JP7770280B2 - Signal processing device and signal processing method - Google Patents

Description

This disclosure relates to a signal processing device and a signal processing method.

Compressed sensing is used in various fields of inspection technology, such as magnetic resonance imaging. Imaging techniques using compressed sensing assume that high intensity distributions in the visualization region are sparse, making it possible to reconstruct the entire image of an object using a small number of observations, or to image the object with high resolution (see, for example, Patent Document 1).

Patent No. 6734270

The above-described imaging technique using compressed sensing can be applied, for example, when performing ultrasonic flaw detection on an inspection object. When applying compressed sensing to ultrasonic flaw detection, attempting to image a wide area of the inspection object at once increases the number of pixels and the amount of information to be processed at one time. This may make it impossible to implement due to memory capacity constraints on the processing device. In this case, imaging of a narrow area must be repeated, increasing the inspection workload.

The present disclosure has been made in light of the above, and aims to provide a signal processing device and a signal processing method that can process a reduced amount of information at one time.

The signal processing device according to the present disclosure includes a calculation unit that performs the following operations: a read process that reads a predetermined propagation model that indicates the propagation path of a plane wave emitted from a plurality of wave transmitting and receiving elements toward the interface of an object of inspection, propagates through the interior of the object of inspection, reflects at a focal point, and reaches the wave transmitting and receiving elements; an acquisition process that acquires observation data received by the plurality of wave transmitting and receiving elements when the plurality of wave transmitting and receiving elements emit the plane waves toward the object of inspection; a calculation process that calculates corresponding data corresponding to the imaging range of the object of inspection using grid-free compressed sensing based on the acquired observation data; and an estimation process that estimates the position of the focal point of the object of inspection based on the read propagation model and the calculated corresponding data.

The signal processing method disclosed herein includes a reading step of reading a predetermined propagation model that indicates the propagation path of a plane wave transmitted from a plurality of wave transmitting and receiving elements to an interface of an object to be inspected, the plane wave propagating through the interior of the object to be inspected, reflecting at a focal point, and reaching the wave transmitting and receiving elements; an acquisition step of acquiring observation data received by the plurality of wave transmitting and receiving elements when the plurality of wave transmitting and receiving elements transmit the plane waves to the object to be inspected; a calculation step of calculating corresponding data corresponding to the imaging range of the object to be inspected by grid-free compressed sensing based on the acquired observation data; and an estimation step of estimating the position of the focal point of the object to be inspected based on the read propagation model and the calculated corresponding data.

This disclosure provides a signal processing device and a signal processing method that can reduce the amount of information processed at one time.

FIG. 1 is a schematic diagram showing an example of a measurement system including a signal processing device according to this embodiment. FIG. 2 is a flowchart showing an example of a signal processing method according to this embodiment. FIG. 3 is a diagram schematically illustrating an example of a propagation path (outgoing path) of a transmission wave in a propagation model. FIG. 4 is a diagram schematically illustrating an example of a propagation path (return path) of a transmission wave in a propagation model. FIG. 5 is a flowchart showing an example of an algorithm in the compressed sensing processing step. FIG. 6 is a diagram schematically illustrating an example of an imaging range of the measurement system. FIG. 7 is a diagram schematically illustrating an example of monitoring an acoustic image. FIG. 8 is a diagram schematically illustrating an outline of imaging using a plurality of transmission waves. FIG. 9 is a diagram showing an example of a transmission level for each refraction angle of a shear wave. FIG. 10 is a diagram schematically illustrating an outline of imaging using a plurality of transmission waves. FIG. 11 is a diagram showing an example of a transmission level for each refraction angle of a shear wave.

Embodiments of a signal processing device and a signal processing method according to the present disclosure will be described below with reference to the drawings. Note that the present invention is not limited to these embodiments. Furthermore, the components in the following embodiments include those that are easily replaceable by those skilled in the art, or those that are substantially identical.

Figure 1 is a schematic diagram showing an example of a measurement system SYS including a signal processing device 100 according to this embodiment. As shown in Figure 1, the measurement system SYS includes a sensor 10 and a signal processing device 100.

The sensor 10 has multiple wave transmitting and receiving elements 11 that output transmitted waves for detection and receive reflected waves of the output transmitted waves to detect the inspection target 40. The sensor 10 has multiple wave transmitting and receiving elements 11 arranged in an array. In this embodiment, the transmitted waves are plane waves, such as acoustic signals such as ultrasound. This embodiment will be described using an example of plane wave imaging (PWI) using plane waves. In this embodiment, the sensor 10 is a wedge-type sensor that transmits transmitted waves in an inclined direction relative to the normal direction (y direction in Figures 3 and 4) of the interface 41 of the inspection target 40. Note that while this embodiment uses ultrasound for detection, radio waves or the like may also be used. Furthermore, while the sensor is a wedge-type sensor, other types of sensors may be used as long as they are configured to transmit transmitted waves to the interface 41 of the inspection target 40.

The signal processing device 100 is connected to the sensor 10, for example, via a pulser receiver 50. The signal processing device 100 processes signals received by the wave transmitting and receiving element 11 to detect the surroundings. The signal processing device 100 has a calculation unit 20 and a memory unit 30. The calculation unit 20 is, for example, a CPU (Central Processing Unit). The calculation unit 20 performs various calculations. The memory unit 30 includes, for example, at least one of a main memory unit such as RAM (Random Access Memory) or ROM (Read Only Memory), and an external memory unit such as an HDD (Hard Disk Drive).

The calculation unit 20 performs a read process to read a predetermined propagation model that indicates the propagation path of a plane wave transmitted from the multiple wave transmitting and receiving elements 11 to the interface 41 of the inspection object 40, propagates through the inspection object 40, reflects at a focal point 42, and reaches the wave transmitting and receiving elements 11. The focal point 42 is, for example, a defect such as a scratch contained within the inspection object 40. The calculation unit 20 performs an acquisition process to acquire observation data received by the multiple wave transmitting and receiving elements 11 when the multiple wave transmitting and receiving elements 11 transmit plane waves to the inspection object 40. The calculation unit 20 performs an estimation process to estimate the position of the focal point 42 in the inspection object 40 using grid-free compressive sensing (GFCS) based on the read propagation model and the acquired observation data.

In the estimation process, the calculation unit 20 obtains the coefficients of the dual polynomial by solving a predetermined constrained optimization problem based on the observation data, calculates the value of the dual polynomial based on the obtained coefficients of the dual polynomial and the propagation model, and estimates the position of the focal point 42 based on the calculated value of the dual polynomial. The dual polynomial includes a predetermined regularization parameter. The dual polynomial will be described later.

The calculation unit 20 performs each of the above processes by reading and executing a program (software) from the memory unit 30. The memory unit 30 stores various information such as the calculation contents and programs of the calculation unit 20. The memory unit 30 may also store the processing results detected by the sensor 10, i.e., the results of the exploration.

When multiple dual polynomial values are calculated for one position during the estimation process, the calculation unit 20 determines the maximum value of the multiple dual polynomial values as the value of the dual polynomial at that position.

In the estimation process, the calculation unit 20 can estimate the position where the value of the calculated dual polynomial exceeds a predetermined threshold as the position of the focal point 42. Furthermore, in the estimation process, the calculation unit 20 may estimate the position corresponding to the maximum value of the envelope of the values of the dual polynomial when the value of the calculated dual polynomial is the value on the vertical axis and the position inside the object of inspection is the value on the horizontal axis as the position of the focal point 42.

When using observation data in the estimation process, the calculation unit 20 can multiply it by a coefficient corresponding to the plane wave reflection conditions.

The calculation unit 20 may perform a calibration process prior to the estimation process. The calibration process is a process of adjusting the regularization parameter included in the dual polynomial. In the calibration process, the calculation unit 20 estimates the focus position of the test piece using the same procedure as the estimation process, based on a propagation model and observation data for a test piece in which the positions and number of focus points 42 are preset. The calculation unit 20 then adjusts the regularization parameter so that the number of focus points obtained by this estimation corresponds to the number of focus points that was preset.

The calculation unit 20 performs each of the above processes by reading and executing a program (software) from the memory unit 30. The memory unit 30 stores various information such as the calculation contents and programs of the calculation unit 20. The memory unit 30 may also store the processing results detected by the sensor 10, i.e., the results of the exploration.

The memory unit 30 stores signal processing programs that cause the computer to execute the following operations: a read process that reads a predetermined propagation model that indicates the propagation path of a plane wave when the plane wave transmitted from the multiple wave transmitting and receiving elements 11 to the interface 41 of the test object 40 propagates inside the test object 40, is reflected at the focal point 42, and reaches the wave transmitting and receiving elements 11; an acquisition process that acquires observation data received by the multiple wave transmitting and receiving elements 11 when the multiple wave transmitting and receiving elements 11 transmit plane waves to the test object 40; a calculation process that calculates corresponding data corresponding to the imaging range of the test object 40 using grid-free compressed sensing based on the acquired observation data; and an estimation process that estimates the position of the focal point 42 of the test object 40 based on the read propagation model and the calculated corresponding data.

The measurement process of the measurement system according to this embodiment will now be described. Figure 2 is a flowchart showing an example of a signal processing method according to this embodiment. As shown in Figure 2, the signal processing method according to this embodiment includes a reading step S10, an acquisition step S20, a calculation step S30, and an estimation step S40.

In the reading step S10, the calculation unit 20 reads a predetermined propagation model that indicates the propagation path of plane waves emitted from multiple wave transmitting and receiving elements 11 to the interface 41 of the test object 40, propagating through the test object 40, reflecting at the focal point, and reaching the wave transmitting and receiving elements 11. In this embodiment, a directional beam can be formed by changing the transmission time of the plane wave for each wave transmitting and receiving element 11. Furthermore, in this embodiment, by superimposing the transmission signals of multiple wave transmitting and receiving elements 11, the transmission level can be increased compared to when each wave transmitting and receiving element 11 transmits a plane wave individually.

The measurement process of the measurement system according to this embodiment requires a propagation time τ ilk from the time of transmission until the transmitted wave i reaches pixel l corresponding to an arbitrary focus and the reflected wave from there returns to the kth wave transmitting/receiving element 11 (k-th element). The propagation model A(k) loaded in the propagation model loading step S10 is obtained by calculating and recording the propagation time τ _ilk for each focus position of the ultrasonic wave propagating through the _wedge -shaped sensor 10. The propagation model is created offline in advance.

Figure 3 is a diagram that schematically shows an example of the propagation path (outbound path) of a transmitted wave in a propagation model. Figure 3 shows the path from the transmitter of the sensor 10 to the focal point 42. Figure 4 is a diagram that schematically shows an example of the propagation path (return path) of a transmitted wave in a propagation model. Figure 4 shows the path from the focal point 42 to the receiver of the sensor 10.

The propagation time τ _ilk can be calculated by dividing the outward propagation paths d ⁽¹⁾ and d ⁽²⁾ shown in Fig. 3 and the return propagation paths d ⁽³⁾ and d ⁽⁴⁾ shown in Fig. 4 by the speed of sound. If the speed of sound within the sensor 10 is v _w and the speed of sound within the inspection object 40 is _vs , the propagation time τ _ilk can be calculated as follows:

The outgoing propagation paths d ⁽¹⁾ and d ⁽²⁾ can be expressed as follows using the coordinates [x _VIRT y _VIRT ] ^T on the interface 41 of the propagation path, the coordinates x _b of the intersection of the plane wavefront with the interface 41 at the start of emission, and the angle of incidence θ _W at the interface 41:

The return propagation paths d ⁽³⁾ and d ⁽⁴⁾ are paths by which the reflected wave reaches the position [x _k y _k ] ^T of the kth element in the shortest time, and are found by optimizing the coordinates on the interface 41. That is, the return propagation paths d ⁽³⁾ and d ⁽⁴⁾ can be written as follows using the optimized interface coordinates [x _VIRT y _VIRT ] ^T :

The coordinate _xb on the interface 41 is scanned in the range of 0< _xb ≦ _xw , and optimization is performed by setting the coordinate _{xVIRT,k at} which the difference ΔHk in the height direction between the propagation path shown in Fig. 4 and the target element is minimized. Note that although Figs. 3 and 4 show an example where _xVIRT,k = 0, the above relationship holds for sensor 10 of any shape as long as optimization can be performed using the shortest time path.

In the PWI that transmits a plane wave, the plane wave is formed only within a range of width corresponding to the array aperture length of the sensor 10. Therefore, within the range of interface coordinates shown in FIG.
The plane wave does not reach the focal point that does not pass through the above range, and the above propagation model does not hold. In this embodiment, this condition is used as a constraint for modeling, so an invalid value is input for the propagation time of the focal point that does not pass through the above range.
As a result, in the case of GFCS, plane waves that do not pass through the range of the set interface 41 are invalidated.

In the above optimization algorithm, a scanning grid of _xb is defined. Therefore, while the accuracy of the model improves by making the grid interval smaller, the calculation time increases. In order to ensure accuracy within a realistic calculation time, in this embodiment, the grid interval can be determined using the ΔH _k after optimization as an index of accuracy. Specifically,
where _vw is the speed of sound, T is the time equivalent to the pulse width of the ultrasonic wave, and [Equation 6] corresponds to the distance traveled in the time of one pulse. This makes it possible to appropriately set the scanning range of the interface coordinates, which previously required adjustment by trial and error in the optimization algorithm. Note that this concept is also effective in calculating the propagation model for the outbound path in the transmission mode full matrix capture.

Next, in the observation data acquisition step S20, the calculation unit 20 acquires the observation data received by the multiple wave transmitting and receiving elements 11 when the multiple wave transmitting and receiving elements 11 transmit plane waves to the inspection object 40.

Here, if the transmission beam angle from the wave transmitting and receiving element 11 is θ _i and the number of elements of the wave transmitting and receiving element 11 is M, the complex reception signal vector including the defect echo inside the inspection object 40 is
where K is the number of measurement points.

What can be directly observed by the wave transmitting and receiving element 11 is a real signal, but by subjecting this to processing such as Hilbert transform and down-conversion, a complex signal η ⁱ (k) can be obtained.

Next, in the generation step S30, the calculation unit 20 generates imaging data of the inspection object 40 using the GFCS based on the acquired observation data.

Figure 5 is a schematic diagram showing an example of an imaging range by a measurement system. As shown in Figure 5, at measurement time k, a portion of the object of inspection 40 becomes imaging range 40R. Figure 6 is a diagram showing an example of an imaging range divided by pixels. When imaging range 40R is divided by pixels as shown in Figure 6, the number of pixels is set to L. Furthermore, the number of pixels in the range that can be imaged with instantaneous values at measurement time k is set to L(k).

Here, the observation data obtained by the measurement system according to this embodiment
Consider the problem of estimating the position of a focal point 42 (a reflection source such as a defect) using the above equation. Although Fig. 6 shows an image of a two-dimensional array, similar indexing can be applied to the case of a three-dimensional array.

Figure 7 is a flowchart showing an example of the algorithm used in the generation step S30. As shown in Figure 7, in the generation step S30, the calculation unit 20 acquires observation data (step S301), finds a solution to a semidefinite programming problem based on the acquired observation data (step S302), and calculates corresponding data that corresponds to the imaging range of the inspection object 40 (see Figure 5) (step S303).

In step S302, the calculation unit 20 calculates a constrained optimization problem (SDP)
to find a solution to the semidefinite programming problem.

After finding a solution to the semidefinite programming problem, the calculation unit 20 calculates the observed data at time k as
is used as an input to find η ⁱ (k).

where Toep(u) is a vector
represents an operator that expands into a Toeplitz matrix. Furthermore, trace(D) represents the sum of the diagonal elements of the matrix D.

Note that λ (>0) in Equation 9 is a regularization parameter. The user can set the regularization parameter to any value. Qualitatively, the larger the regularization parameter λ, the sparser the solution obtained. How to adjust the regularization parameter will be described later.

In step S303, the calculation unit 20 uses the solution of the above equation 9 to calculate
Therefore, the coefficients of the dual polynomial
The coefficients of the dual polynomial shown in Equation 13 are corresponding data corresponding to the imaging range of inspection object 40 at measurement time k.

The SPD shown in the above equation (9) is an optimization problem that mimics the Lasso problem that should be solved.
is an approximation of

Here, ||η ⁱ || _A represents the atomic norm for the vector η ⁱ . Since the atomic norm is like the _L1 norm defined by an infinite number of unknowns, this optimization problem cannot be solved directly. Therefore, this optimization problem can be solved by approximating it with the SDP of Equation 9. The SDP of Equation 9 can be solved, for example, by a known solver.

Next, in estimation step S40, the calculation unit 20 estimates the position of the focal point 42 of the object of inspection 40 based on the loaded propagation model and the generated imaging data.

Figure 8 is a flowchart showing an example of the algorithm used in estimation step S40. As shown in Figure 8, in estimation step S40, the calculation unit 20 calculates the value of the dual polynomial based on the propagation model loaded in step S10 and the corresponding data calculated in step S30 (step S401). The calculation unit 20 estimates the position of the focal point 42 of the object of inspection 40 based on the calculated value of the dual polynomial (step S402).

In step S401, the calculation unit 20 calculates the coefficients Q(k) of the dual polynomial shown in Equation 13 and the propagation model corresponding to the imaging range 40R (see FIG. 5) at the measurement time k.
Using and, the value of the dual polynomial
of,
It is calculated as follows.

In Equations 16 and 17
The rows of correspond to pixel indices, i.e., pixel coordinates. In this way, the calculation unit 20 can calculate the value of the dual polynomial for each measurement time k.

The values of the dual polynomial calculated in step S402 are the overlap of the imaging range 40R at each measurement time. Figure 9 is a graph showing an example of the values of the dual polynomial for each pixel in the imaging range 40R. The vertical axis of the graph in Figure 9 represents the magnitude of the value of the dual polynomial, and the horizontal axis represents each pixel in the imaging range 40R.

As shown in Figure 9, multiple values of the dual polynomial are calculated for pixels in the overlapping portion of the imaging range 40R. In actual measurements, a strong plane wave is not necessarily incident on the entire imaging range 40R, so the values will differ from those originally expected.

Therefore, when multiple dual polynomial values are calculated for one pixel (position) during the estimation process, the calculation unit 20 can estimate the coordinates of a pixel where at least one of the dual polynomial values exceeds a predetermined threshold as the coordinates of the focal point 42. In the example shown in Figure 9, a threshold value α is set. Figure 9 also shows an enlarged view of the area where the threshold value α is exceeded. The calculation unit 20 can estimate the coordinates of a pixel where the threshold value α is exceeded as the coordinates of the focal point 42. In this example, usability is high when there are many focal points 42. For example, when there are a large number of expected focal points 42, usability is increased by setting the threshold value α to a low value.

Furthermore, when multiple dual polynomial values are calculated for one pixel (position), the calculation unit 20 can use the maximum value of the multiple dual polynomial values as the value of the dual polynomial at that pixel. In this case, the calculation unit 20 finds a curve QL that connects the coordinates of the maximum values of the dual polynomials for each pixel. The calculation unit 20 can estimate the coordinates corresponding to the peak value (maximum value) of the found curve QL as the position of the focal point 42. This example is highly useful when the number of focal points 42 is small.

When multiple focal points 42 are included, if each focal point 42 has the same reflection conditions, the profile of the dual polynomial values can be evaluated correctly and the above methods can be used appropriately. However, in reality, the reflection conditions at the focal point 42 may differ depending on the attenuation over distance of the transmitted wave from the transmitting/receiving element 11 and the reflected wave at the focal point 42, as well as the state of the focal point 42. Therefore, for the above observation data (actual measured values), the reflection conditions depending on the state of the focal point 42 and the distance attenuation can be determined analytically or experimentally in advance, and by multiplying the coefficients corresponding to these reflection conditions, an algorithm that takes into account the effects of the actual environment can be applied.

The calculation unit 20 may also perform an adjustment process to adjust λ (regularization parameter) in Equation 9. The user can set the regularization parameter to any value. Qualitatively, the larger the regularization parameter λ, the sparser the solution obtained. The calculation unit 20 can perform this adjustment process by using a test piece.

Figure 10 is a diagram showing an example of a test piece 51. As shown in Figure 10, the positions and number of artificial defects 52 are preset for the test piece 51. Test pieces 51 are prepared in advance for each material, such as metal, polymer, fluid, etc. The calculation unit 20 estimates the positions of the artificial defects 52 in the test piece 51 using the same procedures as the calculation process and estimation process described above, based on the propagation model and observation data for the test piece 51. The calculation unit 20 then adjusts the regularization parameters so that the number of artificial defects 52 obtained by this estimation corresponds to the number of artificial defects 52 that was preset.

FIG. 11 is a graph showing an example of the value of the dual polynomial for each regularization parameter. As shown in FIG. 11 , for example, when the regularization parameter is λ ₁ , the number of peaks in the value of the dual polynomial is greater than the number of preset artificial defects 52. In FIG. 11 , peaks other than those corresponding to the preset artificial defects 52 are indicated by arrows. In contrast, when the regularization parameter is λ ₂ , the number of peaks in the value of the dual polynomial is the same as the number of preset artificial defects 52. Therefore, when the inspection object 40 is formed of a material corresponding to the test piece 51 (for example, the same or similar material as the test piece), the position of the focal point 42 can be appropriately estimated by setting the regularization parameter to λ ₂ .

As described above, in the present disclosure, the signal processing device according to the first aspect includes a calculation unit 20 that performs the following operations: a read process that reads a predetermined propagation model that indicates the propagation path of a plane wave transmitted from a plurality of wave transmitting and receiving elements 11 to the interface 41 of the object of inspection 40, propagates through the interior of the object of inspection 40, reflects at the focal point 42, and reaches the wave transmitting and receiving elements 11; an acquisition process that acquires observation data received by the plurality of wave transmitting and receiving elements 11 when the plurality of wave transmitting and receiving elements 11 transmits plane waves to the object of inspection 40; a calculation process that calculates corresponding data corresponding to the imaging range of the object of inspection 40 using grid-free compressed sensing based on the acquired observation data; and an estimation process that estimates the position of the focal point 42 of the object of inspection 40 based on the read propagation model and the calculated corresponding data.

Therefore, the inspection object 40 is probed using plane waves emitted from the wave transmitting/receiving element 11 to the interface 41 of the inspection object 40, and based on the acquired observation data, corresponding data corresponding to the imaging range of the inspection object 40 is calculated using the GFCS. The position of the focal point 42 of the inspection object 40 is estimated based on the calculated corresponding data and the propagation model, making it possible to reduce the amount of information processed at one time.

In the signal processing device of the second aspect, the calculation unit 20 of the signal processing device of the first aspect calculates the coefficients of the dual polynomial as corresponding data by solving a predetermined constrained optimization problem based on the observation data in the calculation process, and in the estimation process, finds the value of the dual polynomial based on the obtained coefficients of the dual polynomial and a propagation model, and estimates the position of the focal point 42 based on the found value of the dual polynomial. Therefore, the position of the focal point 42 can be appropriately estimated using the GFSC.

The signal processing device according to the third aspect is the signal processing device according to the second aspect, in which, when multiple dual polynomial values are calculated for one position during the estimation process, the calculation unit 20 estimates the position where at least one dual polynomial value exceeds a predetermined threshold as the position of the focal point 42. Therefore, the position of the focal point 42 can be appropriately estimated.

The signal processing device according to the fourth aspect is the signal processing device according to the second or third aspect, in which, when multiple dual polynomial values are calculated for one position during the estimation process, the calculation unit 20 sets the maximum value of the multiple dual polynomial values as the value of the dual polynomial at that position. Therefore, it is possible to determine a more effective dual polynomial value.

In the signal processing device according to the fifth aspect, in the signal processing device according to the fourth aspect, the calculation unit 20, in the estimation process, estimates the position corresponding to the maximum value of the curve passing through the coordinates indicating the values of the dual polynomial, where the calculated values of the dual polynomial are the values on the vertical axis and the position inside the inspection object 40 is the value on the horizontal axis, as the position of the focal point 42. Therefore, the position of the focal point 42 can be appropriately estimated.

The signal processing device according to the sixth aspect is a signal processing device according to any one of the second to fifth aspects, in which the calculation unit 20 multiplies the observed data in the estimation process by a coefficient corresponding to the plane wave reflection conditions. This makes it possible to apply an algorithm that takes into account the influence of the actual environment.

A signal processing device according to a seventh aspect is a signal processing device according to any one of the second to sixth aspects, in which the dual polynomial includes a predetermined regularization parameter, and the calculation unit 20 estimates the positions of the artificial defects 52 in the test piece using the same procedures as the calculation process and estimation process based on a propagation model and observation data for the test piece 51, in which the positions and number of artificial defects 52 are preset, and performs an adjustment process to adjust the regularization parameter so that the number of artificial defects 52 obtained by this estimation corresponds to the number of artificial defects 52 set in advance. Therefore, since the regularization parameter can be set appropriately, the position of the focal point 42 can be estimated with high accuracy.

The signal processing method according to the eighth aspect includes a reading step S10 of reading a predetermined propagation model that indicates the propagation path of a plane wave transmitted from a plurality of wave transmitting and receiving elements 11 to an interface 41 of an object to be inspected 40, which propagates through the interior of the object to be inspected 40, is reflected at a focal point 42, and reaches the wave transmitting and receiving elements 11; an acquisition step S20 of acquiring observation data received by the plurality of wave transmitting and receiving elements 11 when the plurality of wave transmitting and receiving elements 11 transmits plane waves to the object to be inspected 40; a calculation step S30 of calculating corresponding data corresponding to the imaging range of the object to be inspected 40 by grid-free compressed sensing based on the acquired observation data; and an estimation step S40 of estimating the position of the focal point 42 of the object to be inspected 40 based on the read propagation model and the calculated corresponding data.

Therefore, the inspection object 40 is probed using plane waves emitted from the wave transmitting/receiving element 11 to the interface 41 of the inspection object 40, and based on the acquired observation data, corresponding data corresponding to the imaging range of the inspection object 40 is calculated using the GFCS. The position of the focal point 42 of the inspection object 40 is estimated based on the calculated corresponding data and the propagation model, making it possible to reduce the amount of information processed at one time.

10 Sensor 11 Wave transmitting and receiving element 20 Calculation unit 30 Memory unit 40 Inspection object 40R Imaging range 41 Interface 42 Focus 50 Pulsar receiver 51 Test piece 52 Artificial defect 100 Signal processing device QL Curve SYS Measurement system 10 Sensor 11 Wave transmitting and receiving element 20 Calculation unit 30 Memory unit 40 Inspection object 41 Interface 50 Pulsar receiver 100 Signal processing device SYS Measurement system

Claims (7)

a reading process of reading a predetermined propagation model that indicates a propagation path of a plane wave transmitted from a plurality of wave transmitting and receiving elements to an interface of an object to be inspected, the plane wave propagating through the object to be inspected, reflected at a focal point, and reaching the wave transmitting and receiving elements;
an acquisition process for acquiring observation data received by the plurality of wave transmitting and receiving elements when the plurality of wave transmitting and receiving elements transmit the plane waves to the test object;
a calculation process of calculating corresponding data corresponding to an imaging range of the inspection object by grid-free compressed sensing based on the acquired observation data;
a calculation unit that performs an estimation process of estimating a position of the focus of the inspection object based on the read propagation model and the calculated correspondence data ,
The calculation unit
In the calculation process, coefficients of a dual polynomial are calculated as the corresponding data by solving a predetermined constrained optimization problem based on the observation data;
In the estimation process, a value of the dual polynomial is calculated based on the acquired coefficients of the dual polynomial and the propagation model, and the position of the focal point is estimated based on the calculated value of the dual polynomial.
Signal processing device. The signal processing device according to claim 1 , wherein, when a plurality of values of the dual polynomial are calculated for one position in the estimation process, the calculation unit estimates a position where at least one value of the dual polynomial exceeds a predetermined threshold as the position of the focus. The signal processing device according to claim 1 , wherein, when a plurality of values of the dual polynomial are calculated for one position in the estimation process, the calculation unit sets a maximum value of the plurality of values of the dual polynomial as the value of the dual polynomial at the one position. 4. The signal processing device according to claim 3, wherein, in the estimation process, the calculation unit estimates, as the position of the focus, a position corresponding to a maximum value of a curve passing through coordinates indicating the values of the dual polynomial , where the calculated values of the dual polynomial are the values on the vertical axis and the positions inside the object are the values on the horizontal axis. The signal processing device according to claim 1 , wherein the calculation unit multiplies the observation data by a coefficient corresponding to a reflection condition of the plane wave when the observation data is used in the estimation process. the dual polynomial includes a predetermined regularization parameter;
The signal processing device according to claim 1, wherein the calculation unit estimates the position of the focus of the test piece in the same procedure as the calculation process and the estimation process based on the propagation model and the observation data for the test piece in which the position and number of the focus are preset, and performs an adjustment process to adjust the regularization parameter so that the number of the focus obtained by the estimation corresponds to the number of the focus that was preset. a reading step of reading a predetermined propagation model that indicates a propagation path of a plane wave transmitted from a plurality of wave transmitting and receiving elements to an interface of an object to be inspected, the plane wave propagating through the object to be inspected, reflected at a focal point, and reaching the wave transmitting and receiving elements;
an acquisition step of acquiring observation data received by the plurality of wave transmitting and receiving elements when the plurality of wave transmitting and receiving elements transmit the plane wave to the test object;
a calculation step of calculating corresponding data corresponding to an imaging range of the inspection object by grid-free compressed sensing based on the acquired observation data;
an estimation step of estimating a position of the focal point of the inspection object based on the read propagation model and the calculated correspondence data ,
In the calculation step, coefficients of a dual polynomial are calculated as the corresponding data by solving a predetermined constrained optimization problem based on the observation data;
In the estimation step, a value of the dual polynomial is calculated based on the acquired coefficients of the dual polynomial and the propagation model, and the position of the focal point is estimated based on the calculated value of the dual polynomial.
Signal processing methods.