A wave field imaging method and system based on a reduced order model method

Abstract

The application discloses a wave field imaging method and system based on a reduced order model method, which comprises the following steps: calculating linear Born data corresponding to physical parameters of a target to be imaged by using a reduced order model of a wave field (including mechanical waves and electromagnetic waves); and imaging by using a linear relationship between the Born data and the target to be imaged, so that an image without obvious artifacts is obtained. The application can linearize a nonlinear problem, reduce artifacts in imaging results, and provide high-quality imaging results. The application can realize fast and direct imaging without using an optimization method. Moreover, the application can image a layered target by using only single-transmitting and single-receiving data.

Description

Technical Field

[0001] This invention relates to the field of wave field imaging technology, and in particular to a wave field imaging method and system based on a reduced-order model method. Background Technology

[0002] Wave fields are a commonly used tool in the field of detection imaging. Fields that satisfy the wave equation, such as electromagnetic waves and sound waves, are all wave fields. The inverse scattering problem is the process of inferring the characteristics of an unknown target based on the scattered waves. Depending on the specific application, by illuminating an object with electromagnetic or sound waves, its shape and parameters can be determined without direct contact. From both theoretical and applied perspectives, this type of problem has attracted attention in various fields, including biomedical imaging, remote sensing, and seismic imaging.

[0003] However, due to the nonlinearity of the wave equation, solving the inverse scattering problem has always been difficult. Because the relationship between the scattered field and the target is nonlinear, it is difficult to find closed-form solutions to the inverse scattering problem in high dimensions. To address this nonlinearity, various methods have been proposed, mainly categorized into linear and nonlinear methods.

[0004] Most linear methods are based on the Born or Retoff approximation, using the assumption of weak scattering conditions. Since the scattering process has been linearized, these linear inversion methods are generally fast and stable. These properties are crucial in fields such as ultrasound imaging, where real-time imaging output is required. On the other hand, because linear methods neglect multiple reflections, the imaging results contain significant artifacts, and the amplitude cannot be fully recovered, achieving only qualitative reconstruction.

[0005] Nonlinear methods can be further divided into traditional optimization methods and machine learning methods. The former typically solves for model parameters by minimizing the error between simulated and measured data, such as the perturbation Born iteration method, the contrast source method, and gradient-based methods. Gradient-based methods can be quite effective when dealing with a large number of unknowns and sufficient information, but they often get trapped in local minima during optimization. Conversely, global optimization methods can avoid local minima, but at the cost of usually requiring greater computational resources. Due to the similarity between inverse problems and object recognition tasks, machine learning methods, which have shone brightly in computer vision, are increasingly being used to solve inverse scattering problems, such as supervised descent and deep neural networks inspired by physical laws. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the technical problems in the related art.

[0007] To address this, this invention proposes a wave field imaging method based on a reduced-order model. This method can reduce the nonlinearity of the inverse scattering problem, and because the Born data and the substitution parameters are linearly related, it can be combined with any existing linear or nonlinear method for imaging, quickly obtaining high-quality imaging results.

[0008] Another objective of this invention is to propose a wave field imaging system based on a reduced-order model method.

[0009] To achieve the above objectives, this invention proposes a wave field imaging method based on a reduced-order model, comprising:

[0010] The region of interest is illuminated with a wave to obtain the data to be measured.

[0011] The data to be measured is measured using multiple sensors, the sensors are excited in turn to obtain received signals, and the corresponding received signals are measured using all sensors to obtain measurement data that changes over time.

[0012] Based on the measurement data and the wave equation, a reduced-order model of the new operator obtained by coupling the difference operator with the physical parameters of the target to be imaged is constructed.

[0013] Based on the relationship between the reduced-order model and the physical parameters of the target to be imaged, Born data that are linearly related to the measurement data and the physical parameters of the target to be imaged are calculated according to the chain rule.

[0014] In addition, the wave field imaging method based on the reduced-order model method according to the above embodiments of the present invention may also have the following additional technical features:

[0015] Furthermore, in one embodiment of the present invention, the wave includes one of water waves, sound waves, seismic waves, and electromagnetic waves.

[0016] Furthermore, in one embodiment of the present invention, after calculating the Born data, the method further includes:

[0017] Imaging is performed based on the Born data and a preset imaging method.

[0018] Furthermore, in one embodiment of the present invention, when the region of interest has a hierarchical structure, data measurement is performed using the spontaneously transmitted and received data from a single sensor.

[0019] Furthermore, in one embodiment of the present invention, before measuring the data to be measured using multiple sensors, the method further includes:

[0020] A virtual sensor distribution is performed around the actual single sensor to obtain the sensor distribution result;

[0021] Based on the information of the layered structure of the medium and the distribution results of the sensors, and based on the time-domain Green's function, the data estimation results are obtained by estimating the multiple transmission and reception data of the virtual sensor.

[0022] Based on the data estimation results, the spontaneously transmitted and received data from the single sensor is enhanced into multi-transmitted and multi-received data from multiple sensors.

[0023] To achieve the above objectives, another aspect of the present invention proposes a wave field imaging system based on a reduced-order model method, comprising:

[0024] The measurement data acquisition module is used to obtain the measurement data by illuminating the region of interest with a wave.

[0025] The measurement data determination module is used to measure the data to be measured using multiple sensors, to excite the sensors in turn to obtain received signals, and to obtain measurement data that changes over time by measuring the corresponding received signals using all sensors.

[0026] The order reduction model construction module is used to construct an order reduction model of a new operator obtained by coupling the difference operator with the physical parameters of the target to be imaged, based on the measurement data and the wave equation.

[0027] The Born data calculation module is used to calculate Born data that is linearly related to the measured data and the physical parameters of the target to be imaged, based on the relationship between the reduced-order model and the physical parameters of the target to be imaged, according to the chain rule.

[0028] The wave field imaging method and system based on the reduced-order model method of this invention linearizes the nonlinear problem, reduces artifacts in the imaging results, and provides high-quality imaging results; it can achieve fast and direct imaging without optimization methods; and for layered targets, only single-transmission and single-reception data are needed for imaging.

[0029] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0030] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0031] Figure 1 This is a flowchart of a wave field imaging method based on a reduced-order model method according to an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of the two-dimensional layered structure model to be detected according to an embodiment of the present invention;

[0033] Figure 3This is a schematic diagram for calculating wave propagation paths between different sensors according to an embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram showing the comparison results between the estimated multiple transmission and reception data and the actual multiple transmission and reception data according to an embodiment of the present invention;

[0035] Figure 5 This is a schematic diagram illustrating the comparison results of Born data calculated using different raw data according to an embodiment of the present invention;

[0036] Figure 6 This is a comparison diagram of the imaging results using different Born data according to an embodiment of the present invention with the actual results;

[0037] Figure 7 This is a structural diagram of a wave field imaging system based on a reduced-order model method according to an embodiment of the present invention. Detailed Implementation

[0038] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0039] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0040] The wave field imaging method and system based on the reduced-order model method proposed according to embodiments of the present invention are described below with reference to the accompanying drawings.

[0041] Figure 1 This is a flowchart of a wave field imaging method based on a reduced-order model method according to an embodiment of the present invention.

[0042] like Figure 1 As shown, the method includes, but is not limited to, the following steps:

[0043] S1, use a wave to illuminate the region of interest to obtain the data to be measured;

[0044] S2, using multiple sensors to measure the data to be measured, taking turns to excite the sensors to obtain the received signals, and using all the sensors to measure the corresponding received signals to obtain the measurement data that changes over time;

[0045] S3. Based on the measurement data and the wave equation, construct a reduced-order model of the new operator obtained by coupling the difference operator with the physical parameters of the target to be imaged;

[0046] S4, based on the relationship between the reduced-order model and the physical parameters of the target to be imaged, calculates the Born data, which is linearly related to the measurement data and the physical parameters of the target to be imaged, according to the chain rule.

[0047] It is understood that this invention transforms the nonlinear inverse scattering problem into a linear problem. The inverse scattering problem refers to the problem of probing a region of interest by illuminating it with a wave and then analyzing the received data. The wave includes any physical field that satisfies the wave equation, including mechanical waves (water waves, sound waves, seismic waves) and electromagnetic waves. The steps of this invention can be as follows:

[0048] Step 1: Deploy multiple sensors around the region of interest, and during the measurement process, excite one of the sensors in turn, and use all the sensors to measure the corresponding received signals, thereby obtaining a series of measurement data that change over time;

[0049] Step 2: Using measurement data, and based on the symmetry of the wave equation, construct a reduced-order model of the new operator obtained by coupling the difference operator with the physical parameters to be determined.

[0050] Step 3: Using the reduced-order model, and based on the relationship between the reduced-order model and the physical parameters to be determined, the chain rule is used to calculate the first-order term of the Taylor series expansion of the measurement data with respect to the physical parameters, which is the Born data that is linearly related to the physical parameters.

[0051] Furthermore, there can be a fourth step, which combines the obtained Born data with various existing imaging methods for imaging.

[0052] Furthermore, when the region of interest has a hierarchical structure, it is possible to work using only the spontaneously transmitted and received data from a single sensor. Prior to step one, this involves assuming many virtual sensors around the real single sensor, and estimating the multi-transmit and multi-received data from the virtual sensors based on the hierarchical structure of the medium and the location distribution of the virtual sensors, using a time-domain Green's function. This enhances the spontaneously transmitted and received data from the single sensor into multi-transmit and multi-received data from multiple sensors.

[0053] The wave field imaging method based on the reduced-order model method of this invention is described in detail below with reference to the accompanying drawings. This embodiment uses self-transmitted and self-received data from a single sensor to image a two-dimensional layered structural region.

[0054] like Figure 2The layered region shown measures 384m x 384m and is divided into 128 grids in each direction. A sensor is placed above the region, emitting a Gaussian ultrasonic signal with a maximum frequency of approximately 20Hz and receiving the reflected signal D. SIsO The sound velocity v in the region is 900 m / s. The parameter that this invention seeks to solve for is the distribution of wave impedance η in this region.

[0055] As an example, the first step is to enhance the self-transmitted and self-received data from a single sensor into multi-sensor multi-transmitted and multi-received data. This invention assumes 15 virtual sensors on each side of the real sensor, as shown in the hollow circles. To obtain data from D... SISO To estimate the received data from these virtual sensors, this invention needs to know the received data of the virtual sensors compared to D. SISO The approximate time delay and amplitude attenuation are described. The time delay can be estimated based on the path of signals emitted by different sensors. Figure 3 The path relationships of signal propagation between different sensors are given. This invention can be based on D... SISO The time of the first wave peak in the data is used to estimate the depth (Depth) of the first layer. Combined with the horizontal positional distribution of the sensors, the distance x along different paths can be calculated. Based on path x and the wave propagation speed (v) in the medium, this invention can calculate the time delay of signal propagation between different sensors.

[0056]

[0057] Where x0 is D SISO The propagation path distance. Next, this invention needs to estimate the amplitude attenuation of data received by different sensors. Here, this invention uses a method of estimating this by tracking the peak of the time-domain Green's function over time. The time-domain Green's function in the two-dimensional case is:

[0058]

[0059] Where H() is the step function. Since this invention uses a sufficiently narrow Gaussian pulse to approximate the pulse, its response can be considered as the Green's function itself. For a Gaussian pulse with its peak shifted to t0, the relationship between its peak and time is as follows:

[0060] x=vt-vt0=vt-h#(3)

[0061] Substituting (3) into (2) yields the signals received by different sensors and D. SISO The relationship between them

[0062]

[0063] According to (1) and (4), the present invention can transmit and receive data D from a single sensor. SISO Enhanced to multi-sensor multi-transmit and multi-receive data D MIMO The estimated D MIMO Comparison with correct data Figure 4 As shown, the solid line represents the estimated data, and the dashed line represents the actual data.

[0064] When it is possible to directly obtain data from multiple sensors transmitting and receiving multiple data points (D) MIMO In this case, the above steps can be ignored.

[0065] In the following content, the present invention will D MIMO Abbreviated as D. After obtaining the data D, this invention needs to calculate the reduced-order model of the new operator obtained by coupling the difference operator with the desired physical parameters. For this purpose, this invention needs to calculate matrices M and S, whose elements are:

[0066]

[0067]

[0068] Where D i This represents the received data D at time i. Then, the present invention performs Koleski decomposition on matrix M.

[0069] R = chole(M)#(7)

[0070] Projecting matrix S onto R:

[0071] K = R -T SR -1 #(8)

[0072] Then, the reduced-order model of the new operator obtained by coupling the difference operator with the desired physical parameters is calculated:

[0073]

[0074] L = chol(LL) T )#(10)

[0075] Where τ is the time interval for data acquisition.

[0076] Then, this invention uses a reduced-order model L, based on its relationship with the wave impedance η.

[0077]

[0078] Using the chain rule, calculate the first-order term of the Taylor series expansion of the measured data D with respect to the wave impedance η, which is the Born data that is linearly related to the wave impedance η:

[0079]

[0080] Where η0 is the wave impedance of a uniform background. The calculation results are as follows: Figure 5 As shown, the solid line represents D. SISO Data, dashed lines indicate the use of D SISO The Born data obtained from data calculations, with the dotted line indicating the use of the estimated D. MIMO The calculated Bonn data is shown, while the dotted lines are calculated using real multi-transmission and multi-reception data.

[0081] Furthermore, after obtaining the Born data, this invention can combine various existing imaging methods for imaging. Here, this invention selects the most commonly used linear back projection method for direct imaging, and the results are as follows: Figure 6 As shown, the gray solid line represents the real model, and the black solid line represents the model using 3D modeling. SISO The results of data imaging, the dashed line represents the data obtained using D... SISO The result of re-imaging the Born data obtained from data calculation, with the dotted lines representing the estimated D... MIMO The calculated re-imaging results of the Born data are shown, with the dashed line representing the re-imaging results calculated using real multi-transmission and multi-reception data. It can be seen that the results of imaging using Born data have a much higher degree of overlap with the real model than the results of imaging directly using the initial data.

[0082] The wave field imaging method based on the reduced-order model method according to embodiments of the present invention linearizes the nonlinear problem, reduces artifacts in the imaging results, and provides high-quality imaging results; it can achieve fast and direct imaging without optimization methods; and for layered targets, only single-transmission and single-reception data are needed for imaging.

[0083] To achieve the above embodiments, such as Figure 7 As shown, this embodiment also provides a wave field imaging system 10 based on the reduced-order model method. The system 10 includes a measurement data acquisition module 100, a measurement data determination module 200, a reduced-order model construction module 300, and a Born data calculation module 400.

[0084] The measurement data acquisition module 100 is used to obtain the measurement data by illuminating the region of interest with a wave.

[0085] The measurement data determination module 200 is used to measure the data to be measured using multiple sensors, to excite the sensors in turn to obtain the received signals, and to obtain the measurement data that changes over time by measuring the corresponding received signals using all the sensors.

[0086] The order reduction model construction module 300 is used to construct a new operator's order reduction model based on measurement data and wave equations, after coupling the difference operator with the physical parameters of the target to be imaged.

[0087] The Born data calculation module 400 is used to calculate Born data that is linearly related to the measurement data and the physical parameters of the target to be imaged, based on the relationship between the reduced-order model and the physical parameters of the target to be imaged, according to the chain rule.

[0088] Furthermore, the aforementioned waves include one of the following: water waves, sound waves, seismic waves, and electromagnetic waves.

[0089] Furthermore, following the aforementioned Born data calculation module 400, an imaging module is also included, used for: performing imaging based on the Born data and a preset imaging method.

[0090] Furthermore, when the region of interest has a hierarchical structure, data measurement is performed using the spontaneously transmitted and received data from a single sensor.

[0091] Furthermore, prior to the aforementioned measurement data determination module 200, a data augmentation module is also included, for:

[0092] A virtual sensor distribution is performed around a real single sensor to obtain the sensor distribution results;

[0093] Based on the information of the layered structure of the medium and the distribution results of the sensors, and based on the Green's function in the time domain, the data estimation results are obtained by estimating the multiple transmission and reception data of the virtual sensor.

[0094] Based on the data estimation results, the spontaneously transmitted and received data from a single sensor is enhanced into multi-transmitted and multi-received data from multiple sensors.

[0095] The wave field imaging system based on the reduced-order model method according to embodiments of the present invention linearizes nonlinear problems, reduces artifacts in imaging results, and provides high-quality imaging results; it can achieve fast and direct imaging without optimization methods; and for layered targets, only single-transmission and single-reception data are needed for imaging.

[0096] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0097] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A wave field imaging method based on a reduced-order model, characterized in that, Includes the following steps: The region of interest is illuminated with a wave to obtain the data to be measured. The data to be measured is measured using multiple sensors, the sensors are excited in turn to obtain received signals, and the corresponding received signals are measured using all sensors to obtain measurement data that changes over time. The M-matrix and S-matrix are constructed based on the measurement data that change over time; The lower triangular matrix is ​​obtained by performing Koleski decomposition on the M matrix; The projection matrix is ​​obtained by left-multiplying matrix S by the transpose of the inverse of the lower triangular matrix and then right-multiplying it by the inverse of the lower triangular matrix. The reduced-order model matrix is ​​obtained by taking the inverse cosine of the projection matrix, dividing it by the data acquisition time interval, squaring it, and then performing Koleski decomposition. Based on the relationship between the reduced-order model matrix and the physical parameters of the target to be imaged, the first-order term of the Taylor series expansion of the measurement data with respect to the physical parameters of the target to be imaged is calculated according to the chain rule, and the Born data that is linearly related to the physical parameters of the target to be imaged is obtained. The elements in the matrix are: in Representative data exist Receive data at each moment; then process the matrix. Perform Kolesky decomposition. use For matrix Project: Then, the reduced-order model of the new operator obtained by coupling the difference operator with the desired physical parameters is calculated: in This is the time interval for data collection.

2. The method according to claim 1, characterized in that, The wave includes one of the following: water wave, sound wave, seismic wave, and electromagnetic wave.

3. The method according to claim 1, characterized in that, After calculating the Born data, the method further includes: Imaging is performed based on the Born data and a preset imaging method.

4. The method according to claim 1, characterized in that, When the region of interest has a hierarchical structure, data measurement is performed using the spontaneously transmitted and received data from a single sensor.

5. The method according to claim 4, characterized in that, Before measuring the data to be measured using multiple sensors, the method further includes: A virtual sensor distribution is performed around the actual single sensor to obtain the sensor distribution result; Based on the information of the layered structure of the medium and the distribution results of the sensors, and based on the time-domain Green's function, the data estimation results are obtained by estimating the multiple transmission and reception data of the virtual sensor. Based on the data estimation results, the spontaneously transmitted and received data from the single sensor is enhanced into multi-transmitted and multi-received data from multiple sensors.

6. A wave field imaging system based on a reduced-order model method using the method described in claim 1, characterized in that, include: The measurement data acquisition module is used to obtain the measurement data by illuminating the region of interest with a wave. The measurement data determination module is used to measure the data to be measured using multiple sensors, to excite the sensors in turn to obtain received signals, and to obtain measurement data that changes over time by measuring the corresponding received signals using all sensors. The order reduction model construction module is used to construct an order reduction model of a new operator obtained by coupling the difference operator with the physical parameters of the target to be imaged, based on the measurement data and the wave equation. The Born data calculation module is used to calculate Born data that is linearly related to the measured data and the physical parameters of the target to be imaged, based on the relationship between the reduced-order model and the physical parameters of the target to be imaged, according to the chain rule.

7. The system according to claim 6, characterized in that, The wave includes one of the following: water wave, sound wave, seismic wave, and electromagnetic wave.

8. The system according to claim 6, characterized in that, Following the Born data calculation module, an imaging module is also included, for: Imaging is performed based on the Born data and a preset imaging method.

9. The system according to claim 6, characterized in that, When the region of interest has a hierarchical structure, data measurement is performed using the spontaneously transmitted and received data from a single sensor.

10. The system according to claim 9, characterized in that, Prior to the measurement data determination module, a data augmentation module is also included, for: A virtual sensor distribution is performed around the actual single sensor to obtain the sensor distribution result; Based on the information of the layered structure of the medium and the distribution results of the sensors, and based on the time-domain Green's function, the data estimation results are obtained by estimating the multiple transmission and reception data of the virtual sensor. Based on the data estimation results, the spontaneously transmitted and received data from the single sensor is enhanced into multi-transmitted and multi-received data from multiple sensors.

Images