CN112363161B - Vegetation vertical structure and under-forest topography inversion method and device based on scattering mechanism decomposition - Google Patents

Vegetation vertical structure and under-forest topography inversion method and device based on scattering mechanism decomposition Download PDF

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CN112363161B
CN112363161B CN202011164833.3A CN202011164833A CN112363161B CN 112363161 B CN112363161 B CN 112363161B CN 202011164833 A CN202011164833 A CN 202011164833A CN 112363161 B CN112363161 B CN 112363161B
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汪长城
万杰
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Abstract

The invention discloses a vegetation vertical structure and under-forest topography inversion method and a device based on scattering mechanism decomposition, wherein the method comprises the following steps: acquiring a multi-baseline multi-polarization SAR data set in a forest inversion region, and performing registration and land leveling processing to obtain polarization chromatography SAR data; calculating a multi-baseline multi-polarization covariance matrix of the polarization chromatography SAR data, and decomposing and calculating an interference covariance matrix of canopy scattering and surface scattering; vectorizing and sparsely expressing interference covariance matrixes of canopy scattering and surface scattering to obtain corresponding sparse Bayesian learning models; iteratively updating the hyperparameters in the sparse Bayes learning model by adopting an EM (effective magnetic) algorithm so as to obtain a chromatographic spectrum of canopy scattering and surface scattering; and extracting the under-forest topography and the vegetation height of the forest inversion region respectively according to the chromatographic spectrums of the surface scattering and the canopy scattering. The invention can utilize a small amount of non-uniformly distributed SAR data to invert the vegetation height and the under-forest terrain with high precision.

Description

Vegetation vertical structure and under-forest topography inversion method and device based on scattering mechanism decomposition
Technical Field
The invention relates to a radar remote sensing earth observation technology, in particular to a super-resolution polarization SAR chromatography vegetation vertical structure and an under-forest terrain inversion method and device based on scattering mechanism decomposition under the condition of a small amount of non-uniform sampling data.
Background
Ecological civilization construction is one of the important layouts for the development of China, and the investigation and the protection of forest resources play an important role. Forests contain a wide variety of vegetation and are one of the most valuable natural resources on earth. The forest plays a great role in maintaining global carbon-oxygen balance, maintaining diversity of ecological systems, adjusting atmospheric humidity and the like. The vertical structure of the vegetation in the forest is an important parameter for quantitatively analyzing the forest, and has important significance for estimation of global biomass, measurement of under-forest topography, dynamic monitoring of the forest and the like.
The long-wave band Synthetic Aperture Radar (SAR) technology has strong penetrating power and is applied to perspective mapping of forests. Synthetic Aperture Radar Tomography (TomoSAR) has three-dimensional imaging capability by forming Synthetic apertures in the height direction and the azimuth direction respectively through multiple approximately parallel flights of a sensor (fig. 1). In radar signals, forest vegetation and under-forest landforms have different scattering mechanisms, and different polarization channels of SAR images have different sensitivities to different scattering mechanisms. Therefore, the Polarimetric Synthetic Aperture Radar (Pol-TomoSAR) technique is becoming an important technical means for forest vegetation parameter inversion.
In the field of SAR tomography of vegetation, periodogram methods, adaptive beamforming methods, multiple signal classification methods, and the like have been widely used for three-dimensional imaging of vegetation. The resolution and reconstruction accuracy of such conventional spectral analysis methods are often limited by the number and distribution of samples. The observation quantity is small, the base line distribution is uneven, the chromatographic result has serious side lobe effect, the resolution is low, and the influence of noise is large. Increasing the observation data means a large amount of observation cost, and brings the influence of temporal incoherence. The Compressive Sensing method can well overcome the limitation of data sampling, but the traditional Compressive Sensing method (CS) based on l1 norm convex optimization needs to set user parameters, and it is difficult to select a parameter generally applicable to all models and scenes. In addition, the convex optimization has huge computation load, and the application of the method is limited.
Disclosure of Invention
Based on the technical problems in the prior art, the invention provides a vegetation vertical structure and under-forest terrain inversion method and device based on scattering mechanism decomposition, signals of two different scattering mechanisms of a forest inversion region canopy and the earth surface are sparsely expressed and then are brought into a sparse Bayes learning model of covariance vectors to solve corresponding chromatographic spectrums, and therefore, a small amount of observation data is used for reconstructing a high-precision vegetation vertical structure and under-forest terrain. The method has a global optimal solution closer to the l0 norm, does not need to set user parameters, and has wider practical value.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a vegetation vertical structure and under-forest topography inversion method based on scattering mechanism decomposition comprises the following steps:
step 1, acquiring a multi-baseline multi-polarization SAR data set of a forest inversion region, and carrying out registration and land removing processing to obtain polarization chromatography SAR data;
step 2, calculating a multi-baseline multi-polarization covariance matrix of the polarization chromatography SAR data obtained in the step 1, and decomposing and calculating an interference covariance matrix of canopy scattering and surface scattering;
step 3, vectorizing and sparsely expressing interference covariance matrixes of canopy scattering and surface scattering to respectively obtain sparse Bayesian learning models of canopy scattering and surface scattering;
step 4, iteratively updating the hyperparameters in the two sparse Bayes learning models by adopting an EM (effective magnetic resonance) algorithm, and further obtaining chromatography spectrums of canopy scattering and surface scattering;
and 5, extracting the under-forest topography of the forest inversion region according to the chromatographic spectrum of the surface scattering, and extracting the vegetation height of the forest inversion region according to the chromatographic spectrum of the canopy scattering.
In a more preferred technical solution, the method for calculating the multi-baseline multi-polarization covariance matrix in step 2 is as follows:
Figure GDA0003824745830000021
wherein y is the polarimetric SAR data obtained in step 1,
Figure GDA0003824745830000022
g HV ＝g VH ，g HH 、g HV 、g VH 、g VV respectively forming an N-dimensional SAR data observation matrix by SAR data corresponding to HH, HV, VH and VV polarization modes, wherein N is the number of baselines; (*) H For conjugate transpose operations, E [. Cndot]To evaluate the desired operation; w is a multi-baseline multi-polarization covariance matrix obtained through calculation; c g And R g Polarization covariance matrix and interference covariance matrix, C, of surface scattering, respectively v And R v Polarization covariance matrix and interference covariance matrix for the canopy scatter,
Figure GDA0003824745830000023
is kronecker product;
SVD decomposition is carried out on the multi-baseline multi-polarization covariance matrix W, and the interference covariance matrix R of the canopy scattering is calculated by using the feature vector obtained by decomposition v Interference covariance matrix R with surface scattering g 。
In a more preferred technical scheme, the interference covariance matrix R of the canopy scatter is calculated using the eigenvectors obtained by decomposition v Interference covariance matrix R with surface scattering g The method comprises the following steps:
firstly, obtaining R by using eigenvector remodeling matrixes corresponding to the first two maximum eigenvalues obtained by SVD decomposition 1 And R 2 Using R 1 And R 2 Interference covariance matrix R representing canopy scatter v Interference covariance matrix R with surface scattering g Comprises the following steps:
Figure GDA0003824745830000031
in the formula, a and b are a pair of real numbers;
then, interference covariance matrix R based on canopy scattering v Interference covariance matrix R with surface scattering g Semi-positive definite constraint of (i.e. R) v And R g Solving the value intervals of the real numbers a and b when the characteristic value of (2) is not negative;
then, according to the following criterion of maximum separation of scattering mechanisms, solving the real numbers a and b:
Figure GDA0003824745830000032
wherein trace () is the trace of the matrix, | ·| non | F Is the Frobenius norm of the matrix. Finally, according to the real numbers a and b and the matrix R obtained by solving 1 And R 2 Obtaining the interference covariance matrix R of the canopy scattering v Interference covariance matrix R with surface scattering g 。
In a more preferred technical scheme, the sparse bayesian learning models of the surface scattering and the canopy scattering obtained in the step 3 are respectively as follows:
Figure GDA0003824745830000033
in the formula, R g 、R v Interference covariance matrices for surface and canopy scatter, respectively, vec (-) is a vectorization operation, y g 、y v Vector representations of the interference covariance matrices for the surface scatter and the canopy scatter, respectively;
b is an intermediate parameter, and B = A ^ conj (A), "Khatri-Rao product", A is an intermediate parameter, A = exp (j 2 π ξ) n s d )，s d Is the spatial height, ξ, of the scattering body n Is the spatial frequency; Ψ g The sparse basis of wavelet representing the scattering of earth surface adopts unit orthogonal basis, psi v A wavelet sparsity representing canopy scattering;
p g 、p v respectively are backscattering power vectors of surface scattering and canopy scattering;
σ g 、σ v noise power, t, corresponding to surface scattering and canopy scattering, respectively g ＝vec(σ g I)、t v ＝vec(σ v I) Respectively carrying out vectorization operation on corresponding noise power matrixes, wherein I is an identity matrix; delta g And delta v The estimated error between the covariance matrix of the surface scatter and the canopy scatter, respectively, and the corresponding true covariance matrix.
In a more preferable technical scheme, the EM algorithm is adopted in the step 4 to iteratively update the hyperparameter in the sparse Bayesian learning model and obtain the chromatography spectrum of the canopy scattering and the surface scattering, and the method specifically comprises the following steps:
step a, defining prior distribution:
for convenience of explanation, the sparse bayesian learning model of the surface scattering and the canopy scattering obtained in step 3 is represented as follows: y = Gx + δ; wherein G = [ B Ψ ] H ,I]Represents a new measurement matrix under sparse basis, x = [ Ψ p, t =]The method comprises the following steps of (1) obtaining a backscattering power and a noise vector under a sparse domain to be solved, wherein Y is vector representation of an interference covariance matrix of surface scattering or canopy scattering;
according to the prior information that the scattering signals after the sparse operation are sparse, the scattering signals are defined to obey Gaussian distribution, namely x-N (0, Λ); where Λ = diag (Γ),
Figure GDA0003824745830000041
representing the spatial distribution of x for a hyper-parameter vector of a sparse Bayesian learning model; first D hyperparameters tau 1 ,...τ D Controlling the sparsity of the backscattering power of D scatterers with height upwards, then N 2 Individual parameter of
Figure GDA0003824745830000042
Is the system noise; the probability density function of Y with respect to Γ is:
p(Y|Γ)＝∫p(Y|x)p(x|Γ)dx；
step b, defining initial values of parameters:
setting a hyper-parameter vector gamma initial value and an iteration termination condition of the sparse Bayesian learning model;
step c, calculating posterior probability distribution:
calculating a mean vector and a covariance matrix of x based on Bayesian criterion and the prior distribution defined in step a:
Figure GDA0003824745830000043
Figure GDA0003824745830000044
Σ Y ＝V+GΛ (i) G H
in the formula, the superscript i represents the current iteration number, μ is the mean vector of x, Σ x Sum-sigma Y Covariance matrices of x and Y, respectively, and V is the second order statistic of the sample covariance matrix estimation error δ.
And d, based on the mean vector and the covariance matrix obtained in the step c, learning and updating the hyperparametric vector by adopting an EM algorithm:
Figure GDA0003824745830000045
e, repeating the steps c and D until the iteration termination condition is met, and using the first D hyper-parameters gamma in the hyper-parameter vector gamma (1…D) Calculating the chromatograms of canopy and surface scattering:
Figure GDA0003824745830000046
in a more preferred technical scheme, the iteration termination condition is | | | Γ i+1 -Γ i || 2 /||Γ i || 2 Tol is less than or equal to tol, and/or the maximum iteration times are reached.
In a more preferred technical scheme, the method for extracting the under-forest topography of the forest inversion region according to the surface scattering chromatographic profile comprises the following steps: and extracting the position of the maximum power value in the chromatographic spectrum of the surface scattering as an estimated value of the ground height.
In a more preferred technical scheme, the method for extracting the vegetation height of the forest inversion region according to the chromatographic profile of canopy scattering comprises the following steps: the position of the top of the canopy is determined by power attenuation, i.e.: the method comprises the steps that a canopy phase center is taken as a starting point, a preset step length is used for upwards attenuating, and when the root mean square error of a height value extracted from a power attenuation position and a canopy height (DSM) extracted from Lidar data reaches the minimum, the height value at the moment is taken as an estimated value of the canopy height; the height of the ground is subtracted from the height of the canopy to obtain the height of the vegetation.
The invention also provides a vegetation vertical structure and under-forest topography inversion device based on scattering mechanism decomposition, which comprises:
a data pre-processing module to: acquiring a multi-baseline multi-polarization SAR data set of a forest inversion region, and performing registration and land leveling processing to obtain polarization chromatography SAR data;
a covariance calculation decomposition module to: calculating a multi-baseline multi-polarization covariance matrix of the polarization chromatography SAR data obtained by the data preprocessing module, and decomposing and calculating an interference covariance matrix of canopy scattering and surface scattering;
a model building module to: vectorizing and sparsely expressing interference covariance matrixes of canopy scattering and surface scattering to respectively obtain sparse Bayes learning models of canopy scattering and surface scattering;
a chromatogram calculation module to: iteratively updating the hyperparameters in the two sparse Bayes learning models by adopting an EM (effective magnetic field) algorithm so as to obtain chromatographic spectrums of canopy scattering and surface scattering;
vegetation vertical structure and under-forest topography inversion module for: and extracting the under-forest topography of the forest inversion region according to the chromatographic spectrum of the surface scattering, and extracting the vegetation height of the forest inversion region according to the chromatographic spectrum of the canopy scattering.
Advantageous effects
The invention uses multi-baseline full-polarization SAR data to separate and chromatograph two different scattering mechanisms of the canopy and the earth surface. On one hand, a more accurate phase center estimated value can be obtained, and the inversion precision of the under-forest terrain and vegetation height is improved; on the other hand, different sparse bases are used for carrying out sparse expression on different scattering mechanisms, so that the method disclosed by the invention can be reasonably applied to forest vegetation areas.
Moreover, the method is a sparse reconstruction method similar to l0 norm, compared with the traditional compressed sensing method based on l1 norm convex optimization, a more sparse global optimal solution can be obtained, and RIP conditions (namely uncorrelated G columns of the sensing matrix) can be met by less measurement data; the noise upper limit parameter is not needed to be set difficultly, the influence of noise can be adapted, and the vegetation height and the reconstruction precision of the under-forest terrain are higher; meanwhile, the method has higher operation efficiency, is suitable for large-scale and large-scale under-forest topographic mapping and vegetation height inversion, and has higher production practical value.
In addition, the method considers the estimation error of the covariance matrix of the chromatography SAR data sample, and is more stable.
Drawings
FIG. 1 is a schematic diagram of tomography SAR forest three-dimensional imaging;
FIG. 2 is a flow chart of a method according to an embodiment of the present invention;
FIG. 3 is a sub-flow chart of the steps of the method according to the embodiment of the present invention.
Detailed Description
In order to more clearly illustrate the object, implementation process and technical advantages of the present invention, the present embodiment selects P-band fully polarized SAR data obtained by a Tropi-SAR 2009 item ONERA SETHI flight system, and further details the method provided by the present invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention relates to a vegetation vertical structure decomposed based on a scattering mechanism and an under-forest terrain inversion method, which are super-resolution sparse reconstruction methods. In order to illustrate the superior performance of the method, the performance of different chromatography SAR methods under different numbers of fully polarized SAR data is analyzed in the specific implementation, and then the understory terrain and vegetation height are inverted by only adopting the fully polarized SAR data with 3 baselines.
The specific implementation steps of this embodiment are shown in fig. 2 and fig. 3, and include:
step 1, acquiring a multi-baseline multi-polarization SAR data set of a forest inversion region, and performing registration and land leveling processing to obtain polarization chromatography SAR data. The method comprises the following specific steps:
(1) And selecting a tropiSAR2009 project full-polarization SAR image as experimental data.
(2) And (3) registration: for a specified polarization channel (such as an HH polarization channel), one of the acquired N scenes of SAR images is selected as a reference image, and the rest N-1 scenes of SAR images are registered into a coordinate frame of the reference image by applying a maximized coherence coefficient. The SAR images of the remnant polarization channels (HV, VH, VV) are then registered using the same polynomial as the HH polarization channel.
(3) Land leveling: i.e. removing the interference phase caused by the land effect.
(4) Data discretization: after the above processing, for the polarized SAR tomographic data with the selected polarization mode, the complex value after focusing the distance-azimuth plane pixel (r, x) is:
Figure GDA0003824745830000061
in the formula b n Is a vertical baseline, Δ s is the elevation-wise sampling range, γ (r, x, s) is the elevation-wise reflectance function, ξ n ＝2πb n And/λ r is the spatial frequency.
HH. The observed values of N-dimensional SAR data formed by SAR data corresponding to HV, VH and VV polarization modes are respectively g HH 、g HV 、g VH 、g VV (ii) a N is the number of baselines; g in the single-station backscatter regime HV ＝g VH Therefore, the polarimetric SAR data finally obtained in step 1 can be expressed as
Figure GDA0003824745830000062
For a multi-baseline tomographic SAR dataset, after D discrete samplings of the highly up-going continuous signal, (1) can be expressed as the following matrix form:
g＝Aγ+e (2)
where g is an N-dimensional observation. A = exp (j 2 π ξ) n s d )，s d E is an N-dimensional noise vector for the spatial height of the scatterers.
And 2, calculating a multi-baseline multi-polarization covariance matrix of the polarization chromatography SAR data, and decomposing and calculating an interference covariance matrix of canopy scattering and surface scattering.
For SAR chromatography of forest vegetation, the different sensitivities of different polarization channels to different scattering mechanisms are often used to extract the under-forest topography and vegetation height, for example, the under-forest topography is extracted in the chromatogram of HH polarization channel, and the canopy height is extracted in the chromatogram of HV polarization channel. However, because the forest scene is complex, the backscatter energy of each polarization does not have such a regular distribution, and the foregoing strategy for extracting different scattering mechanisms may cause a certain deviation. In addition, the polarized SAR tomography technique based on scattering mechanism decomposition of the present invention requires that the measured signal be sparse (only a few elements in the signal vector are non-zero). In forest regions, the scattering of vegetation signals is a continuous process, and ground signals have sparsity, so that the method adopts different sparsity bases to sparsely express signals of two different scattering mechanisms of a canopy and the earth surface.
In order to more accurately extract the positions of phase centers of different scattering mechanisms and carry out sparse expression on the different scattering mechanisms, the method calculates the covariance matrix of the polarization chromatography SAR data obtained in the step 1 to obtain a multi-baseline multi-polarization covariance matrix, and then separates two different scattering mechanisms (surface scattering and canopy scattering) by using an algebraic synthesis method:
Figure GDA0003824745830000071
(*) H for conjugate transpose operations, E [. Cndot]To solve the expectation operation; w is a multi-baseline multi-polarization covariance matrix obtained through calculation; c g And R g Polarization covariance matrix and interference covariance matrix, C, of the surface scattering, respectively v And R v Polarization covariance matrix and interference covariance matrix for the canopy scatter,
Figure GDA0003824745830000072
is kronecker product.
After a multi-baseline multi-polarization covariance matrix W is obtained, SVD decomposition is carried out on the multi-baseline multi-polarization covariance matrix W, and an interference covariance matrix R of canopy scattering is calculated by using a feature vector obtained by decomposition v Interference covariance matrix R with surface scattering g ：
Firstly, obtaining R by taking a feature vector remodeling matrix corresponding to the first two maximum feature values obtained by SVD decomposition 1 And R 2 Using a matrix R 1 And R 2 Interference covariance matrix R representing canopy scatter v Interference covariance matrix R with surface scattering g Comprises the following steps:
Figure GDA0003824745830000073
in the formula, a and b are a pair of real numbers;
then, an interference covariance matrix R based on the canopy scattering v Interference covariance matrix R with surface scattering g With a semi-positive definite constraint of, i.e. R v And R g Solving the value intervals of the real numbers a and b when the characteristic value of (a) is not negative;
then, solving the real numbers a and b according to the following scattering mechanism maximization separation criterion:
Figure GDA0003824745830000081
wherein trace () is the trace of the matrix, | ·| non | F Is the Frobenius norm of the matrix. Finally, according to the real numbers a and b and the matrix R obtained by solving 1 And R 2 Obtaining the interference covariance matrix R of the canopy scattering v Interference covariance matrix R with surface scattering g 。
And 3, vectorizing and sparsely expressing the interference covariance matrixes of the canopy scattering and the surface scattering to respectively obtain sparse Bayesian learning models of the canopy scattering and the surface scattering.
Decomposing in step 2 to obtain interference covariance matrix R of canopy scattering v Interference covariance matrix R with surface scattering g Then, vectorization and sparse expression are respectively carried out, and the sparse Bayesian learning models for obtaining the surface scattering and the canopy scattering respectively comprise:
Figure GDA0003824745830000082
in the formula, R g 、R v Interference covariance matrices for surface and canopy scatter, respectively, vec (-) is a vectorization operation, y g 、y v Vector representations of the interference covariance matrices for the surface scatter and the canopy scatter, respectively;
b is an intermediate parameter, and B = A ^ conj (A), "Khatri-Rao product", A is an intermediate parameter, A = exp (j 2 π ξ) n s d )，s d Is the spatial height, ξ, of the scattering body n Is the spatial frequency; Ψ g The sparse basis of wavelet representing the scattering of earth surface adopts unit orthogonal basis, psi v A wavelet sparse basis representing canopy scattering;
p g 、p v respectively are backscattering power vectors of surface scattering and canopy scattering;
σ g 、σ v noise power, t, corresponding to surface scattering and canopy scattering, respectively g ＝vec(σ g I)、t v ＝vec(σ v I) Respectively carrying out vectorization operation on corresponding noise power matrixes, wherein I is an identity matrix; delta g And delta v The estimated error between the covariance matrix of the surface scatter and the canopy scatter, respectively, and the corresponding true covariance matrix, the second order statistic of which is V, respectively g ,V v 。
And 4, iteratively updating the hyperparameters in the two sparse Bayes learning models by adopting an EM (effective magnetic resonance) algorithm, and further obtaining the chromatographic spectrums of the canopy scattering and the earth surface scattering. The method comprises the following specific steps:
step a, defining prior distribution:
for convenience of explanation, the sparse bayesian learning model of the surface scattering and the canopy scattering obtained in step 3 is represented in a unified manner as follows: y = Gx + δ; wherein G = [ B Ψ ] H ,I]Representing new under sparse basisMeasurement matrix, x = [ Ψ p, t =]The method comprises the following steps of (1) obtaining a backscattering power and a noise vector under a sparse domain to be solved, wherein Y is vector representation of an interference covariance matrix of surface scattering or canopy scattering;
according to the prior information that the scattering signal (namely x) after the sparse operation is sparse, defining that the scattering signal obeys Gaussian distribution, namely x-N (0, Λ); where Λ = diag (Γ),
Figure GDA0003824745830000091
representing the spatial distribution of x for the hyperparametric vector of the sparse Bayesian learning model; first D hyperparameters tau 1 ,...τ D Controlling the sparsity of the backscattering power of D scatterers with height upwards, then N 2 Individual hyperparameter
Figure GDA0003824745830000092
Is the system noise; the probability density function of Y with respect to Γ is then:
p(Y|Γ)＝∫p(Y|x)p(x|Γ)dx；
step b, defining initial values of parameters:
setting the initial value of the hyper-parameter vector gamma of the sparse Bayesian learning model and iteration termination conditions, such as: (gamma) 0 Is a D + N 2 Random non-negative vector of dimensions, Λ (0) ＝diag(Γ (0) ) (ii) a Iteration termination error | | Γ i+1 -Γ i || 2 /||Γ i || 2 ≤tol＝10 -4 The maximum iteration number is 10;
step c, calculating posterior probability distribution:
calculating a mean vector and a related covariance matrix of x based on Bayesian criterion and the prior distribution defined in step a:
Figure GDA0003824745830000093
Figure GDA0003824745830000094
Σ Y ＝V+GΛ (i) G H
in the formula, the superscript i represents the current iteration number, μ is the mean vector of x, Σ x Sum-sigma Y Covariance matrixes of x and Y are respectively, and V is second-order statistics of a sample covariance matrix estimation error delta;
and d, learning and updating the hyperparametric vector by adopting an EM algorithm (namely an expected maximization algorithm) based on the mean vector and the covariance matrix obtained in the step c:
Figure GDA0003824745830000095
the updating of the hyper-parameter vector is performed by minimizing the following objective function:
Figure GDA0003824745830000096
e, repeating the steps c and D until any iteration termination condition is met, and using the first D hyper-parameters gamma in the hyper-parameter vector gamma (1…D) The chromatograms (i.e. spatial power spectra) of the canopy scatter and surface scatter were calculated:
Figure GDA0003824745830000097
because the signals of different scattering mechanisms are subjected to sparsification operation, the values of most positions of wavelet coefficients for expressing the backscattering power in a sparse domain are all 0 values, so that the sparse forest observation signal x is assumed to obey Gaussian distribution and accord with prior information, and the method has reasonableness. Meanwhile, gaussian prior distribution is very beneficial to development of sparse Bayesian learning.
And 5, calculating the under-forest terrain of the forest inversion region according to the chromatographic spectrum of the surface scattering, and calculating the vegetation height of the forest inversion region according to the chromatographic spectrum of the canopy scattering. The method specifically comprises the following steps:
the calculation method of the under-forest terrain comprises the following steps: and taking the position of the maximum power value in the chromatographic spectrum of the surface scattering as an estimated value of the ground height.
The calculation method of the vegetation height comprises the following steps: the position of the top of the canopy is determined by power attenuation, i.e.: taking the phase center of the canopy as a starting point, upwardly attenuating by a preset step length of-0.1 db, and taking the height value at the moment as an estimated value of the height of the canopy when the height value extracted from the power attenuation position and the root mean square error of the Lidar data DSM reach minimum; the height of the ground is subtracted from the height of the canopy to obtain the height of the vegetation.
And traversing each pixel in the multi-baseline and multi-polarization SAR data according to the method to obtain the under-forest terrain and vegetation height of the whole forest inversion region.
By analyzing different scattering chromatographic spectrums, under-forest landforms and vegetation heights inverted by example data, the method can obtain clear chromatographic spectrums under a small amount of observation data, hardly receives noise images and has high resolution. Whereas traditional spectral analysis methods beamformming and Capon, even using fully polarized data, are still unable to completely distinguish between scatterers of different scattering mechanisms. As the number of baselines decreases, the performance of both methods is so greatly affected that scatterers of different heights cannot be distinguished. The method of the invention is less affected by the number of images, and even under the condition of only using 3 pieces of baseline SAR data, the reconstruction performance is still kept high. In addition, the method of the invention can obtain reliable inversion results of the under-forest terrain and vegetation height only under the condition of using 3 pieces of baseline full polarization SAR data.
The invention also provides a vegetation vertical structure and under-forest topography inversion device based on scattering mechanism decomposition, which corresponds to the inversion method and comprises the following steps:
a data pre-processing module to: acquiring a multi-baseline multi-polarization SAR data set in a forest inversion region, and performing registration and land leveling processing to obtain polarization chromatography SAR data;
a covariance computational decomposition module to: calculating a multi-baseline multi-polarization covariance matrix of the polarization chromatography SAR data obtained by the data preprocessing module, and decomposing and calculating an interference covariance matrix of canopy scattering and surface scattering;
a model building module to: vectorization and sparse expression are carried out on interference covariance matrixes of canopy scattering and surface scattering, and sparse Bayesian learning models of canopy scattering and surface scattering are obtained respectively;
a chromatogram calculation module to: iteratively updating the hyperparameters in the two sparse Bayes learning models by adopting an EM (effective magnetic field) algorithm so as to obtain chromatographic spectrums of canopy scattering and surface scattering;
vegetation vertical structure and under-forest topography inversion module for: and extracting the under-forest topography of the forest inversion region according to the chromatographic spectrum of the surface scattering, and extracting the vegetation height of the forest inversion region according to the chromatographic spectrum of the canopy scattering.
The above embodiments are preferred embodiments of the present application, and those skilled in the art can make various changes or modifications without departing from the general concept of the present application, and such changes or modifications should fall within the scope of the claims of the present application.

Claims (7)

1. A vegetation vertical structure and under-forest terrain inversion method based on scattering mechanism decomposition is characterized by comprising the following steps:
step 1, acquiring a multi-baseline multi-polarization SAR data set in a forest inversion region, and performing registration and flat ground removal to obtain polarization chromatography SAR data;
step 2, calculating a multi-baseline multi-polarization covariance matrix of the polarization chromatography SAR data obtained in the step 1, and decomposing and calculating an interference covariance matrix of canopy scattering and surface scattering;
the calculation method and the decomposition method of the multi-baseline multi-polarization covariance matrix are as follows:
Figure FDA0003930916930000011
wherein y is the polarimetric SAR data obtained in step 1,
Figure FDA0003930916930000012
g HV ＝g VH ，g HH 、g HV 、g VH 、g VV the N-dimensional SAR data observation values are respectively formed by SAR data corresponding to HH, HV, VH and VV polarization modes; (*) H For conjugate transpose operations, E [. Cndot]To solve the expectation operation; w is a multi-baseline multi-polarization covariance matrix obtained through calculation; c g And R g Polarization covariance matrix and interference covariance matrix, C, of the surface scattering, respectively v And R v Respectively the polarization covariance matrix and the interference covariance matrix of the canopy scatter,
Figure FDA0003930916930000013
is kronecker product;
SVD decomposition is carried out on the multi-baseline multi-polarization covariance matrix W, and the interference covariance matrix R of the canopy scattering is calculated by using the feature vector obtained by decomposition v Interference covariance matrix R with surface scattering g ：
Firstly, obtaining R by using eigenvector remodeling matrixes corresponding to the first two maximum eigenvalues obtained by SVD decomposition 1 And R 2 Using R 1 And R 2 Interference covariance matrix R representing canopy scatter v Interference covariance matrix R of surface scattering g Comprises the following steps:
Figure FDA0003930916930000014
in the formula, a and b are a pair of real numbers;
then, an interference covariance matrix R based on the canopy scattering v Interference covariance matrix R with surface scattering g Semi-positive definite constraint of (i.e. R) v And R g Solving the value intervals of the real numbers a and b when the characteristic value of (a) is not negative;
then, solving the real numbers a and b according to the following scattering mechanism maximization separation criterion:
Figure FDA0003930916930000015
wherein trace () is the trace of the matrix, | ·| non | F Is the Frobenius norm of the matrix;
finally, according to the real numbers a and b and the matrix R obtained by solving 1 And R 2 Obtaining the interference covariance matrix R of the canopy scattering v Interference covariance matrix R of surface scattering g ；
Step 3, vectorizing and sparsely expressing interference covariance matrixes of canopy scattering and surface scattering to respectively obtain sparse Bayes learning models of canopy scattering and surface scattering;
step 4, iteratively updating the hyperparameters in the two sparse Bayes learning models by adopting an EM (effective electromagnetic) algorithm so as to obtain chromatographic spectrums of canopy scattering and surface scattering;
and 5, extracting the under-forest topography of the forest inversion region according to the chromatographic spectrum of the surface scattering, and extracting the vegetation height of the forest inversion region according to the chromatographic spectrum of the canopy scattering.
2. The method according to claim 1, wherein the sparse bayesian learning models of the surface scattering and the canopy scattering obtained from step 3 are:
Figure FDA0003930916930000021
in the formula, R g 、R v Interference covariance matrices for surface and canopy scatter, respectively, vec (-) is a vectorization operation, y g 、y v Vector representations of the interference covariance matrices for the surface scatter and the canopy scatter, respectively;
b is an intermediate parameter, and B = A ^ conj (A), "Khatri-Rao product", A is an intermediate parameter, A = exp (j 2 π ξ) n s d )，s d Is the spatial height, xi, of the diffuser n Is the spatial frequency; psi g The sparse basis of wavelet representing the scattering of earth surface adopts unit orthogonal basis, psi v Wavelet sparsity basis representing canopy scattering；
p g 、p v Backscattering power vectors of earth surface scattering and canopy scattering respectively;
σ g 、σ v noise power, t, corresponding to surface scattering and canopy scattering, respectively g ＝vec(σ g I)、t v ＝vec(σ v I) Respectively carrying out vectorization operation on corresponding noise power matrixes, wherein I is an identity matrix; delta. For the preparation of a coating g And delta v The estimated error between the covariance matrix of the surface scatter and the canopy scatter, respectively, and the corresponding true covariance matrix.
3. The method according to claim 2, wherein the step 4 comprises iteratively updating the hyperparameter in the sparse Bayesian learning model by using an EM algorithm and obtaining the chromatography spectra of the canopy scatter and the surface scatter, and specifically comprises the following steps:
step a, defining prior distribution:
for convenience of explanation, the sparse bayesian learning model of the surface scattering and the canopy scattering obtained in step 3 is represented in a unified manner as follows: y = Gx + δ; wherein G = [ B Ψ ] H ,I]Represents a new measurement matrix under sparse basis, x = [ Ψ p, t =]The method comprises the following steps of (1) obtaining a backscattering power and a noise vector under a sparse domain to be solved, wherein Y is vector representation of an interference covariance matrix of surface scattering or canopy scattering;
according to the prior information that the backscattering power and the noise vector x under the sparse domain to be solved are sparse, defining that the backscattering power and the noise vector x obey Gaussian distribution, namely x-N (0, Λ); where Λ = diag (Γ),
Figure FDA0003930916930000031
representing the spatial distribution of x for a hyper-parameter vector of a sparse Bayesian learning model; first D hyperparameters tau 1 ,...τ D Controlling the sparsity of the backscattering power of D scatterers with height upwards, then N 2 Individual parameter of
Figure FDA0003930916930000032
Is the system noise; the probability density function of Y with respect to Γ is then:
p(Y|Γ)＝∫p(Y|x)p(x|Γ)dx；
step b, defining initial values of parameters:
setting a hyper-parameter vector gamma initial value and an iteration termination condition of the sparse Bayesian learning model;
step c, calculating posterior probability distribution:
calculating a mean vector and a covariance matrix of x based on Bayesian criterion and the prior distribution defined in step a:
Figure FDA0003930916930000033
Figure FDA0003930916930000034
Σ Y ＝V+GΛ (i) G H
in the formula, the superscript i represents the current iteration number, μ is the mean vector of x, Σ x Sum-sigma Y Covariance matrixes of x and Y are respectively, and V is second-order statistics of a sample covariance matrix estimation error delta;
and d, based on the mean vector and the covariance matrix obtained in the step c, learning and updating the hyperparametric vector by adopting an EM algorithm:
Figure FDA0003930916930000035
e, repeating the steps c and D until the iteration termination condition is met, and using the first D hyper-parameters gamma in the hyper-parameter vector gamma (1 8230d) calculation of the chromatograms of canopy and surface scattering:
Figure FDA0003930916930000036
4. according to claim 3The method is characterized in that the iteration termination condition is | | Γ i+1 -Γ i || 2 /||Γ i || 2 Tol is less than or equal to and/or the maximum iteration times are reached.
5. The method of claim 1, wherein the extracting the under-forest topography of the forest inversion region from the surface-scattered tomography comprises: and extracting the position of the maximum power value in the chromatographic spectrum of the surface scattering as an estimated value of the ground height.
6. The method of claim 3, wherein the method of extracting vegetation height of the forest inversion region from the chromatogram of the canopy scatter is: the position of the top of the canopy is determined by power attenuation, i.e.: the method comprises the steps that a canopy phase center is taken as a starting point, a preset step length is used for upwards attenuating, and when the root mean square error of a height value extracted from a power attenuation position and a canopy height DSM extracted from Lidar data reaches the minimum, the height value at the moment is taken as an estimated value of the canopy height; the height of the ground is subtracted from the height of the canopy to obtain the height of the vegetation.
7. The utility model provides a vegetation vertical structure and forest topography inversion device based on scattering mechanism decomposes which characterized in that includes:
a data pre-processing module to: acquiring a multi-baseline multi-polarization SAR data set in a forest inversion region, and performing registration and land leveling to obtain polarization chromatography SAR data;
a covariance calculation decomposition module to: calculating a multi-baseline multi-polarization covariance matrix of the polarization chromatography SAR data obtained by the data preprocessing module, and decomposing and calculating an interference covariance matrix of canopy scattering and surface scattering;
the calculation method and the decomposition method of the multi-baseline multi-polarization covariance matrix are as follows:
Figure FDA0003930916930000041
wherein y is the polarimetric SAR data obtained in step 1,
Figure FDA0003930916930000042
g HV ＝g VH ，g HH 、g HV 、g VH 、g VV the N-dimensional SAR data observation values are formed by SAR data corresponding to HH, HV, VH and VV polarization modes respectively; (*) H For conjugate transpose operations, E [. Cndot]To solve the expectation operation; w is a multi-baseline multi-polarization covariance matrix obtained through calculation; c g And R g Polarization covariance matrix and interference covariance matrix, C, of surface scattering, respectively v And R v Respectively the polarization covariance matrix and the interference covariance matrix of the canopy scatter,
Figure FDA0003930916930000043
is kronecker product;
SVD decomposition is carried out on the multi-baseline multi-polarization covariance matrix W, and the interference covariance matrix R of the canopy scattering is calculated by using the feature vector obtained by decomposition v Interference covariance matrix R with surface scattering g ：
Firstly, obtaining R by using eigenvector remodeling matrixes corresponding to the first two maximum eigenvalues obtained by SVD decomposition 1 And R 2 Using R 1 And R 2 Interference covariance matrix R representing canopy scatter v Interference covariance matrix R with surface scattering g Comprises the following steps:
Figure FDA0003930916930000044
in the formula, a and b are a pair of real numbers;
then, an interference covariance matrix R based on the canopy scattering v Interference covariance matrix R with surface scattering g With a semi-positive definite constraint of, i.e. R v And R g Solving the value intervals of the real numbers a and b when the characteristic value of (2) is not negative;
then, solving the real numbers a and b according to the following scattering mechanism maximization separation criterion:
Figure FDA0003930916930000051
wherein trace () is the trace of matrix, | | · | | caly F Is the Frobenius norm of the matrix;
finally, according to the real numbers a and b and the matrix R obtained by solving 1 And R 2 Obtaining the interference covariance matrix R of the canopy scattering v Interference covariance matrix R with surface scattering g ；
A model building module to: vectorization and sparse expression are carried out on interference covariance matrixes of canopy scattering and surface scattering, and sparse Bayesian learning models of canopy scattering and surface scattering are obtained respectively;
a chromatogram calculation module to: iteratively updating the hyperparameters in the two sparse Bayes learning models by adopting an EM (effective magnetic resonance) algorithm so as to obtain chromatography spectrums of canopy scattering and surface scattering;
vegetation vertical structure and under-forest topography inversion module for: and extracting the under-forest topography of the forest inversion region according to the chromatographic spectrum of the surface scattering, and extracting the vegetation height of the forest inversion region according to the chromatographic spectrum of the canopy scattering.
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