CN117057998A - DEM super-resolution reconstruction method of interpretable deep learning network based on Lp norm - Google Patents

DEM super-resolution reconstruction method of interpretable deep learning network based on Lp norm Download PDF

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CN117057998A
CN117057998A CN202311107678.5A CN202311107678A CN117057998A CN 117057998 A CN117057998 A CN 117057998A CN 202311107678 A CN202311107678 A CN 202311107678A CN 117057998 A CN117057998 A CN 117057998A
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卜丽静
杨贝妮
张正鹏
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Xiangtan University
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    • G06T3/4053—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution
    • G06T3/4076—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution using the original low-resolution images to iteratively correct the high-resolution images

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Abstract

The invention provides a DEM super-resolution reconstruction method based on an Lp norm interpretable deep learning network, and relates to the technical field of DEM manufacturing. The method mainly comprises the following steps: and constructing an Lp norm-based DEM super-resolution reconstruction mathematical model, and deducing an interpretable deep learning DEM super-resolution reconstruction network. The processing process of the method is not similar, the deep learning network established by the method has the interpretability of a mathematical model, so that the result is more reliable, the aim of improving the quality of the DEM can be achieved, and the effect is better than that of the traditional DEM interpolation method.

Description

DEM super-resolution reconstruction method of interpretable deep learning network based on Lp norm
Technical Field
The invention relates to the technical field of DEM manufacturing, in particular to a DEM super-resolution reconstruction method of an interpretable deep learning network based on Lp norms.
Background
The DEM data is important basic data applied to the field of earth science, and currently, two main methods for acquiring high-resolution DEM data are available, namely, the high-precision DEM data are acquired through mapping platforms such as remote sensing satellites, aerial survey planes, ground total stations and the like; secondly, the existing DEM is improved in resolution by designing a related model or algorithm in combination with the DEM data published in the prior art. The high-resolution DEM data obtained by the second method has lower realization cost and stronger operability. Therefore, it is of great importance to explore how to obtain DEM data with high accuracy from a model or algorithm level quickly and efficiently.
Most of the current DEM data is displayed and stored in the form of a gray scale raster image, and each pixel point of the gray scale raster image represents a ground elevation value corresponding to the coordinate. The traditional DEM lifting algorithm is mainly an interpolation method, such as an inverse distance weighted interpolation method, a Kriging interpolation algorithm and a local polynomial interpolation, which are commonly used at present (reference: han Fujiang, liu Xuejun, pan Shengling. Similarity research of a DEM interpolation method and a visibility analysis result [ J ]. Geographical and geographic information science, 2007,23 (1): 5.), and along with the development of a deep learning algorithm, a residual network is used in the super-resolution reconstruction problem of the DEM by students (reference: zhang Hongming, full Kai, yang Yanan and the like; mountain area DEM super-resolution reconstruction based on a deep residual network [ J ]. Agricultural machinery academy, 2021,52 (01): 178-184). However, the traditional DEM interpolation method is simple and easy to implement, but the precision after super-division is not improved much, the existing deep learning-based method is good in effect and poor in interpretability, and uncertainty elevation information is easy to generate in super-resolution reconstruction, so that the method is very unfavorable for DEM production and application.
The invention provides a DEM super-resolution reconstruction method of an interpretable deep learning network based on an Lp norm. Aiming at the problem of poor network interpretability of a DEM deep learning super-resolution reconstruction algorithm, the invention provides an interpretability DEM super-resolution reconstruction method combining deep learning and a regularized mathematical model based on a regularized model frame.
Disclosure of Invention
Aiming at the technical problems, the invention aims to overcome the defects of the prior art, and provides a DEM super-resolution reconstruction method based on an Lp norm interpretable deep learning network.
In order to achieve the above purpose, the present invention provides a DEM super-resolution reconstruction method based on Lp norm interpretable deep learning network, comprising the following steps:
s1: making a DEM training data set;
s2: establishing a DEM super-resolution reconstruction mathematical model based on Lp (0<P is less than or equal to 2) norms;
s3: solving L established in step S2 by using iterative shrinkage threshold algorithm P A mathematical model is reconstructed by the DEM super-resolution of the norm;
s4: will solve for L p Iterative shrinkage threshold algorithm of norm DEM super-resolution reconstruction mathematical model is combined with deep learning network to construct L-based model P Reconstructing a deep learning network model by using the DEM super-resolution of the norm;
s5: the training data set in the step S1 is adopted to learn and train parameters of the network model, and parameters of the DEM super-resolution reconstruction network model are obtained;
s6: adopting the DEM super-resolution reconstruction network model and parameters in the step S5 to test the input DEM to be super-divided to obtain a high-precision DEM image after super-division;
s7: and (3) evaluating the accuracy of the DEM obtained in the step S6.
Preferably, the training data set in step S1 is selected to be 90 meters of SRTM1 and 30 meters of SRTM3 data.
Preferably, in the step S2, L is used as a base P The construction of the mathematical model for the super-resolution reconstruction of the DEM of the norm comprises the following steps:
establishing a model under a DEM quality improvement mathematical framework, and establishing the following L P The problem of optimizing norms to reconstruct a high resolution DEM, I representing the high resolution DEM:
wherein the first term is a data fidelity term and the second term is a regularization term. g is the DEM of low resolution,representing the square of the two norms, p represents L P Norms, gamma 2 As regular term coefficients, ψ 2 (I) Is a linear expression that utilizes a DEM elevation value gradient prior, a sparse prior, a self-similar prior, or other prior knowledge.
Preferably, in the step S3, the iterative shrinkage threshold algorithm is used to solve the L-based model created in the step S2 P The mathematical model for reconstructing the DEM super-resolution of the norm comprises the following steps of:
(1) For the L-based established in step S2 P First term data fidelity term in mathematical model for DEM super-resolution reconstruction of normIt is evident that S (I) is a convex function and satisfies Lipschitz continuity, i.e. that a constant l1 > 0 is present such that +.>For some Ik-1 and any l2 > l1 > 0,S (I), the method can be approximately developed at Ik-1:
where c is a constant term. Obtainable L according to the above P The equivalent form of the norm DEM super-resolution reconstruction model is used for explicitly solving I:
wherein the method comprises the steps of
(2) Iterative shrink threshold algorithm solves for L by iterating the following steps P Norm DEM super-resolution reconstruction model:
preferably, in the step S4, the step is based on L P The construction of the model of the DEM super-resolution reconstruction deep learning network of the norm comprises the following steps:
(1) Model building and solving: by non-linear transformation F 2 (. Cndot.) instead of ψ in the iterative shrink threshold algorithm above 2 (I) Obtaining
(2) And (3) network structure design: based on L P Each step of the super-resolution reconstruction network structure of the norms of the DEM corresponds to the iterative process, the input is the low-resolution DEM, the initial reconstruction is the low-resolution DEM, and the output result I N Results after N cycles. In particular, the network has N phases, each phase being exactly oppositeCorresponding to one iteration in the network. Nonlinear transformation F 2 (k) Two linear convolution operations (Conv) separated for a linear unit (ReLU), anAnd F is equal to 2 (k) Symmetrical structure (I)>The kth iteration detailed process: through the k-1 th iteration result I k-1 Calculating r k ，r k Through F 2 (k) After transformation, F is obtained 2 (r k )，F 2 (r k ) Obtaining F through solving and processing of two norms threshold value 2 (I k ) Finally F 2 (I k ) Through F 2 (I k ) Inverse transformation of->Obtaining the k iteration output result I k ；
(3) Network loss design: given training data g, first, taking low-resolution DEM as input, generating I of high-resolution DEM as output result through network, in order to ensure I i And I i+1 The difference between them is satisfied at the same timeThe loss function is thus as follows:
wherein, loss 1 Loss of difference, loss of Loss 2 For constraint Loss, N is the total number of training blocks, and the total Loss of network is loss=loss 1 +Loss 2 。
Preferably, in the step S6, an input image of a to-be-superdivided DEM of a certain test area is tested, for example, a DEM with a resolution of 90 meters is input, meanwhile, 30 meters of DEM data of a certain area is prepared, super-resolution reconstruction is performed on the 90 meters of DEM data according to a patent method, and finally, the precision evaluation is performed on the superdivided result and the existing 30 meters of DEM with a resolution, so that the network can superdivide DEM with other resolutions.
By the method, aiming at the problem of improving the DEM data resolution, nonlinear transformation is utilized to replace the regularization term of the regularization model, the regularization model is solved by the deep learning network, and the interpretability of the deep learning network is improved while the model is solved. Experimental results show that the super-resolution reconstruction result can achieve the aim of improving the quality of DEM data, and the effect is superior to that of the traditional interpolation method.
Drawings
The description of the present disclosure will become apparent and readily appreciated in conjunction with the following drawings, wherein:
fig. 1 is a flow chart of a DEM super-resolution reconstruction method of an interpretable deep learning network based on Lp norms;
FIG. 2 is a diagram of the overall network architecture;
FIG. 3 is a diagram of an original low resolution DEM effect;
fig. 4 is a DEM effect diagram after super-resolution reconstruction.
Detailed Description
According to the steps shown in fig. 1, a DEM super-resolution reconstruction method based on an Lp norm interpretable deep learning network of the present invention is described in detail.
Step S1: a training set was made, with the training data set selected to be 90 meters of SRTM1 and 30 meters of SRTM3 data.
Step S2: constructing a DEM super-resolution reconstruction mathematical model based on Lp (0<P is less than or equal to 2) norm, which comprises the following steps:
establishing a model under a DEM quality improvement mathematical framework, and establishing the following L P Problem of optimizing norms to reconstruct high resolution DEM, generation ITable high resolution DEM:
wherein the first term is a data fidelity term and the second term is a regularization term. g is the DEM of low resolution,representing the square of the two norms, I p Represents L P Norms, gamma 2 As regular term coefficients, ψ 2 (I) Is a linear expression that utilizes a DEM elevation value gradient prior, a sparse prior, a self-similar prior, or other prior knowledge.
Step S3: solving L established in step S2 by using iterative shrinkage threshold algorithm P The mathematical model for reconstructing the DEM super-resolution of the norm comprises the following steps of:
(1) For the L-based established in step S2 P First term data fidelity term in mathematical model for DEM super-resolution reconstruction of normIt is evident that S (I) is a convex function and satisfies Lipschitz continuity, i.e. there is a constant l 1 > 0 makes->For some I k-1 And optionally l 2 ＞l 1 > 0,S (I) can be found in I k-1 Approximate expansion:
where c is a constant term. Obtainable L according to the above P The equivalent form of the norm DEM super-resolution reconstruction model is used for explicitly solving I:
wherein the method comprises the steps of
(2) Iterative shrink threshold algorithm solves for L by iterating the following steps P Norm DEM super-resolution reconstruction model:
step S4: construction based on L P The DEM super-resolution reconstruction deep learning network model of the norm comprises the following steps of:
(1) Model building and solving: by non-linear transformation F 2 (. Cndot.) instead of ψ in the iterative shrink threshold algorithm above 2 (I) Obtaining
(2) And (3) network structure design: based on L P Each step of the super-resolution reconstruction network structure of the norms of the DEM corresponds to the iterative process, the input is the low-resolution DEM, the initial reconstruction is the low-resolution DEM, and the output result I N Results after N cycles. In particular, the network has N phases, each phase corresponding exactly to one iteration in the network. Nonlinear transformation F 2 (k) Two linear convolution operations (Conv) separated for a linear unit (ReLU), anAnd F is equal to 2 (k) Symmetrical structure (I)>The kth iteration detailed process: through the k-1 th iteration result I k-1 Calculating r k ，r k Through F 2 (k) After transformation, F is obtained 2 (r k )，F 2 (r k ) Obtaining F through solving and processing of two norms threshold value 2 (I k ) Finally F 2 (I k ) Through F 2 (I k ) Inverse transformation of->Obtaining the k iteration output result I k ；
(3) Network loss design: given training data g, first, taking low-resolution DEM as input, generating I of high-resolution DEM as output result through network, in order to ensure I i And I i+1 The difference between them is satisfied at the same timeThe loss function is thus as follows:
wherein, loss 1 Loss of difference, loss of Loss 2 For constraint Loss, N is the total number of training blocks, and the total Loss of network is loss=loss 1 +Loss 2 。
Step S5: and (3) carrying out parameter learning and training on the network model by adopting the training data set in the step (S1), and setting training parameters: the learning rate is 1e-5 (200 epochs), and the iteration number is 9. After tuning to the appropriate parameters, smooth convergence is lost.
Step S6: and testing an input DEM image to be super-divided in a certain test area, for example, inputting a DEM with the resolution of 90 meters, preparing DEM data of a certain area at the same time, reconstructing the super-resolution of the DEM data of 60 meters according to a patent method, and finally evaluating the precision of the super-divided result and the existing DEM with the resolution of 30 meters, wherein the DEM with the other resolutions can be super-divided by the network after the precision meets the requirement.
Step S7: and (3) evaluating the accuracy of the DEM obtained in the step (S6), wherein the original DEM data are shown in fig. 3, and the experimental result of the method is shown in fig. 4, so that the accuracy of the DEM data is improved to a certain extent after super-resolution reconstruction, and the super-resolution reconstruction method for interpretable deep learning is strong in robustness.
The above description is only specific embodiments of the present invention, the protection scope of the present invention is not limited thereto, and any person skilled in the art should understand that modifications and substitutions within the scope of the present invention are included in the scope of the present invention, and the protection scope of the present invention should be defined by the claims.

Claims (4)

1. The DEM super-resolution reconstruction method based on the Lp norm interpretable deep learning network is characterized by comprising the following steps of:
s1: making a DEM training data set;
s2: establishing a DEM super-resolution reconstruction mathematical model based on Lp (0<P is less than or equal to 2) norms;
s3: solving L established in step S2 by using iterative shrinkage threshold algorithm P A mathematical model is reconstructed by the DEM super-resolution of the norm;
s4: will solve for L p Iterative shrinkage threshold algorithm of norm DEM super-resolution reconstruction mathematical model is combined with deep learning network to construct L-based model P Reconstructing a deep learning network model by using the DEM super-resolution of the norm;
s5: the training data set in the step S1 is adopted to learn and train parameters of the network model, and parameters of the DEM super-resolution reconstruction network model are obtained;
s6: adopting the DEM super-resolution reconstruction network model and parameters in the step S5 to test the input DEM to be super-divided to obtain a high-precision DEM image after super-division;
s7: and (3) evaluating the accuracy of the DEM obtained in the step S6.
2. The method for reconstructing the super resolution of the DEM of the Lp-norm based interpretive deep learning network according to claim 1, wherein said step S2 is based on L P The construction of the mathematical model for the super-resolution reconstruction of the DEM of the norm comprises the following steps:
establishing a model under a DEM quality improvement mathematical framework, and establishing the following L P The problem of optimizing norms to reconstruct a high resolution DEM, I representing the high resolution DEM:
wherein the first term is a data fidelity term and the second term is a regularization term. g is the DEM of low resolution,representing the square of the two norms, I p Represents L P Norms, gamma 2 As regular term coefficients, ψ 2 (I) To utilize the prior of the DEM elevation value gradient,Linear expression of sparse priors, self-similar priors, or other prior knowledge.
3. The method for reconstructing the super-resolution of the DEM of the Lp-norm based interpretive deep learning network according to claim 1, wherein said step S3 is performed by solving the L-based set up in step S2 with an iterative shrinkage threshold algorithm P The mathematical model for reconstructing the DEM super-resolution of the norm comprises the following steps of:
(1) For the L-based established in step S2 P First term data fidelity term in mathematical model for DEM super-resolution reconstruction of normIt is evident that S (I) is a convex function and satisfies Lipschitz continuity, i.e. there is a constant l 1 > 0 such thatFor some I k-1 And optionally l 2 ＞l 1 > 0,S (I) can be found in I k-1 Approximate expansion:
where c is a constant term. Obtainable L according to the above P The equivalent form of the norm DEM super-resolution reconstruction model is used for explicitly solving I:
wherein the method comprises the steps of
(2) Iterative shrink threshold algorithm solves for L by iterating the following steps P Norm DEM super-resolution reconstruction model:
4. the method for reconstructing the super-resolution of the DEM of the Lp-norm-based interpretive deep learning network according to claim 1, wherein said step S4 is based on L P The construction of the model of the DEM super-resolution reconstruction deep learning network of the norm comprises the following steps:
(1) Model building and solving: by non-linear transformation F 2 (. Cndot.) instead of ψ in the iterative shrink threshold algorithm above 2 (I) Obtaining
(2) And (3) network structure design: based on L P Each step of the super-resolution reconstruction network structure of the norms of the DEM corresponds to the iterative process, the input is the low-resolution DEM, the initial reconstruction is the low-resolution DEM, and the output result I N Results after N cycles. In particular, the network has N phases, each phase corresponding exactly to one iteration in the network. Nonlinear transformation F 2 (k) Two linear convolution operations (Conv) separated for a linear unit (ReLU), anAnd F is equal to 2 (k) Symmetrical structure (I)>The kth iteration detailed process: through the k-1 th iteration result I k-1 Calculating r k ，r k Through F 2 (k) After transformation, F is obtained 2 (r k )，F 2 (r k ) Obtaining F through solving and processing of two norms threshold value 2 (I k ) Finally F 2 (I k ) Through F 2 (I k ) Is inverse transformed of (a)Obtaining the k iteration output result I k ；
(3) Network loss design: given training data g, first, taking low-resolution DEM as input, generating I of high-resolution DEM as output result through network, in order to ensure I i And I i+1 The difference between them is satisfied at the same timeThe loss function is thus as follows:
wherein, loss 1 Loss of difference, loss of Loss 2 For constraint Loss, N is the total number of training blocks, and the total Loss of network is loss=loss 1 +Loss 2 。
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