CN116184400A - Wave field imaging method and system based on reduced order model method - Google Patents

Abstract

The invention discloses a wave field imaging method and a wave field imaging system based on a reduced order model method. The invention can linearize the nonlinear problem, reduce the artifact in the imaging result and provide high-quality imaging result; the method can be used for realizing rapid and direct imaging without an optimization method; and the imaging can be realized by only single-shot and single-received data for the layering target.

Description

Wave field imaging method and system based on reduced order model method

Technical Field

The invention relates to the technical field of wave field imaging, in particular to a wave field imaging method and system based on a reduced order model method.

Background

The wave field is one of the common tools in the field of detection imaging, and is similar to electromagnetic waves, sound waves and the like which meet wave equations. The backscattering problem is the process of deducing its characteristics from scattered waves of an unknown object. Depending on the particular application, by illuminating an object with electromagnetic or acoustic waves, one can determine its shape and parameters without direct contact. Such problems have attracted attention from a theoretical and practical perspective in a number of different fields including biomedical imaging, remote sensing and seismic imaging.

However, the solution of the backscatter problem has been difficult to solve due to the nonlinearity of wave equation. Since the relationship of the scattered field to the target is nonlinear, it is difficult to find a closed-form solution to the backscatter problem at Gao Weishang. In order to cope with such nonlinearity, various methods have been proposed, which can be largely classified into a linear method and a nonlinear method.

Most linear methods are based on the born approximation or Lei Tuofu approximation, used by assuming weak scattering conditions. Since the scattering process has been linearized, the linear inversion methods of the type shown are generally both fast and stable. These characteristics are critical in the field of ultrasound imaging and the like, as they require real-time imaging output. On the other hand, the linear method ignores the multiple refraction and reflection effects, so that the imaging result has obvious artifacts, the amplitude cannot be completely recovered, and only qualitative reconstruction can be realized.

The nonlinear method can be further classified into a conventional optimization method and a machine learning method. The former typically solves for model parameters by minimizing errors between simulation data and measured data, such as perturbation-born iterative methods, contrast-source methods, gradient-like methods, and the like. Gradient-based methods can be quite effective in handling large amounts of unknowns and enough information, but they tend to fall into local minima during optimization. Conversely, global optimization methods can avoid local minima, but at the cost of generally greater computational effort. Due to the similarity between the inverse problem and the object recognition task, machine learning methods that amplify the highlights in the field of computer vision are also increasingly used to solve the problem of backscatter, such as supervised descent methods, and deep neural networks inspired by physical laws, etc.

Disclosure of Invention

The present invention aims to solve at least one of the technical problems in the related art to some extent.

Therefore, the invention provides a wave field imaging method based on a reduced order model method. The nonlinearity of the backscattering problem can be reduced, and because the Boen data and the substitution parameter are in a linear relation, imaging can be performed by combining any existing linear or nonlinear method, and a high-quality imaging result can be obtained rapidly.

Another object of the present invention is to provide a wave field imaging system based on a reduced order model method.

In order to achieve the above object, in one aspect, the present invention provides a method for imaging a wave field based on a reduced order model method, including:

irradiating the region of interest with waves to obtain data to be measured;

measuring the data to be measured by using a plurality of sensors, exciting the sensors in turn to obtain receiving signals, and measuring the corresponding receiving signals by using all the sensors to obtain time-varying measuring data;

constructing a reduced order model of a new operator obtained after coupling the differential operator and the physical parameters of the target to be imaged according to the measurement data and the wave equation;

based on the relation between the reduced order model and the physical parameters of the target to be imaged, calculating the Boen data of which the measured data and the physical parameters of the target to be imaged form a linear relation according to a chain rule.

In addition, the wave field imaging method based on the reduced order model method according to the above embodiment of the present invention may further have the following additional technical features:

further, in an embodiment of the present invention, the wave includes one of a water wave, an acoustic wave, a seismic wave, and an electromagnetic wave.

Further, in one embodiment of the present invention, after calculating the born data, the method further comprises:

and imaging according to the Boen data and a preset imaging method.

Further, in one embodiment of the present invention, when the region of interest is a layered structure, data measurement is performed using self-received data of a single sensor.

Further, in an embodiment of the present invention, before the measuring the data to be measured with the plurality of sensors, the method further includes:

virtual sensor distribution is carried out around the real single sensor, and a sensor distribution result is obtained;

estimating the multi-transmission and multi-reception data of the virtual sensor based on a time domain green function according to the information of the medium in a layered structure and the sensor distribution result to obtain a data estimation result;

the autonomous self-receiving data of the single sensor is enhanced to multiple-input multiple-output data of the plurality of sensors based on the data estimation results.

In order to achieve the above object, another aspect of the present invention provides a wave field imaging system based on a reduced order model method, including:

the data acquisition module to be measured is used for irradiating the region of interest by utilizing waves to obtain data to be measured;

the measurement data determining module is used for measuring the data to be measured by utilizing a plurality of sensors, exciting the sensors in turn to obtain receiving signals, and measuring the corresponding receiving signals by utilizing all the sensors to obtain measurement data changing along with time;

the reduced order model construction module is used for constructing a reduced order model of a new operator obtained after the differential operator is coupled with the physical parameters of the target to be imaged according to the measurement data and the wave equation;

and the Boen data calculation module is used for calculating the Boen data of which the measured data and the physical parameters of the target to be imaged form a linear relation according to a chain rule based on the relation between the reduced order model and the physical parameters of the target to be imaged.

According to the wave field imaging method and system based on the reduced order model method, the nonlinear problem is linearized, artifacts in an imaging result are reduced, and a high-quality imaging result is provided; the method can be used for realizing rapid and direct imaging without an optimization method; only single-shot and single-received data is needed for imaging the layered object.

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.

Drawings

The foregoing and/or additional aspects and advantages of the invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a flow chart of a method of wave field imaging based on a reduced order model method in accordance with an embodiment of the present invention;

FIG. 2 is a schematic diagram of a two-dimensional hierarchical model to be probed in accordance with an embodiment of the invention;

FIG. 3 is a schematic diagram for calculating wave propagation paths between different sensors according to an embodiment of the present invention;

FIG. 4 is a diagram of a comparison of estimated MIMO data with actual MIMO data according to an embodiment of the present invention;

FIG. 5 is a schematic diagram of a comparison of the calculated Boen data using different raw data in accordance with an embodiment of the present invention;

FIG. 6 is a graph of results of imaging using different Boen data versus real results according to an embodiment of the present invention;

fig. 7 is a block diagram of a wave field imaging system based on a reduced order model method in accordance with an embodiment of the present invention.

Detailed Description

It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The invention will be described in detail below with reference to the drawings in connection with embodiments.

In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.

The following describes a wave field imaging method and system based on a reduced order model method according to an embodiment of the present invention with reference to the accompanying drawings.

FIG. 1 is a flow chart of a method of wave field imaging based on a reduced order model method in accordance with an embodiment of the present invention.

As shown in fig. 1, the method includes, but is not limited to, the steps of:

s1, irradiating a region of interest with waves to obtain data to be measured;

s2, measuring data to be measured by using a plurality of sensors, exciting the sensors in turn to obtain received signals, and measuring the corresponding received signals by using all the sensors to obtain time-varying measured data;

s3, constructing a reduced order model of a new operator obtained after coupling the differential operator and the physical parameters of the target to be imaged according to the measurement data and the wave equation;

s4, based on the relation between the reduced order model and the physical parameters of the target to be imaged, calculating the Boen data of which the measured data and the physical parameters of the target to be imaged form a linear relation according to a chain rule.

It will be appreciated that the present invention converts the nonlinear backscatter problem, which refers to the problem of detecting a region of interest from received data by illuminating the region of interest with a wave, into a linear problem. Waves include any physical field satisfying wave equation, including mechanical waves (water waves, acoustic waves, seismic waves) and electromagnetic waves. The steps of the invention can be as follows:

arranging a plurality of sensors around a region of interest, exciting one of the sensors in turn in a measurement process, and measuring corresponding received signals by using all the sensors so as to obtain a series of measurement data changing with time;

step two, using measurement data, constructing a reduced order model of a new operator obtained after coupling a differential operator and the physical parameter according to symmetry of the wave equation;

and thirdly, using the reduced order model, and calculating a primary term part of the Taylor series expanded by the measurement data about the physical parameter, namely, the Boen data in a linear relation with the physical parameter based on the relation between the reduced order model and the physical parameter by using a chain rule.

Further, there may be a fourth step of imaging the obtained born data in combination with various existing imaging methods.

Further, when the region of interest is a layered structure, it is possible to work with spontaneous self-received data of only a single sensor. The method further comprises the step of estimating the multi-transmission and multi-reception data of the virtual sensor by combining a time domain green function according to the information of the medium in a layered structure and the position distribution condition of the virtual sensor around the real single sensor and assuming a plurality of virtual sensors, and enhancing the self-transmission and self-reception data of the single sensor into the multi-transmission and multi-reception data of the multi-sensor.

The wave field imaging method based on the reduced order model method according to the embodiment of the invention is described in detail below with reference to the accompanying drawings. This embodiment employs imaging of a two-dimensional layered structure region using self-received data from a single sensor.

The layered region, shown in fig. 2, has a size of 384m x 384m, and is divided into 128 grids in each direction. A sensor is arranged above the region, transmits Gaussian ultrasonic signals with the highest frequency of about 20Hz, and receives reflected signals D _SIsO . The sound velocity v of the region is 900m/s, and the parameter to be solved by the invention is the wave impedance eta distribution condition of the region.

As one example, it is first necessary to enhance the spontaneous self-received data of a single sensor to the multiple-received data of multiple sensors. The invention assumes 15 virtual sensors on the left and right sides of the real sensor, as shown by the open circles. To from D _SISO Estimating the received data of these virtual sensors requires that the invention knows the received data of the virtual sensors compared to D _SISO The approximate time delay and amplitude decay conditions that exist. Time delay the present invention can be estimated from the paths of signals from different sensors. Fig. 3 shows the path relationship of signal propagation between different sensors. Wherein the invention can be according to D _SISO The time of the first wave crest in the data is used for estimating the Depth of the first layer of layering, and the distance x of different paths can be calculated by combining the horizontal position distribution relation among the sensors. Based on the path x and the propagation velocity v of the wave in the medium, the invention can calculate the time delay of signal propagation between different sensors,

wherein x is ₀ For D _SISO Is a propagation path distance of the optical fiber. The present invention then entails estimating the amplitude decay of the data received by the various sensors. The invention herein employs a method of estimation by tracking the peak of the time domain green function over time. The time domain green function for the two-dimensional case is:

where H () is a step function. Here, since the present invention uses a sufficiently narrow gaussian pulse to approximate the pulse, its response can be seen as the green function itself. For a peak offset to t ₀ The peak versus time relationship of the gaussian pulse of (c) is as follows,

x＝vt-vt ₀ ＝vt-h#(3)

substituting (3) into (2) to obtain signals received by different sensors and D _SISO The relationship between the two components is that,

according to (1) and (4), the invention can automatically receive data from a single sensorD _SISO Multiple-input multiple-output data D enhanced as multiple sensors _MIMO . Estimated D _MIMO The comparison with the correct data is shown in fig. 4, where the solid line is the estimated data and the dotted line is the true data.

When the data D of multiple sensors, multiple transmissions and multiple receptions can be directly obtained _MIMO When this is the case, the above steps can be omitted.

In the following the invention will be D _MIMO Abbreviated as D. After the data D is obtained, the invention calculates a reduced order model of the new operator obtained after the differential operator is coupled to the desired physical parameter. For this purpose, the invention needs to calculate matrices M and S, wherein the elements in the matrices are:

wherein D is _i Representing the received data of data D at instant i. The invention then performs a kowski decomposition on matrix M,

R＝chol(M)#(7)

projecting the matrix S with R:

K＝R ^-T SR ^-1 #(8)

and then calculating to obtain a reduced order model of the new operator obtained after the differential operator is coupled with the physical parameter:

L＝chol(LL ^T )#(10)

where τ is the time interval of data acquisition.

The present invention then uses a reduced order model L which, based on its relationship to the wave impedance eta,

using the chain law, the first order component of the taylor series, in which the measured data D is spread with respect to the wave impedance η, that is, the born data in a linear relationship with the wave impedance η, is calculated:

wherein eta ₀ Is the wave impedance of a uniform background. The calculation result is shown in FIG. 5, in which the solid line is D _SISO Data, dotted line is using D _SISO The data calculated from the data are the Boen data, the dash-dot line is the estimated D _MIMO The calculated born data and the dotted line is the calculated born data using the real multiple-input multiple-output data.

Further, the present invention can be imaged in conjunction with various existing imaging methods after the born data is obtained. The invention selects the most commonly used linear back projection method to directly image, the obtained result is shown in figure 6, wherein the gray solid line is a real model, and the black solid line is D _SISO As a result of data imaging, the dashed line is using D _SISO The dotted line is the result of re-imaging the data calculated from the data using the estimated D _MIMO And (3) the calculated Boen data re-imaging result, wherein the dash-dot line is the calculated Boen data re-imaging result by using the real multiple-shot data. It can be seen that the results of imaging using the born data are far more coincident with the real model than the results of direct imaging using the initial data.

According to the wave field imaging method based on the reduced order model method, the nonlinear problem is linearized, artifacts in an imaging result are reduced, and a high-quality imaging result is provided; the method can be used for realizing rapid and direct imaging without an optimization method; only single-shot and single-received data is needed for imaging the layered object.

In order to implement the above-described embodiment, as shown in fig. 7, a wave field imaging system 10 based on a reduced order model method is also provided in this embodiment, and the system 10 includes a data acquisition module to be measured 100, a measurement data determination module 200, a reduced order model construction module 300, and a born data calculation module 400.

The data to be measured acquisition module 100 is used for irradiating the region of interest by utilizing waves to obtain data to be measured;

the measurement data determining module 200 is configured to measure data to be measured by using a plurality of sensors, excite the sensors in turn to obtain received signals, and measure corresponding received signals by using all the sensors to obtain measurement data that varies with time;

the reduced order model construction module 300 is used for constructing a reduced order model of a new operator obtained after coupling the differential operator and the physical parameters of the target to be imaged according to the measurement data and the wave equation;

the born data calculation module 400 is configured to calculate, based on the relation between the reduced order model and the physical parameter of the object to be imaged, born data of the measured data in a linear relation with the physical parameter of the object to be imaged according to the chain rule.

Further, the wave includes one of a water wave, an acoustic wave, a seismic wave, and an electromagnetic wave.

Further, after the above-mentioned born data calculation module 400, an imaging module is further included for: imaging is carried out according to the Boen data and a preset imaging method.

Further, when the region of interest is a layered structure, data measurements are made using self-received data from a single sensor.

Further, before the measurement data determining module 200, a data enhancing module is further included for:

virtual sensor distribution is carried out around a real single sensor, so that a sensor distribution result is obtained;

according to the information of the medium in a layered structure and the sensor distribution result, estimating the multi-transmission and multi-reception data of the virtual sensor based on the time domain green function to obtain a data estimation result;

the autonomous self-receiving data of a single sensor is enhanced to the multiple-receiving data of multiple sensors based on the data estimation results.

According to the wave field imaging system based on the reduced order model method, the nonlinear problem is linearized, artifacts in an imaging result are reduced, and a high-quality imaging result is provided; the method can be used for realizing rapid and direct imaging without an optimization method; only single-shot and single-received data is needed for imaging the layered object.

In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means 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 present invention. In this specification, schematic representations of the above terms are not necessarily directed 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. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.

Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise.

Claims (10)

1. The wave field imaging method based on the reduced order model method is characterized by comprising the following steps of:

irradiating the region of interest with waves to obtain data to be measured;

measuring the data to be measured by using a plurality of sensors, exciting the sensors in turn to obtain receiving signals, and measuring the corresponding receiving signals by using all the sensors to obtain time-varying measuring data;

constructing a reduced order model of a new operator obtained after coupling the differential operator and the physical parameters of the target to be imaged according to the measurement data and the wave equation;

based on the relation between the reduced order model and the physical parameters of the target to be imaged, calculating the Boen data of which the measured data and the physical parameters of the target to be imaged form a linear relation according to a chain rule.

2. The method of claim 1, wherein the wave comprises one of a water wave, an acoustic wave, a seismic wave, and an electromagnetic wave.

3. The method of claim 1, wherein after computing the born data, the method further comprises:

and imaging according to the Boen data and a preset imaging method.

4. The method of claim 1, wherein when the region of interest is a layered structure, data measurements are made using self-received data from a single sensor.

5. The method of claim 4, wherein prior to said measuring said data to be measured with a plurality of sensors, the method further comprises:

virtual sensor distribution is carried out around the real single sensor, and a sensor distribution result is obtained;

estimating the multi-transmission and multi-reception data of the virtual sensor based on a time domain green function according to the information of the medium in a layered structure and the sensor distribution result to obtain a data estimation result;

the autonomous self-receiving data of the single sensor is enhanced to multiple-input multiple-output data of the plurality of sensors based on the data estimation results.

6. A reduced order model based wave field imaging system, comprising:

the data acquisition module to be measured is used for irradiating the region of interest by utilizing waves to obtain data to be measured;

the measurement data determining module is used for measuring the data to be measured by utilizing a plurality of sensors, exciting the sensors in turn to obtain receiving signals, and measuring the corresponding receiving signals by utilizing all the sensors to obtain measurement data changing along with time;

the reduced order model construction module is used for constructing a reduced order model of a new operator obtained after the differential operator is coupled with the physical parameters of the target to be imaged according to the measurement data and the wave equation;

and the Boen data calculation module is used for calculating the Boen data of which the measured data and the physical parameters of the target to be imaged form a linear relation according to a chain rule based on the relation between the reduced order model and the physical parameters of the target to be imaged.

7. The system of claim 6, wherein the wave comprises one of a water wave, an acoustic wave, a seismic wave, and an electromagnetic wave.

8. The system of claim 6, further comprising, after the born data calculation module, an imaging module to:

and imaging according to the Boen data and a preset imaging method.

9. The system of claim 6, wherein when the region of interest is a layered structure, data measurements are made using self-received data from a single sensor.

10. The system of claim 9, further comprising, prior to the measurement data determination module, a data enhancement module for:

virtual sensor distribution is carried out around the real single sensor, and a sensor distribution result is obtained;

estimating the multi-transmission and multi-reception data of the virtual sensor based on a time domain green function according to the information of the medium in a layered structure and the sensor distribution result to obtain a data estimation result;

the autonomous self-receiving data of the single sensor is enhanced to multiple-input multiple-output data of the plurality of sensors based on the data estimation results.

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