CN110850432A - Method for resolving reflectivity distribution of laser reflection tomography target - Google Patents
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Abstract
The invention relates to the technical field of laser reflection tomography, in particular to a method for calculating target reflectivity distribution in the laser reflection tomography process. Deconvoluting the reflection echo data by adopting an iterative maximum likelihood estimation method, estimating the deconvolution solution by using a parameter estimation method under the condition that a convolution kernel is known, and finally extracting a reflectivity distribution function of a detection target to improve the accuracy of laser reflection tomography reconstructed images. The method can effectively obtain the optimal estimation quantity of the reflectivity distribution of the target surface, thereby compressing the pulse width of the echo, improving the image resolution in the reconstruction link of the laser reflection tomography image, reducing the influence caused by pulse broadening, and forming the high-precision tomography image more quickly and effectively.
Description
Technical Field
The invention relates to the technical field of Laser Reflective Tomography (LRT for short), in particular to application of target reflectivity distribution calculation in the Laser Reflective Tomography imaging process.
Background
In many fields such as military affairs, aerospace and remote sensing, in order to complete tasks such as observation, identification, reconnaissance and tracking of a long-distance target, a high-resolution image of the target needs to be acquired at a long distance. The imaging resolution of the conventional optical imaging technology is limited by the diffraction limit of the system, and the imaging aperture of the system cannot be infinitely increased, so that the conventional optical imaging technology cannot be completely competent. New remote, high resolution imaging technology is in strong demand. The laser reflection tomography imaging based on distance resolution is a novel laser radar imaging system which gives consideration to the characteristics of long distance and high resolution imaging. The laser radar reflection tomography technology is a technology which detects a plurality of angles of a target through a laser radar, collects echo information, obtains spatial information gain of the target from multiple angles, and calculates and reconstructs a fault plane profile image of the target by utilizing a computer tomography algorithm. The core idea of laser reflection tomography is to obtain partial information gain by using incoherent accumulated projection generated by space diversity to form an image, and a projection reconstruction two-dimensional image method is a core processing method of the imaging method. The laser reflection tomography technology is more suitable for observation and detection among space vehicles, in particular to imaging of satellites by satellites.
However, when the width of the emitted laser pulse is larger than the sampling period, the adjacent distance sampling of the effective reflection portion of the object surface is overlapped, which means that the generated echo is the convolution of the projected value of the reflectivity distribution and the laser gaussian pulse. This convolution effect causes waveform broadening and pulse peak reduction in the time domain of the received echo; broadening of the pulse width leads to a reduced resolution of the reconstructed image. In order to solve the convolution effect, deconvolution processing needs to be performed on the echo data. In the deconvolution problem, the solution to the problem cannot be given by an analytical expression, due to the inadequacy of the problem. However, since the transmitted pulse signal is known, that is, under the condition that the convolution kernel is known, the deconvolution is estimated by using a parameter estimation method, a better deconvolution result can be obtained.
Disclosure of Invention
The invention aims to provide a technical method for reversely solving the reflectivity distribution of a target surface when the width of a transmitted laser pulse is greater than a sampling period and an echo caused by overlapping of adjacent distance samples of an effective reflection part of the surface of an object is the convolution of a target reflectivity distribution projection value and a transmitted Gaussian pulse.
The invention is realized by the following technical scheme:
a method for resolving target reflectivity distribution of laser reflection tomography comprises the steps of irradiating a detection target by using pulse laser, receiving a detection echo by using a non-coherent detection system, regarding echo data as a convolution result of a target body reflectivity projection distribution function and a transmission pulse waveform, extracting the target reflectivity projection distribution function from the echo data by using an iterative maximum likelihood estimation method, introducing a noise error in a deconvolution operation process, and minimizing the target function by using a conjugate gradient method to obtain an optimal estimation value of the reflectivity projection distribution function.
Preferably, the method specifically comprises the following steps:
(1) the laser emits laser beams with Gaussian pulse waveforms, the emission end modulates the laser pulses by a signal generator, the emitted beams pass through an adjustable attenuation mirror and are split by a spectroscope, one beam of light is detected by a detector and records the pulse waveform, the other beam of light is expanded by a beam expanding mirror and points to a target, and a target body is completely covered by laser spots;
(2) the target body reflects the echo after being irradiated by the laser beam, an incoherent detection system is used for detecting the echo, a single-pixel detector is used at a receiving end for directly detecting the reflected echo, and a waveform is displayed by an oscilloscope and echo data are collected after an output signal of the detector passes through a radio frequency high-speed electric signal amplifier;
(3) the target body is arranged on a rotatable turntable, the rotating speed of the turntable is uniform and controllable, the rotating angle of the turntable is adjusted, and target echo data of different angles are obtained;
(4) observing reflection echo data, wherein the reflection echo is a non-trivial convolution result of a target body reflectivity projection distribution function and a transmitted Gaussian pulse, and deconvoluting the reflection echo data by adopting an iterative maximum likelihood estimation method to obtain the target body reflectivity projection distribution function;
(5) and substituting the projection data obtained by the deconvolution processing method into a laser reflection tomography processing algorithm to obtain a reconstructed detection target two-dimensional contour image.
Preferably, the detector in the step (2) is a high-bandwidth high-sensitivity Si-APD detector, and the lens is an industrial standard C-shaped optical lens with adjustable aperture and variable focus.
Preferably, the optical path of step (2) is designed to be in a non-transceiving coaxial mode.
Preferably, the deconvolution in step (4) specifically includes the following steps:
(41) performing maximum likelihood estimation on the reflectivity distribution: constructing a probability calculation formula of the reflectivity projection distribution;
(42) introducing noise error quantity: assuming that the error amount is generated by Gaussian white noise, introducing the error amount into a deconvolution process;
(43) explicit expression of the probability of the estimator solved: constructing and simplifying a probability expression of the reflectivity distribution by using a discrete approximation condition;
(44) the stirling asymptotic approximation approximates: approximating a probability expression of the simplified reflectivity distribution using a stirling asymptotic approximation;
(45) solving the optimal estimator by a conjugate gradient method: and minimizing the constructed target function by using a conjugate gradient method, obtaining an optimal estimation value by using search iteration, and stopping iteration after the limit or the specified calculation precision is reached.
Preferably, the probability expression of the error amount in step (42) is:
wherein
For the target reflectivity distribution estimator to be solved, I is the original hypothetical image of the target reconstructed by the echo data, and N is
The finite, small distance measure of the component is denoted as Δ pj，χ2The method specifically comprises the following steps:
the invention has the beneficial effects that:
a laser reflection fault echo deconvolution method based on iteration maximum likelihood estimation. The deconvolution process is a typical ill-conditioned problem (ill-conditioned solved), and any small disturbance of the noise n has a great influence on the variation of the deconvolved solution p, so that it is impossible to solve the analytic solution p from a series of finite discrete data, and the method is characterized in that: the method avoids solving a first class of Fredholm integral equation, utilizes the known prerequisite of a convolution kernel G and the prior condition to carry out parameter estimation on the solution on the premise that the analytic expression of the deconvolution solution p is difficult to be given in an explicit form, and can still obtain a better deconvolution result so as to compensate the resolution reduction caused by distance overlapping.
The method can effectively obtain the optimal estimation quantity of the reflectivity distribution of the target surface, thereby compressing the pulse width of the echo, improving the image resolution in the reconstruction link of the laser reflection tomography image, reducing the influence caused by pulse broadening, and forming the high-precision tomography image more quickly and effectively.
Drawings
Fig. 1 is a schematic diagram of a transmitting module of an LRT system.
Fig. 2 is a schematic diagram of a receiving module of the LRT system.
Fig. 3 is a reconstructed image before/after deconvolution.
Fig. 4 is a schematic diagram of the positions of two adjacent points with the minimum distance resolution of the target surface (a), D ═ Δ D; (b) d is less than delta D.
Fig. 5 is a schematic diagram of pulse waveform compression after deconvolution (a) D ═ Δ D; (b) d is less than delta D.
Fig. 6 is a flow chart of a method for high-precision LRT reconstruction.
Detailed Description
For a better understanding of the present invention, the present invention will be further described with reference to the following examples and the accompanying drawings, which are illustrative of the present invention and are not to be construed as limiting thereof.
A method for resolving the reflectivity distribution of a laser reflection tomography target, as shown in fig. 6, includes the following steps:
1. the laser emits laser beams with Gaussian pulse waveform in pulse, the emitting end modulates the laser pulse by a signal generator, the emitted beams pass through an adjustable attenuation mirror and are split by a spectroscope, one beam of light is detected by a detector and records the pulse waveform, the other beam of light is expanded by a beam expanding mirror and points to a target (a polygonal model), and a target body is completely covered by laser spots, as shown in figure 1.
2. The target body reflects the echo after being irradiated by the laser beam, and the echo is detected by using an incoherent detection system. The receiving end directly detects the reflection echo by using a single-pixel detector, and the detector adopts a high-bandwidth high-sensitivity Si-APD detector. The lens adopts an industrial standard C-shaped aperture adjustable and zooming optical lens. After the output signal of the detector passes through a radio frequency high-speed electric signal amplifier, the oscilloscope displays the waveform and collects echo data (the maximum sampling rate is 20 GHz). The system is in non-transceiving coaxial mode, as shown in fig. 2.
3. The target body is arranged on a rotatable turntable, and the rotating speed of the turntable is uniform and controllable. Setting the rotary index value of the rotary table to be 1 degree, detecting a target laser reflection echo once when the rotary table rotates by an angle index value, obtaining target full-angle echo data after the rotary table rotates by a circle (360 degrees), and recording the target full-angle echo data as W1(t,θ1),W2(t,θ2),...,WN(t,θN) Wherein N is 360. The detection distance is 40m, and the echo sampling rate is kept at 2 GHz. And under the condition of not carrying out deconvolution processing on the echo data, carrying out tomography by using filtered back projection to obtain a result shown in the left image of the figure 3.
4. The laser pulse is reflected by the detection target to reflect the echo signal received by the detector, and actually the reflectivity projection distribution J of the detection target surfaceθWith the laser emitting a Gaussian pulse GjThe non-trivial convolution result of (2):
wherein r isjThe distance from a point on the target to the center of rotation, d the distance from the detector to the center of rotation, and c the speed of light.
Solving for J from integer 1θUsually defined as the first Fredholm problem, J can be found by direct approximation of the integral and solving linear systems using some orthogonal ruleθSome of the values of (1), but adjusting the interval of the summation JθAnd (4) rapidly oscillating. This means that J is paired from equation 1θDeconvolution is an ill-defined problem, and J cannot be reconstructed from finite discrete valuesθ. Even if JθThe whole analytical function can not be solved, and some proper estimation data can be still found to help the deconvolution process. The deconvolution process is the same at different detection angles, so the following step omits the angle scalar θ.
5. And (3) deconvoluting the formula 1 by adopting an iterative maximum likelihood estimation method. Equation 1 is considered as an inference problem based on bayesian theory. Determination of the estimators under known conditions of the echo data W
Is defined as
Correspondingly, use
Representing the data W at a projection distribution value of
Probability under the condition. These two probability values satisfy the bayesian total probability formula:
wherein,and P (W | I) are the estimators, respectively
And the prior probability of the echo data W. Explicit expression to the right side of equation 2 equal sign, optimal data estimation value by maximization
To obtain the final product.
6. Introducing an amount of error. In the estimation of
The probability of the data W under certain conditions depends on the type of measurement error. For example, assuming that the error is white gaussian noise, the error expression is:
wherein σjIs the standard error value and n is the unit gaussian noise. For simplicity of analysis, the standard error value σ herejIs set to a specific value on the denominatorDue to the estimation
Is a deterministic value, convolution 3 can be approximated here as an orthogonal term, and the probability expression is then written as:
wherein N isThe finite, small distance measure of the component is denoted as Δ pj，χ2The method specifically comprises the following steps:
the prior probability of the echo data W in equation 2 is a normalization constant, the estimator
Prior probability of (2)
Is non-trivial. Estimator
Is a distribution function with respect to s, which can be understood as a background arising from different paths. These paths may be assumed to be equal when there are no other additional constraints. Hence a priori probability
Is proportional to the number of paths. To calculate the number of paths, the paths may be divided into large numbers at infinite intervals. At the same time, the distribution function of s is also discrete.
7. Solution (II)An explicit representation of the probability of the estimator is calculated. The complete reflectivity of the target is defined as
Using discrete approximation to obtain
Wherein
For each estimation interval increment ofDelta is the dirac function, epsilon is a small positive quantity, and the amount of error introduced by discretization is o (epsilon). Number of path intervals
Then the prior probability is proportional to the generation
Number of possible combinations:
wherein the stirling asymptotic approximation is applied in the second approximation equation. The order of ln epsilon is ignored in the power term. Then the probability of estimating the quantity
The transformation is:
where Δ s ═ c τ/2, c is the speed of light, τ is the pulse width;
may be estimated by minimizing
Is obtained byIs a controlled variable.
8. And solving the problem of minimizing the multidimensional variable by adopting a conjugate gradient method so as to solve the optimal estimation value. Limiting an estimator
Are non-negative values. For each step, a search direction is determined and the landing point is calculated on the basis of a subspace of a small space. The length of each step then introduces a normalization factor control before the direction vector, which is a combination of non-negative constraints and the speed of computation to reach the minimum point. By search iteration, an optimal estimator can be achieved
The condition for stopping the iteration is that the calculation accuracy reaches a limit.
9. And (3) performing back projection by using the optimal estimator after the iterative maximum likelihood deconvolution processing to obtain a reconstructed detection target two-dimensional contour image (the right image in figure 3), wherein the distance resolution is obviously improved. After deconvolution, the echo waveform has obvious waveform compression, and as shown in fig. 5, the range resolution is obviously improved. According to the rayleigh criterion, the detection range resolution of the LRT system based on range resolution should satisfy Δ d ═ c τ/2, c is the speed of light, τ is the pulse width. Two points A, B (shown in fig. 4 (a)) located adjacent to each other in the optical axis direction on the reflection surface correspond to two values of adjacent interval Δ d in the echo waveform. After deconvolution, the pulse waveform is obviously compressed, and the distance resolution after deconvolution is considered to be obviously improved. On the other hand, if the axial distance is smaller than the two points A, B (as shown in fig. 4 (b)), the reflected echo before pulse compression exhibits a unimodal distribution, and the estimate after deconvolution exhibits a bimodal distribution, it can be considered that A, B two points are distinguishable from the rayleigh criterion, and the comparison effect is shown in the figure.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims (6)
1. A method for resolving the reflectivity distribution of a laser reflection tomography target is characterized by comprising the following steps: the method comprises the steps of irradiating a detection target by using pulse laser, receiving a detection echo by using a non-coherent detection system, regarding echo data as a convolution result of a target body reflectivity projection distribution function and a transmission pulse waveform, extracting the target reflectivity projection distribution function from the echo data by using an iterative maximum likelihood estimation method, introducing a noise error in a deconvolution operation process, and minimizing the target function by using a conjugate gradient method to obtain an optimal estimation value of the reflectivity projection distribution function.
2. The method for resolving the reflectivity distribution of the laser reflection tomography target according to claim 1, specifically comprising the following steps:
(1) the laser emits laser beams with Gaussian pulse waveforms, the emission end modulates the laser pulses by a signal generator, the emitted beams pass through an adjustable attenuation mirror and are split by a spectroscope, one beam of light is detected by a detector and records the pulse waveform, the other beam of light is expanded by a beam expanding mirror and points to a target, and a target body is completely covered by laser spots;
(2) the target body reflects the echo after being irradiated by the laser beam, an incoherent detection system is used for detecting the echo, a single-pixel detector is used at a receiving end for directly detecting the reflected echo, and a waveform is displayed by an oscilloscope and echo data are collected after an output signal of the detector passes through a radio frequency high-speed electric signal amplifier;
(3) the target body is arranged on a rotatable turntable, the rotating speed of the turntable is uniform and controllable, the rotating angle of the turntable is adjusted, and target echo data of different angles are obtained;
(4) observing reflection echo data, wherein the reflection echo is a non-trivial convolution result of a target body reflectivity projection distribution function and a transmitted Gaussian pulse, and deconvoluting the reflection echo data by adopting an iterative maximum likelihood estimation method to obtain the target body reflectivity projection distribution function;
(5) and substituting the projection data obtained by the deconvolution processing method into a laser reflection tomography processing algorithm to obtain a reconstructed detection target two-dimensional contour image.
3. The laser reflection tomography target reflectance distribution calculation method according to claim 2, characterized in that: the detector in the step (2) is a high-bandwidth high-sensitivity Si-APD detector, and the lens is an industrial standard C-shaped optical lens with adjustable aperture and zooming.
4. The laser reflection tomography target reflectance distribution calculation method according to claim 2, characterized in that: and (3) designing the optical path in the step (2) into a non-transceiving coaxial mode.
5. The method for resolving the reflectivity distribution of a laser reflection tomography target according to claim 2, wherein the deconvolution of the step (4) comprises the following steps:
(41) performing maximum likelihood estimation on the reflectivity distribution: constructing a probability calculation formula of the reflectivity projection distribution;
(42) introducing noise error quantity: assuming that the error amount is generated by Gaussian white noise, introducing the error amount into a deconvolution process;
(43) explicit expression of the probability of the estimator solved: constructing and simplifying a probability expression of the reflectivity distribution by using a discrete approximation condition;
(44) the stirling asymptotic approximation approximates: approximating a probability expression of the simplified reflectivity distribution using a stirling asymptotic approximation;
(45) solving the optimal estimator by a conjugate gradient method: and minimizing the constructed target function by using a conjugate gradient method, obtaining an optimal estimation value by using search iteration, and stopping iteration after the limit or the specified calculation precision is reached.
6. The method of resolving a reflectivity distribution of a laser reflection tomography target as set forth in claim 5, wherein the probability expression of the error amount of step (42) is:
wherein
For the target reflectivity distribution estimator to be solved, I is the original hypothetical image of the target reconstructed by the echo data, and N is
The finite, small distance measure of the component is denoted as Δ pj，χ2The method specifically comprises the following steps:
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