CN112285702A - Ground penetrating radar imaging method based on LASSO algorithm - Google Patents
Ground penetrating radar imaging method based on LASSO algorithm Download PDFInfo
- Publication number
- CN112285702A CN112285702A CN202010915542.7A CN202010915542A CN112285702A CN 112285702 A CN112285702 A CN 112285702A CN 202010915542 A CN202010915542 A CN 202010915542A CN 112285702 A CN112285702 A CN 112285702A
- Authority
- CN
- China
- Prior art keywords
- model
- inversion
- curvelet
- radar
- ground penetrating
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/885—Radar or analogous systems specially adapted for specific applications for ground probing
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/418—Theoretical aspects
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
Landscapes
- Engineering & Computer Science (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- General Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Computer Networks & Wireless Communication (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention provides a ground penetrating radar imaging method based on a LASSO algorithm, which comprises the following steps: s1: establishing a true model of full waveform inversion of the ground penetrating radar; s2: forward operation is carried out based on the real model, and a gather is extracted to obtain observation radar data; s3: establishing an initial model of the full-waveform inversion of the ground penetrating radar and setting the inversion termination precision; s4: forward operation is carried out based on the initial model, and a gather is extracted to obtain initial theoretical radar data; s5: constructing an objective function; s6: performing Curvelet transformation on the model updating quantity to obtain a Curvelet domain objective function S7: carrying out inversion according to frequency scale groups from low to high to obtain corresponding model gradient g under each frequencykStep length akAnd CurvModel update quantity Deltax of elet domaink(ii) a S8: updating the model; s9: calculating a target function value based on the data extracted by the new model, and judging whether an inversion result meets a termination condition; s10: if the terminal condition is not met, updating the model, if the terminal condition is met, outputting a final inversion result, and performing Curvelet inverse transformation on the final inversion result to obtain a model updating amount delta m; s11: updating model m ═ m0And obtaining a final radar parameter inversion result by the + delta m.
Description
Technical Field
The invention relates to a ground penetrating radar imaging technology, in particular to a ground penetrating radar imaging method based on an LASSO algorithm.
Background
The ground penetrating radar is one of important means for shallow surface detection, and plays an important role in a plurality of fields such as highway water transportation, building engineering, ground disaster assessment and the like. The ground penetrating radar identifies characteristics of diffracted waves and reflected waves by exciting the ultrahigh-frequency short pulses and analyzing travel time information and section continuity of radar waves after passing through the abnormal body, has the advantages of being capable of judging existence, distribution and types of the abnormal body, efficient, lossless, capable of imaging in real time, visual in result and the like.
However, the ground penetrating radar obtains the spatial distribution of the underground target without inversion, and the reliability of the final interpretation result cannot be guaranteed. The distribution of underground space media in cities is complex and changeable, besides natural structures, the underground space media also comprise various pipelines and gravels, and the structures can cause the abnormal travel of radar waves, so that the occurrence state of a target body is judged by only depending on the velocity analysis of a common central point, the resolution and the reliability are not high, and the reliability of interpretation results is further reduced.
If the underground medium can be subjected to parametric inversion by utilizing information carried by radar waves reflected back to the ground so as to depict physical property distribution of the medium, more specific target form and distribution information can be obtained, so that the detection result is more visual and reliable, but underground shallow spaces of cities are full of a large number of artificial structures such as pipelines, steel bars and the like, and the originally complex shallow spaces become more complex by the structures. The radar wave may undergo a series of scattering and diffraction after being reflected at different structures, and finally, the different structures may have the same influence on the wave field, which is also an important reason for the ambiguity of the radar data. For radar imaging, people often think that much information can better describe the underground medium, but in the actual imaging process, only a part of data has great influence on the imaging result, and much remaining data has little weight on the imaging result. If all data are inverted, the burden of inversion is increased undoubtedly, and meanwhile, other information which is not needed by inversion and can be regarded as noise is contained in a large amount of data, so that the reliability of the inversion result is reduced. If can compress and refine data, not only can improve the speed of radar formation of image, can also filter partial noise simultaneously, play and improve the formation of image precision.
Disclosure of Invention
The invention discloses a ground penetrating radar imaging method based on an LASSO algorithm, which solves the problems that the space distribution of an underground target body is obtained without inversion of a ground penetrating radar, and the reliability of a final interpretation result of the underground target body cannot be guaranteed, converts the inversion problem of radar waves into the LASSO problem, and improves the efficiency and the reliability of radar data inversion by reasonably compressing data.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the invention discloses a ground penetrating radar imaging method based on an LASSO algorithm, which comprises the following steps:
s1: establishing a true model of full waveform inversion of the ground penetrating radar;
s2: forward operation is carried out based on the real model, and a gather is extracted to obtain observation radar data;
s3: establishing an initial model of the full-waveform inversion of the ground penetrating radar and setting the inversion termination precision;
s4: forward operation is carried out based on the initial model, and a gather is extracted to obtain initial theoretical radar data;
s5: constructing an objective function;
s6: performing Curvelet transformation on the model update quantity to obtain a target function of a Curvelet domain
S7: carrying out inversion according to frequency scale groups from low to high to obtain corresponding model gradient g under each frequencykStep length akAnd a model update quantity Deltax of the Curvelet domaink；
S8: updating model xk+1＝xk+Δxk；
Wherein, Δ xkIs a Curvelet coefficient vector, xkAnd xk+1Coefficients corresponding to the kth iteration and the (k + 1) th iteration are respectively set;
s9: calculating a target function value based on the data extracted by the new model, and judging whether an inversion result meets a termination condition;
s10: if the termination condition is not met, updating the model, and repeating the steps S6 to S9 until the termination condition is met; if the end condition is met, outputting a final inversion result and performing Curvelet inverse transformation on the final inversion result;
s11: updating model m ═ m0+ Δ m, where Δ m is the model update after inverse Curvelet transformation, m0Is the initial model and m is the final inverse model.
Further, the forward operation is numerically simulated by a frequency domain finite difference method based on a staggered grid, and the boundary adopts a boundary condition of a complete matching layer.
Further, the objective function is:
wherein Δ D ═ Dobs-Dcal，DcalAs theoretical data, DobsIn order to observe the data, it is,
u is the radar wave field, and Δ m is the model update quantity.
Further, the objective function of the Curvelet domain is as follows:
wherein C is Curvelet operator.
The beneficial technical effects are as follows:
the invention discloses a ground penetrating radar imaging method based on an LASSO algorithm, which comprises the following steps:
s1: establishing a true model of full waveform inversion of the ground penetrating radar;
s2: forward operation is carried out based on the real model, and a gather is extracted to obtain observation radar data;
s3: establishing an initial model of the full-waveform inversion of the ground penetrating radar and setting the inversion termination precision;
s4: forward operation is carried out based on the initial model, and a gather is extracted to obtain initial theoretical radar data;
s5: constructing an objective function;
s6: performing Curvelet transformation on the model update quantity to obtain a target function of a Curvelet domain
S7: carrying out inversion according to frequency scale groups from low to high to obtain corresponding model gradient g under each frequencykStep length akAnd a model update quantity Deltax of the Curvelet domaink；
S8: updating model xk+1＝xk+Δxk；
Wherein, Δ xkIs a Curvelet coefficient vector, xkAnd xk+1Coefficients corresponding to the kth iteration and the (k + 1) th iteration are respectively set;
s9: calculating a target function value based on the data extracted by the new model, and judging whether an inversion result meets a termination condition;
s10: if the termination condition is not met, updating the model, and repeating the steps S6 to S9 until the termination condition is met; if the end condition is met, outputting a final inversion result and performing Curvelet inverse transformation on the final inversion result;
s11: updating model m ═ m0+ Δ m, where Δ m is the model update after inverse Curvelet transformation, m0Is the initial model and m is the final inverse model.
The method solves the problems that the space distribution of the underground target body is obtained without inversion of the ground penetrating radar, and the reliability of the final interpretation result can not be guaranteed, converts the inversion problem of the radar waves into the LASSO problem, and improves the efficiency and the reliability of radar data inversion through reasonably compressing data.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for imaging a ground penetrating radar based on a LASSO algorithm according to the present invention;
FIG. 2 is a real model of dielectric constant in a LASSO algorithm-based ground penetrating radar imaging method according to the present invention;
FIG. 3 is an initial model of dielectric constant in a LASSO algorithm-based ground penetrating radar imaging method according to the present invention;
FIG. 4 is an inverse model of the dielectric constant in the method for imaging a ground penetrating radar based on the LASSO algorithm.
Detailed Description
In order to make the technical scheme and advantages of the invention more apparent, the invention is further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The LASSO method (Least absolute similarity and selection operator) is a biased estimation that can process complex collinear data and compresses partial coefficients by constructing a penalty function. The research utilizes the characteristic of the LASSO method and the sparsity of a wave field in a curvelet domain to convert the radar wave inversion problem into the LASSO problem for solving, so that the inversion speed and the inversion precision are improved.
The invention relates to a basic principle of a ground penetrating radar imaging method based on an LASSO algorithm, which comprises the following steps:
at the beginning of inversion, firstly establishing a real model for simulating actual collected data, and carrying out forward simulation on the basis to obtain observation data; then establishing an initial model, and setting corresponding parameters and inversion termination precision; then forward modeling is carried out based on the initial model to obtain theoretical data; and then constructing an objective function and carrying out Curvelet transformation on the objective function to obtain the objective function of the Curvelet domain. The first derivative of the Curvelet domain objective function is solved to obtain the gradient of the dielectric constant (the research only uses the dielectric constant as an example to discuss the radar imaging method based on the LASSO problem, and the conductivity is set to be known); calculating step length and according to formula xk+1＝xk+ΔxkUpdating the model; the updated objective function value is recalculated,judging whether the new objective function value meets the termination condition of iteration, if not, making k equal to k +1 to carry out the iteration of the next frequency, and if so, terminating the iteration; for model xk+1Performing inverse Curvelet transformation to obtain model update quantity delta m, and according to a formula m ═ m0+ Δ m yields the final model parameter m.
Specifically, the method for imaging the ground penetrating radar based on the LASSO algorithm comprises the following steps:
s1: establishing a true model of full waveform inversion of the ground penetrating radar;
the real model is a partial marmousi model and is assigned according to the numerical value change range of the dielectric constant;
s2: forward operation is carried out based on the real model, and a gather is extracted to obtain observation radar data;
the data is equivalent to radar data acquired in actual engineering, numerical simulation is carried out by adopting a frequency domain finite difference method based on staggered grids during forward operation, and boundary conditions of a complete matching layer are adopted in the boundary. Simulating the equation form of the forward part in the full waveform inversion of the earthquake, the wave equation of the full waveform inversion of the ground penetrating radar can be written as follows: a (m) U ═ S, where a is the forward operator and U is the wavefield (electric field E in TM mode)y) S is a discrete source, m is the dielectric constant, and the conductivity is known. By calculating the positive operator A and loading the discrete source S, single-frequency wave fields under different frequencies can be obtained. When m represents a real model, the observed radar data is obtained by extracting a gather from a wave field U and performing time domain conversion.
S3: establishing an initial model of the full-waveform inversion of the ground penetrating radar and setting the inversion termination precision;
the initial model is obtained by smoothing the real model.
S4: forward operation is carried out based on the initial model, and a gather is extracted to obtain initial theoretical radar data;
step four is similar to step two, and the forward equation is still: a (m) U ═ S
Where A is the forward operator and U is the wave field (electric field E in TM mode)y) S is a discrete source, m is a dielectric constant, and when m represents an initial model, the wavefield U is extracted from a gatherNamely theoretical radar data;
s5: constructing an objective function;
the objective function is expressed in a two-norm form, and the objective function is as follows:
wherein Δ D ═ Dobs-Dcal，DcalAs theoretical data, DobsIn order to observe the data, it is,
u is the radar wave field, and Δ m is the model update quantity.
S6: performing Curvelet transformation on the model updating quantity to obtain a target function of a Curvelet domain;
curvelet domain objective function:
wherein C is Curvelet operator.
The optimization problem of the LASSO's tape-constrained form can be written as:
wherein beta is a parameter to be optimized and has sparsity.
Following the form of the LASSO problem, the optimization problem of the ground penetrating radar waves can be written as:
and the column vector in x is a Curvelet coefficient vector and has sparsity. Therefore, by utilizing the sparsity of the wave field in the Curvelet domain, the research converts the radar wave inversion problem into the LASSO problem. χ is a threshold value, and the compression amount of the coefficient can be controlled by the limitation of the threshold value, and is 0.87 in the patent of the invention.
S7: carrying out inversion according to frequency scale groups from low to high to obtain corresponding model gradient g under each frequencykStep length akAnd a model update quantity Deltax of the Curvelet domaink；
Wherein the step size is determined by non-monotonic line search method, and the model update amount is determined according to the formula Deltaxk＝akgkAnd (4) determining.
S8: updating model xk+1＝xk+Δxk；
Wherein, Δ xkIs a Curvelet coefficient vector, xkAnd xk+1Coefficients corresponding to the kth iteration and the (k + 1) th iteration are respectively set;
s9: calculating a target function value based on the data extracted by the new model, and judging whether an inversion result meets a termination condition;
s10: if the termination condition is not met, updating the model, and repeating the steps S6 to S9 until the termination condition is met; if the end condition is met, outputting a final inversion result and performing Curvelet inverse transformation on the final inversion result to obtain Cx;
s11: updating model m ═ m0+ Δ m, where Δ m is the model update after inverse Curvelet transformation, m0Is the initial model and m is the final inverse model.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and alternate implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present invention.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The above examples are only for describing the preferred embodiments of the present invention, and are not intended to 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 (4)
1. A ground penetrating radar imaging method based on a LASSO algorithm is characterized by comprising the following steps:
s1: establishing a true model of full waveform inversion of the ground penetrating radar;
s2: forward operation is carried out based on the real model, and a gather is extracted to obtain observation radar data;
s3: establishing an initial model of the full-waveform inversion of the ground penetrating radar and setting the inversion termination precision;
s4: forward operation is carried out based on the initial model, and a gather is extracted to obtain initial theoretical radar data;
s5: constructing an objective function;
s6: performing Curvelet transformation on the model update quantity delta m to obtain a target function of a Curvelet domain
S7: carrying out inversion according to frequency scale groups from low to high to obtain corresponding model gradient g under each frequencykStep length akAnd a model update quantity Deltax of the Curvelet domaink；
S8: updating model xk+1＝xk+Δxk；
Wherein, Δ xkIs a Curvelet coefficient vector, xkAnd xk+1Coefficients corresponding to the kth iteration and the (k + 1) th iteration are respectively set;
s9: calculating a target function value based on the data extracted by the new model, and judging whether an inversion result meets a termination condition;
s10: if the termination condition is not met, updating the model, and repeating the steps S6 to S9 until the termination condition is met; if the end condition is met, outputting a final inversion result and performing Curvelet inverse transformation on the final inversion result;
s11: updating model m ═ m0+ Δ m, where Δ m is the model update after inverse Curvelet transformation, m0Is the initial model and m is the final inverse model.
2. The LASSO algorithm-based ground penetrating radar imaging method as claimed in claim 1, wherein the forward operation is numerical simulation using a frequency domain finite difference method based on staggered grids, and the boundary uses a perfect matching layer boundary condition.
3. A method as claimed in claim 1, wherein the objective function is:
wherein Δ D ═ Dobs-Dcal，DcalAs theoretical data, DobsIn order to observe the data, it is,
u is the radar wave field, and Δ m is the model update quantity.
4. The method of claim 1, wherein the objective function of the Curvelet domain is as follows:
wherein C is Curvelet operator.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010915542.7A CN112285702A (en) | 2020-09-03 | 2020-09-03 | Ground penetrating radar imaging method based on LASSO algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010915542.7A CN112285702A (en) | 2020-09-03 | 2020-09-03 | Ground penetrating radar imaging method based on LASSO algorithm |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN112285702A true CN112285702A (en) | 2021-01-29 |
Family
ID=74420518
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010915542.7A Withdrawn CN112285702A (en) | 2020-09-03 | 2020-09-03 | Ground penetrating radar imaging method based on LASSO algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112285702A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113376629A (en) * | 2021-05-13 | 2021-09-10 | 电子科技大学 | In-well radar least square inversion method based on non-uniform input parameter grid |
-
2020
- 2020-09-03 CN CN202010915542.7A patent/CN112285702A/en not_active Withdrawn
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113376629A (en) * | 2021-05-13 | 2021-09-10 | 电子科技大学 | In-well radar least square inversion method based on non-uniform input parameter grid |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108710153B (en) | Wave number domain method for magnetic full tensor gradient inversion underground three-dimensional magnetic distribution | |
| Giannakis et al. | A machine learning-based fast-forward solver for ground penetrating radar with application to full-waveform inversion | |
| KR101958674B1 (en) | Actually-measured marine environment data assimilation method based on sequence recursive filtering three-dimensional variation | |
| Giannakis et al. | A machine learning scheme for estimating the diameter of reinforcing bars using ground penetrating radar | |
| CN109683161B (en) | Inverse synthetic aperture radar imaging method based on depth ADMM network | |
| CN109490861B (en) | Blast furnace burden line extraction method | |
| CN111123374A (en) | Ground penetrating radar full-waveform inversion method based on matched filtering | |
| CN110673138B (en) | Ground penetrating radar image processing method based on singular value decomposition and fuzzy C mean value method | |
| KR20080023946A (en) | 3-d gravity inversion method of underground cavities using euler deconvolution and 3-d imaging method using it | |
| CN104766090A (en) | Ground penetrating radar data visualization method based on BEMD and SOFM | |
| CN112285702A (en) | Ground penetrating radar imaging method based on LASSO algorithm | |
| Peng et al. | Rapid surrogate modeling of electromagnetic data in frequency domain using neural operator | |
| Lei et al. | GPR detection localization of underground structures based on deep learning and reverse time migration | |
| CN112084655A (en) | Ground penetrating radar parameter inversion method based on non-monotonic line search | |
| CN116256722B (en) | Method and device for suppressing multiple interference of B-scan image of ground penetrating radar | |
| CN115598714B (en) | Time-space coupling neural network-based ground penetrating radar electromagnetic wave impedance inversion method | |
| CN112085060A (en) | Dual-polarization meteorological radar precipitation particle classification method and device based on SVT-DTSVMs | |
| CN111564188A (en) | Quantitative analysis method for mineral information based on variational self-coding | |
| CN109655910A (en) | The two-parameter full waveform inversion method of Ground Penetrating Radar based on phasing | |
| CN110907912B (en) | Pole characteristic solving method in target narrow-band mode of resonance region | |
| CN110794469B (en) | Gravity inversion method based on minimum geological feature unit constraint | |
| Xu et al. | Coupled-learning GAN for inversion of GPR pipe images | |
| CN114626987B (en) | Electromagnetic backscatter imaging method based on physical depth expansion network | |
| CN116990772B (en) | Ground penetrating radar double-parameter real-time inversion method based on multi-scale convolution network | |
| CN115390031B (en) | High-resolution sea clutter modeling and simulation method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WW01 | Invention patent application withdrawn after publication | ||
| WW01 | Invention patent application withdrawn after publication |
Application publication date: 20210129 |