not largeThe finite difference image of the laser image is considered to be sparse
Figure 234905DEST_PATH_IMAGE098
Is a two-dimensional reflection tomography laser image, and its finite difference image is defined as
Figure 257088DEST_PATH_IMAGE099
. Therefore, the projection data does not need to be sparsely represented in the reconstruction process, and only the original projection data subjected to the back projection center alignment processing needs to be subjected to compressed sensing observation sampling. In this embodiment, a local hadamard matrix is used to perform sparse observation sampling on projection data after angle undersampling and backprojection center alignment processing, where the local hadamard matrix is obtained by partially extracting the hadamard matrix, and the specific steps are as follows:
1) construction of
Figure 718769DEST_PATH_IMAGE100
A hadamard matrix of an order of,
Figure 560823DEST_PATH_IMAGE101
the number of discrete sampling points of the laser echo signal under a certain projection angle is satisfied
Figure 769081DEST_PATH_IMAGE102
(
Figure 645770DEST_PATH_IMAGE103
Is a positive integer not less than 1);
2) setting the measurement matrix as
Figure 281282DEST_PATH_IMAGE104
Stage (A)
Figure 610632DEST_PATH_IMAGE105
) At a sampling rate of
Figure 622582DEST_PATH_IMAGE106
；
3) According to the sampling rate, even rows are first extracted from the complete hadamard matrix. If the sampling rate is lower than the required sampling rate, the even lines are reserved, and the insufficient lines are extracted from the odd lines according to an even extraction principle;
4) if the sampling rate is higher than the required sampling rate, the even lines continue to be decimated according to the even decimation principle until the required sampling rate is met.
5) Obtaining the required local Hadamard matrix
Figure 353778DEST_PATH_IMAGE107
Local Hadamard matrix
Figure 157261DEST_PATH_IMAGE108
And performing matrix operation on the projection data set after processing to obtain projection data after sparse observation sampling.
And step four, carrying out iterative processing of joint algebraic reconstruction and total variation minimization adjustment on the projection data after sparse observation sampling in sequence.
The image iterative reconstruction of the projection data after sparse observation sampling by using the conjugate gradient optimization-based total variation minimization combined algebraic reconstruction includes SART image reconstruction iteration and conjugate gradient optimization-based total variation TV minimization iteration.
Two-dimensional laser reflection tomography image total variation
Figure 973907DEST_PATH_IMAGE098
The expression of (a) is:
Figure 789548DEST_PATH_IMAGE109
image processing method
Figure 375250DEST_PATH_IMAGE110
Arranged as one-dimensional vectors
Figure 352564DEST_PATH_IMAGE111
Then image
Figure 656507DEST_PATH_IMAGE111
Can be obtained by solving the following optimization problem
Figure 10259DEST_PATH_IMAGE112
Constraint condition in the above formula
Figure 450467DEST_PATH_IMAGE113
This can be achieved by means of an iterative reconstruction,
Figure 861333DEST_PATH_IMAGE114
representing projection data at various angles after sparse observation sampling,
Figure 386992DEST_PATH_IMAGE115
to represent the reconstructed laser reflectance tomography image,
Figure 544435DEST_PATH_IMAGE116
is a system matrix. An algebraic reconstruction Algorithm (ART) is the most commonly used iterative reconstruction algorithm, but is easily affected by measurement noise in the process of reconstructing an image, and has the disadvantages of large iteration number, large calculation amount, low reconstruction speed and low efficiency. The combined algebraic reconstruction (SART) is an improved iterative reconstruction algorithm, and has the advantages of high convergence rate, small influence of noise, small required iteration times and the like. Referring to fig. 5, the specific implementation process is as follows:
step 401, setting an initial value of a laser reflection tomography image to be reconstructed
Figure 839150DEST_PATH_IMAGE117
，kIs the iteration number;
step 402, assigning the projection data after the projection center alignment processing to a projection matrix
Figure 423846DEST_PATH_IMAGE014
(ii) a And solving the system matrix by using a fast grid traversal method
Figure 436801DEST_PATH_IMAGE015
；
Step 403, according to the initial value and projection matrix of the laser reflection tomography image to be reconstructed
Figure 132356DEST_PATH_IMAGE014
And a system matrix
Figure 343895DEST_PATH_IMAGE016
Calculated according to the following formula
Figure 299825DEST_PATH_IMAGE017
Figure 800076DEST_PATH_IMAGE118
；
Wherein the content of the first and second substances,
Figure 299322DEST_PATH_IMAGE019
is as follows
Figure 568629DEST_PATH_IMAGE020
In sub-SART reconstruction
Figure 495128DEST_PATH_IMAGE014
Middle projection data of
Figure 482676DEST_PATH_IMAGE025
Obtaining a pixel value of an image to be reconstructed by the projection values of the sampling points;
Figure 520033DEST_PATH_IMAGE022
is as follows
Figure 909426DEST_PATH_IMAGE023
sub-SART reconstructed peptides
Figure 738317DEST_PATH_IMAGE024
Middle projection data of
Figure 213161DEST_PATH_IMAGE025
Projection of sampling pointsObtaining a pixel value of an image to be reconstructed by the shadow value;
Figure 54209DEST_PATH_IMAGE026
is a projection matrix
Figure 298109DEST_PATH_IMAGE027
Middle projection data of
Figure 566410DEST_PATH_IMAGE025
Projection values of sampling points;
Figure 262971DEST_PATH_IMAGE028
is a system matrix
Figure 642130DEST_PATH_IMAGE015
To (1) a
Figure 6116DEST_PATH_IMAGE025
A row-row vector;
Figure 465826DEST_PATH_IMAGE119
is composed of
Figure 649683DEST_PATH_IMAGE028
The transposed vector of (1);
Figure 832534DEST_PATH_IMAGE030
，
Figure 51025DEST_PATH_IMAGE031
the number of points of discrete sampling of target original projection data;
Figure 661129DEST_PATH_IMAGE032
is a relaxation factor;
step 404, judge
Figure 332282DEST_PATH_IMAGE022
Whether it is greater than or equal to 0, if yes, then order
Figure 53245DEST_PATH_IMAGE033
Go forward and go forwardGo to step 405; if not, then order
Figure 922980DEST_PATH_IMAGE034
Go to step 405;
step 405, initialization
Figure 904318DEST_PATH_IMAGE120
Get it
Figure 859505DEST_PATH_IMAGE121
；
Step 406, calculating the incremental factor
Figure 587421DEST_PATH_IMAGE037
：
Figure 514925DEST_PATH_IMAGE122
Wherein the content of the first and second substances,
Figure 466832DEST_PATH_IMAGE123
the method comprises the steps of obtaining an initial pixel value of a laser reflection tomography image to be reconstructed;
step 407, calculate Total variation gradient
Figure 112577DEST_PATH_IMAGE124
And direction of negative gradient
Figure 440921DEST_PATH_IMAGE125
；
Wherein the content of the first and second substances,
Figure 222933DEST_PATH_IMAGE042
，
Figure 342811DEST_PATH_IMAGE043
for an image to be reconstructed
Figure 475852DEST_PATH_IMAGE044
Go to the first
Figure 342308DEST_PATH_IMAGE045
The values of the pixels of the column are,
Figure 244405DEST_PATH_IMAGE046
for an image to be reconstructed
Figure 538114DEST_PATH_IMAGE047
Go to the first
Figure 158451DEST_PATH_IMAGE045
The values of the pixels of the column are,
Figure 563019DEST_PATH_IMAGE048
for the image to be reconstructed
Figure 706906DEST_PATH_IMAGE044
Go to the first
Figure 171516DEST_PATH_IMAGE049
The values of the pixels of the column are,
Figure 13570DEST_PATH_IMAGE126
，
Figure 484478DEST_PATH_IMAGE051
，
Figure 361167DEST_PATH_IMAGE127
and
Figure 731100DEST_PATH_IMAGE053
respectively representing the line number and the example number of the image to be reconstructed;
Figure 326029DEST_PATH_IMAGE128
is as follows
Figure 72400DEST_PATH_IMAGE055
The pixel values of the image to be reconstructed resulting from the sub-TV minimization,
Figure 803595DEST_PATH_IMAGE056
，
Figure 610008DEST_PATH_IMAGE057
minimizing a maximum number of iterations of the process for the TV;
step 408, iteratively correcting the image along the negative gradient of the TV according to the following formula:
Figure 426655DEST_PATH_IMAGE129
；
wherein the content of the first and second substances,
Figure 239365DEST_PATH_IMAGE130
is as follows
Figure 559488DEST_PATH_IMAGE055
Pixel values of the image to be reconstructed obtained when the secondary TV is minimized;
Figure 802382DEST_PATH_IMAGE060
is as follows
Figure 106324DEST_PATH_IMAGE061
Second in TV
Figure 194497DEST_PATH_IMAGE023
Iterative SART of sub-SART
Figure 165864DEST_PATH_IMAGE062
Middle projection data of
Figure 48501DEST_PATH_IMAGE063
Obtaining a pixel value of an image to be reconstructed by the projection values of the sampling points;
Figure 839739DEST_PATH_IMAGE064
is a regulatory factor;
step 409, judgment
Figure 728673DEST_PATH_IMAGE055
Whether or not less than
Figure 288968DEST_PATH_IMAGE057
If yes, then order
Figure 873664DEST_PATH_IMAGE065
Returning to step 408; if not, then go to step 410;
step 410, judge
Figure 886619DEST_PATH_IMAGE131
Whether less than or equal to the threshold value, if yes, order
Figure 582174DEST_PATH_IMAGE132
And ending; if not, go to step 411;
step 411, calculate
Figure 262554DEST_PATH_IMAGE068
And
Figure 752572DEST_PATH_IMAGE069
；
step 412, when
Figure 518403DEST_PATH_IMAGE133
Then give an order
Figure 772577DEST_PATH_IMAGE071
Proceed to step 403; otherwise, it gives
Figure 307464DEST_PATH_IMAGE072
Step 408 is entered.
Iteration times in SART reconstructed image iteration loop in the embodiment
Figure 968383DEST_PATH_IMAGE134
Has a value of [10,1000]Relaxation factor
Figure 221510DEST_PATH_IMAGE032
Value of [0.1,1]And the specific value can be optimally selected according to the quality of the reconstructed laser image.
In the embodiment, the initial image reconstructed by SART iteration is subjected to total variation minimization adjustment by adopting optimization based on a conjugate gradient method, so that the optimization convergence rate is acceleratedAnd the image reconstruction efficiency is improved. Minimizing maximum number of iterations in iterative loop based on total variation TV
Figure 993288DEST_PATH_IMAGE135
Has a value of [5,20]Regulating factor of
Figure 382681DEST_PATH_IMAGE064
The value is [0.2,0.5 ]]。
This embodiment carries out the back projection center alignment in proper order to angle under-sampled projection data, sparsely observe the sampling, the iterative processing of joint algebra reconstruction and total variation minimizing adjustment, restrain the influence of noise among the projection data effectively, realized rebuilding out higher quality laser image through less angle sampling projection data, image iteration has been accelerated and has been rebuild the convergence, rebuild image quality has been guaranteed, the Nyquist sampling theorem restriction has been broken through simultaneously, laser scanning time has been reduced, image reconstruction speed and efficiency have been improved, laser reflection tomography's practicality has been promoted.
Another embodiment provides a storage medium having stored thereon computer-executable instructions; when the computer executes the instructions, the reconstruction method provided by the embodiment is realized.
Yet another embodiment provides a laser reflectance tomography undersampled reconstruction system including the storage medium set forth in the preceding embodiment.
Although the embodiments of the present invention have been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the embodiments of the present invention.

Claims (6)

1. A reconstruction method for laser reflectance tomography undersampling, the reconstruction method comprising the steps of:
the method comprises the following steps that firstly, a laser emits narrow laser pulses to irradiate a target, laser scanning is carried out around the target at equal projection angle intervals, and original projection data of the multi-view target under-sampled projection angles at complete angles are obtained;
step two, carrying out back projection center alignment processing on the multi-view target original projection data under the projection angle under the complete angle;
thirdly, sparse observation sampling is carried out on the projection data subjected to the back projection center alignment processing by utilizing a local Hadamard matrix;
step four, carrying out iterative processing of joint algebraic reconstruction and total variation minimization adjustment on the projection data after sparse observation sampling in sequence;
the concrete implementation process of the fourth step is as follows:
step 401, setting an initial value of a laser reflection tomography image to be reconstructed
Figure FDA0002581302430000011
k is the number of iterations;
step 402, assigning projection data subjected to projection center alignment processing to a projection matrix P; solving a system matrix W by using a fast grid traversal method;
step 403, according to the initial value of the laser reflection tomography image to be reconstructed, the projection matrix P and the system matrix W, calculating according to the following formula to obtain
Figure FDA0002581302430000012
Figure FDA0002581302430000013
Wherein the content of the first and second substances,
Figure FDA0002581302430000014
obtaining a pixel value of an image to be reconstructed from a projection value of an S-th sampling point of projection data in P in the kth SART reconstruction;
Figure FDA0002581302430000015
obtaining a pixel value of an image to be reconstructed, which is reconstructed by the projection value of the S-th sampling point of the projection data in P for the (k-1) -th SART reconstruction; psThe projection value of the S-th sampling point of the projection data in the projection matrix P is obtained; wsIs the S-th row vector of the system matrix W;
Figure FDA0002581302430000016
is WsThe transposed vector of (1); s is 1, 2, …, M is the number of points of discrete sampling of the target original projection data; λ is a relaxation factor;
step 404, judge
Figure FDA0002581302430000017
Whether it is greater than or equal to 0, if yes, then order
Figure FDA0002581302430000018
Step 405 is entered; if not, let f (k) be 0, go to step 405;
step 405, initialization
Figure FDA0002581302430000019
Get
Figure FDA00025813024300000110
Step 406, calculating the incremental factor
Figure FDA00025813024300000111
Wherein the content of the first and second substances,
Figure FDA00025813024300000112
the method comprises the steps of obtaining an initial pixel value of a laser reflection tomography image to be reconstructed;
step 407, calculate Total variation gradient
Figure FDA0002581302430000021
And direction of negative gradient
Figure FDA0002581302430000022
Wherein the content of the first and second substances,
Figure FDA0002581302430000023
fi，jfor the ith row and jth column pixel value, f, of the image to be reconstructedi-1，jIs the j column pixel value, f of the i-1 th row of the image to be reconstructedi，j-1For the ith row and jth-1 column pixel value of the image to be reconstructed, i is 1, 2, … N1，j＝1，2，…N2，N1And N2Respectively representing the line number and the example number of the image to be reconstructed;
Figure FDA0002581302430000024
for the pixel value of the image to be reconstructed obtained in the nth TV minimization, n is 1, 2, …, m, m is the maximum iteration number of the TV minimization process;
step 408, iteratively correcting the image along the negative gradient of the TV according to the following formula:
Figure FDA0002581302430000025
wherein the content of the first and second substances,
Figure FDA0002581302430000026
pixel values of an image to be reconstructed obtained when the nth TV is minimized;
Figure FDA0002581302430000027
the pixel value of the image to be reconstructed, which is obtained by the projection value of the sampling point of the projection data in P and is the (k-1) th SART iteration during the (n-1) th TV time, α is an adjusting factor;
step 409, judging whether n is smaller than m, if so, making n equal to n +1, and returning to step 408; if not, then go to step 410;
step 410, judge
Figure FDA0002581302430000028
Whether less than or equal to the threshold value, if yes, order
Figure FDA0002581302430000029
Finishing; if not, go to step 411;
step 411, calculate
Figure FDA00025813024300000210
And
Figure FDA00025813024300000211
step 412, when
Figure FDA00025813024300000212
Then order
Figure FDA00025813024300000213
Entering step 403; otherwise, let k be k +1, go to step 408.
2. The reconstruction method according to claim 1, wherein the step one is implemented by:
step 11, emitting narrow laser pulses by a laser to irradiate a target, and carrying out one-step one-stop laser scanning within a 360-degree range around the target object at equal projection angle intervals;
and step 12, detecting and receiving laser echo pulse signals reflected by the target, and performing discrete sampling on the echo signals to obtain target original projection data under the projection angle undersampled at the complete angle.
3. The reconstruction method according to claim 2, wherein the narrow laser pulse width is 100 ps; the detection receiving bandwidth is 4GHz, and the discrete sampling rate is 20 GS/s.
4. The reconstruction method according to claim 1 or 2, wherein in the step one, the projection angle interval has a value in a range of 6 ° ≦ Δ Φ ≦ 12 °.
5. A storage medium having stored thereon computer-executable instructions; the computer executes the instructions and realizes the reconstruction method of any one of claims 1-4 when executing the instructions.
6. A laser reflectance tomography undersampled reconstruction system, the reconstruction system comprising the storage medium of claim 5.
CN202010459498.3A 2020-05-27 2020-05-27 Laser reflection tomography undersampled reconstruction method, storage medium and system Active CN111369638B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010459498.3A CN111369638B (en) 2020-05-27 2020-05-27 Laser reflection tomography undersampled reconstruction method, storage medium and system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010459498.3A CN111369638B (en) 2020-05-27 2020-05-27 Laser reflection tomography undersampled reconstruction method, storage medium and system

Publications (2)

Publication Number Publication Date
CN111369638A CN111369638A (en) 2020-07-03
CN111369638B true CN111369638B (en) 2020-08-21

Family

ID=71212266

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010459498.3A Active CN111369638B (en) 2020-05-27 2020-05-27 Laser reflection tomography undersampled reconstruction method, storage medium and system

Country Status (1)

Country Link
CN (1) CN111369638B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114397668B (en) * 2022-01-13 2022-09-23 中国人民解放军国防科技大学 Method and system for estimating centroid distance of small space debris based on laser reflection chromatography

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2010141128A2 (en) * 2009-03-05 2010-12-09 Board Of Trustees Of Michigan State University Laser amplification system
CN103150744B (en) * 2013-03-30 2015-10-14 重庆大学 A kind of X ray multi-power spectrum CT data for projection process and image rebuilding method
CN105701847A (en) * 2016-01-14 2016-06-22 重庆大学 Algebraic reconstruction method of improved weight coefficient matrix
CN108921807A (en) * 2018-08-15 2018-11-30 苏州蛟视智能科技有限公司 A kind of compression sensing method based on adaptive-filtering
CN109613556B (en) * 2018-11-26 2021-05-18 武汉大学 Photon counting laser three-dimensional detection imaging method based on sparse representation
CN109901160B (en) * 2019-02-22 2022-12-16 华中光电技术研究所（中国船舶重工集团有限公司第七一七研究所） Three-dimensional laser imaging radar and three-dimensional depth image reconstruction method thereof

Also Published As

Publication number Publication date
CN111369638A (en) 2020-07-03

Similar Documents

Publication Publication Date Title
US11100638B2 (en) Medical imaging device and medical image processing method using a neutral network
US9335410B2 (en) System and method for multiple spotlight synthetic radar imaging using random beam steering
Dong et al. A novel compressive sensing algorithm for SAR imaging
US8310233B2 (en) Method for image reconstruction from undersampled medical imaging data
US8989465B2 (en) System and method for medical image reconstruction and image series denoising using local low rank promotion
JP6456312B2 (en) Method and system for generating a three-dimensional image
CN104898118B (en) Sparse frequency point-based three-dimensional holographic imaging reconstruction method
CN111208513A (en) Space target ISAR image sequence energy back projection and three-dimensional reconstruction method
US9316734B2 (en) Free-hand scanning and imaging
US8971599B2 (en) Tomographic iterative reconstruction
JP5588849B2 (en) System for increasing the time resolution of X-ray images
US7672421B2 (en) Reduction of streak artifacts in low dose CT imaging through multi image compounding
US10102651B2 (en) Image processing device, radiation detecting device, and image processing method
US20130004040A1 (en) Left ventricle epicardium estimation in medical diagnostic imaging
US8625870B2 (en) Method and system for supplementing detail image in successive multi-scale reconstruction
JP2008200478A (en) Localized and highly constrained image reconstruction method
NL2009710A (en) Method and apparatus for iterative reconstruction.
JPH11253441A (en) Method for correcting image having spectrum artifact
US20130315453A1 (en) System and method for wide cone helical image reconstruction
CN111369638B (en) Laser reflection tomography undersampled reconstruction method, storage medium and system
US9704223B2 (en) Method and system for substantially reducing cone beam artifacts based upon adaptive scaling factor in circular computer tomography (CT)
CN110850433A (en) Method for detecting mass center of space debris based on laser reflection tomography technology
US20050100127A1 (en) Methods and apparatus for image reconstruction in distributed x-ray source CT systems
US20130083986A1 (en) Method and system for reconstruction of tomographic images
CN109959933B (en) Multi-baseline circular synthetic aperture radar imaging method based on compressed sensing

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant