CN106841402A - A kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm - Google Patents
A kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm Download PDFInfo
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Abstract
The invention discloses a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm, the signal reconstruction optimization method is comprised the following steps：Ultrasonic phase array defect detecting system is built, the ultrasonic echo reflected via the defective locations of test specimen is obtained, and is extracted A and sweep signal；Signal is swept to A using orthogonal basis carries out sparse transformation, and optimal sparse base is chosen by calculating degree of rarefication；According to optimal sparse base, using match tracing, orthogonal matching pursuit, the orthogonal matching pursuit of regularization, progressively orthogonal matching pursuit, compression sampling match tracing are reconstructed respectively to ultrasonic phase array signal；The ultrasonic phase array signal reconstruction errors that above-mentioned five kinds greedy restructing algorithms are used under different compression ratios are calculated, and optimal algorithm is selected according to result.The present invention is also contrasted come the quality reconstruction and applicability of verification algorithm by with what Traditional Wavelet compressed.
Description
Technical field
Field, more particularly to a kind of phased array based on greedy algorithm are perceived the present invention relates to ultrasonic phase array Signal Compression
Ultrasonic signal reconstruction and optimization method.
Background technology
Ultrasonic phase array is a technology of field of ultrasonic nondestructive detection newly-developed, in recent years with its detection speed it is fast,
Imaging precision is high, adapt to complex topography component the advantages of detection and get growing concern for.The technology is by controlling each hair
Penetrate the actuation duration of array element to change the phase that sound wave reaches target area, so as to be deflected and focused beam.Use ultrasound
Phased-array technique can obtain the defect distribution situation in whole detected region and can be real-time in the case of not mobile probe
Display testing result, for industrial nondestructive testing provides convenience.
With continuing to develop for the technology, it is a burst of that phased array probe has developed into Two-Dimensional Moment by traditional one-dimensional linear array
Row, annular array, fan-shaped array, flexible array etc. greatly improve detection suitable for the array format of more high detection demand
Efficiency and imaging precision.But, the increase of matrix number and improving for shape also bring a very big problem simultaneously ---
The surge of data volume, increased the difficulty of data transmission and processing and the pressure of front-end collection sensor.
The content of the invention
The invention provides a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm, the present invention uses pressure
Contracting perception algorithm is compressed to signal and reconstructs and determine optimal greedy algorithm by experimental result, the present invention also by with tradition
The contrast of wavelet compression carrys out the quality reconstruction and applicability of verification algorithm, described below：
A kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm, the signal reconstruction optimization method includes
Following steps：
Ultrasonic phase array defect detecting system is built, the ultrasonic echo reflected via the defective locations of test specimen is obtained,
And extract A and sweep signal；
Signal is swept to A using orthogonal basis carries out sparse transformation, and optimal sparse base is chosen by calculating degree of rarefication；
According to optimal sparse base, using match tracing, orthogonal matching pursuit, the orthogonal matching pursuit of regularization, progressively just
Match tracing, compression sampling match tracing is handed over to be reconstructed ultrasonic phase array signal respectively；
Calculate and the above-mentioned five kinds ultrasonic phase array signal reconstruction errors of greedy restructing algorithm and root are used under different compression ratios
Optimal algorithm is selected according to result；
The result of optimal algorithm is compared with traditional wavelet compression result, the applicability of verification algorithm.
The ultrasonic phase array defect detecting system includes：The host computer that is sequentially connected electrically, ultrasonic phase array detector, with
And ultrasonic phase array probe.
The use orthogonal basis sweeps signal to A and carries out sparse transformation, and optimal sparse base is chosen by calculating degree of rarefication
The step of be specially：
Using the degree of rarefication of each sparse transformation of formula quantitative description between L1 norms and L2 norms；
Signal is swept to A carry out discrete Fourier transform and obtain X (k), carry out discrete cosine transform and obtain D (k), and calculate phase
The degree of rarefication answered；Wavelet transform is carried out to x (n) using the sym4 wavelet basis of four layers of decomposition and obtains WTf(m, n), and calculate
Its degree of rarefication；
Choose common db, totally 54 kinds of wavelet basis are swept signal and decomposed to A for sym, bior, rbio and coif family, point
The solution number of plies is set as 2 to 6 layers, and optimal sparse base is chosen according to degree of rarefication result of calculation.
It is described to be specially according to optimal sparse base, the step of be reconstructed to ultrasonic phase array signal using match tracing：
Obtain the coefficient n of corresponding column vector in matrix Ak, column vector a is chosen from matrix An, make it that there is highest with residual error
Correlation；
Update and rebuild echo signal；Residual error is updated, is iteratively repeated, update residual values；Return to reconstruction signal s1。
It is described according to optimal sparse base, it is specific the step of be reconstructed to ultrasonic phase array signal using orthogonal matching pursuit
For：
Column vector a is chosen from matrix An, make it that there is highest correlation, record coefficient correlation n with residual errork；Calculate and work as
Optimal approximation coefficient under preceding column vector；
It is iteratively repeated：Residual values are updated, reconstruction signal s is returned2。
It is described according to optimal sparse base, ultrasonic phase array signal is reconstructed using the orthogonal matching pursuit of regularization
Step is specially：
Coefficient correlation u is calculated, the index position corresponding to K maximum is found from u, be deposited into indexed set J；K
It is sparse angle value；
Postsearch screening, the maximum corresponding atom index value of one group of coefficient correlation of selection energy are carried out using regularization method
It is stored in J0In, J0It is first element of set J；
Make Ω=Ω ∪ J0, update supported collection AΩ；Signal approximation is carried out using least square method and residual error updates；Ω is rope
Draw collection；
| Ω | >=2K is steps be repeated alternatively until, reconstruction signal s is returned3。
It is described according to optimal sparse base, the step of being reconstructed to ultrasonic phase array signal using progressively orthogonal matching pursuit
Specially：
Set up soft-threshold and calculate the atom set J under the threshold valuek={ j:|Ck(j) | ＞ tkσk, wherein2≤t of threshold parameterk≤3；CkJ () represents interim index set CkIn j-th element；rk-1It is residual error
Value；M is the line number of calculation matrix Φ；
Coefficients of Approximation vector is calculated, residual values are updated, reconstruction signal s is returned4。
It is described according to optimal sparse base, the step of being reconstructed to ultrasonic phase array signal using compression sampling match tracing
Specially：
α K column vectors are chosen from matrix A, makes it that there is highest correlation, recording indexes Ω with residual error；α is tuning
Parameter, K is sparse angle value；
Supported collection merges；Calculate the optimal approximation coefficient under current column vector；Preserve maximum preceding K coefficient, iteration weight
It is multiple, residual values are updated, return to reconstruction signal s5。
Described calculating use the above-mentioned five kinds ultrasonic phase array signal reconstruction errors of greedy restructing algorithm under different compression ratios
And be specially according to the step of result selection optimal algorithm：
It the ratio between is the signal length compressed with original signal strength to define compression ratio, chooses percentage mean square error and quantifies
Evaluate the precision of restructing algorithm；Part primary signal is removed by random, it is 20%~80% to set compression ratio scope, every
5% 1 grade, calculate the A under different compression ratios and sweep signal reconstruction error and optimal algorithm is selected according to result.
The result by optimal algorithm compares with traditional wavelet compression result, the step of the applicability of verification algorithm
Specially：
By the compression ratio for setting different threshold values to adjust wavelet compression, all defect signal is entered using wavelet compression
Row is decomposed and reconstituted, and the result of compressed sensing algorithm and wavelet compression, the usability of verification algorithm are compared under identical compression ratio.
The beneficial effect of technical scheme that the present invention is provided is：
1st, the compressed sensing algorithm that the present invention will be invented in recent years is applied to ultrasonic phase array Signal Compression field, achieves
Good effect；
2nd, the present invention is reconstructed using five kinds of greedy algorithms to ultrasonic phase array flaw echo, is compared in different compressions
Reconstruction accuracy under rate, have selected the optimal restructing algorithm (OMP) of suitable such signal；
3rd, the present invention is tested using multigroup flaw indication, and by the compression effectiveness of new algorithm and classical wavelet compression
Contrasted.Result shows, when compression ratio reaches 70%, the average percent reconstructed error of compressed sensing algorithm is only
3.0054%, the reconstruction accuracy with wavelet compression is suitable, fully meets industrial detection demand.
Brief description of the drawings
Fig. 1 is a kind of flow chart of the phased array supersonic signal reconstruction optimization method based on greedy algorithm；
Fig. 2 is the structural representation of ultrasonic phase array defect detecting system；
Fig. 3 is the schematic diagram that defect sets and numbers；
Fig. 4 (a) is the schematic diagram that No. 8 defect A sweep signal；
Fig. 4 (b) is No. 8 schematic diagrames of defect discrete Fourier transform result；
Fig. 4 (c) is No. 8 schematic diagrames of defect discrete cosine transform result；
Fig. 4 (d) is No. 8 schematic diagrames of defect wavelet transform result；
Fig. 5 is the reconstructed error result figure that different restructing algorithms are used under different compression ratios；
Fig. 6 for when compression ratio is 70% all defect use the reconstructed error comparison diagram of OMP algorithms and wavelet compression respectively.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, further is made to embodiment of the present invention below
Ground is described in detail.
In recent years, a kind of emerging compressed sensing algorithm receives many such as signal transacting, computer science, applied mathematics
The concern of area research person.In classical signal process field, in order to avoid distorted signals, sample frequency necessarily be greater than signal highest
More than the twice of frequency, and compressed sensing can keep the prototype structure of signal and by most by non-self-adapting linear projection
Optimization method accurate reconstruction signal, such that it is able to break through the limitation of aromatic sampling thheorem.In terms of ultrasonic phase array data compression,
What researcher before used is all the conventional methods such as wavelet compression, huffman coding compression, although these methods can also be obtained
Good compression effectiveness and reconstruction accuracy, but aromatic sampling thheorem is still followed, sampled signal is not reduced fundamentally.This hair
It is bright that compressed sensing algorithm is innovatively applied to ultrasonic phase array Signal Compression field, probe into its effect and feasibility.
The core theory of compressed sensing includes three aspects, is respectively the reconstruct of sparse signal representation, encoding measurement and algorithm.
Focal point is placed on algorithm reconstruct aspect by the embodiment of the present invention.The reconstruct of signal is vital one during compressed sensing
Step, and quality reconstruction and reconstruction accuracy are to weigh the most important index of compressed sensing application effect.Signal reconstruction is typically to solve for
One optimization problem of minimum L0 norms, but the presenter Donoho of compressed sensing etc. points out that the problem is NP-hard problems
And cannot solve.In consideration of it, researcher proposes a series of alternate algorithms, mainly include minimal L1 norm method, greedy algorithm, most
The small full calculus of variations, iteration method etc..
In restructing algorithm mentioned above, greedy algorithm because fast operation, computation complexity is low, reconstruction accuracy is high and
It is widely adopted.Therefore, the embodiment of the present invention have selected a series of greedy algorithms and ultrasonic phase array signal be reconstructed, including
Matching pursuit algorithm (MP), orthogonal matching pursuit algorithm (OMP), the orthogonal matching pursuit algorithm (ROMP) of regularization, progressively just
Matching pursuit algorithm (StOMP) and compression sampling matching pursuit algorithm (CoSaMP) are handed over, by comparing under different compression ratios
Reconstruct mean square error to select optimal algorithm, there is provided a kind of ultrasonic phase array signal reconstruction optimization side based on greedy algorithm
Method.Finally, the embodiment of the present invention is also contrasted come the quality reconstruction and applicability of verification algorithm by with what Traditional Wavelet compressed.
Embodiment 1
A kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm, referring to Fig. 1, signal reconstruction optimization bag
Include following steps：
101：Ultrasonic phase array defect detecting system is built, the ultrasound reflected via the defective locations of test specimen is obtained and is returned
Ripple, and extract A and sweep signal；
102：Signal is swept to A using orthogonal basis carries out sparse transformation, and optimal sparse base is chosen by calculating degree of rarefication；
103：According to optimal sparse base, using match tracing, orthogonal matching pursuit, the orthogonal matching pursuit of regularization, by
Step orthogonal matching pursuit, compression sampling match tracing are reconstructed to ultrasonic phase array signal；
Wherein, the embodiment of the present invention is not limited to the consequence for reconstruction of above-mentioned five kinds of algorithms.
104：The ultrasonic phase array signal reconstruction errors that above-mentioned five kinds greedy restructing algorithms are used under different compression ratios are calculated,
And optimal algorithm is selected according to result；
105：The result of optimal algorithm is compared with traditional wavelet compression result, the applicability of verification algorithm.
Referring to Fig. 2, the ultrasonic phase array defect detecting system includes：Host computer 1, the ultrasonic phase array inspection being sequentially connected electrically
Survey instrument 2 and ultrasonic phase array probe 3.
Wherein, the use orthogonal basis in step 102 sweeps signal to A and carries out sparse transformation, and is selected by calculating degree of rarefication
The step of taking optimal sparse base is specially：
Using the degree of rarefication of each sparse transformation of formula quantitative description between L1 norms and L2 norms；
Signal is swept to A carry out discrete Fourier transform and obtain X (k), carry out discrete cosine transform and obtain D (k), and calculate phase
The degree of rarefication answered；Wavelet transform is carried out to x (n) using the sym4 wavelet basis of four layers of decomposition and obtains WTf(m, n), and calculate
Its degree of rarefication；
Choose common db, totally 54 kinds of wavelet basis are swept signal and decomposed to A for sym, bior, rbio and coif family, point
The solution number of plies is set as 2 to 6 layers, and optimal sparse base is chosen according to degree of rarefication result of calculation.
Wherein, in step 103 according to optimal sparse base, ultrasonic phase array signal is reconstructed using match tracing
Step is specially：
Obtain the coefficient n of corresponding column vector in matrix Ak, column vector a is chosen from matrix An, make it that there is highest with residual error
Correlation；
Update and rebuild echo signal；Residual error is updated, is iteratively repeated, update residual values；Return to reconstruction signal s1。
Wherein, in step 103 according to optimal sparse base, weight is carried out to ultrasonic phase array signal using orthogonal matching pursuit
The step of structure, is specially：
Column vector a is chosen from matrix An, make it that there is highest correlation, record coefficient correlation n with residual errork；Calculate and work as
Optimal approximation coefficient under preceding column vector；
It is iteratively repeated：Residual values are updated, reconstruction signal s is returned2。
Wherein, in step 103 according to optimal sparse base, the orthogonal matching pursuit using regularization is believed ultrasonic phase array
The step of number being reconstructed is specially：
Coefficient correlation u is calculated, the index position corresponding to K maximum is found from u, be deposited into indexed set J；K
It is sparse angle value；
Postsearch screening, the maximum corresponding atom index value of one group of coefficient correlation of selection energy are carried out using regularization method
It is stored in J0In, J0It is first element of set J；
Make Ω=Ω ∪ J0, update supported collection AΩ；Signal approximation is carried out using least square method and residual error updates；Ω is rope
Draw collection；
| Ω | >=2K is steps be repeated alternatively until, reconstruction signal s is returned3。
Wherein, in step 103 according to optimal sparse base, ultrasonic phase array signal is entered using progressively orthogonal matching pursuit
The step of line reconstruction, is specially：
Set up soft-threshold and calculate the atom set J under the threshold valuek={ j:|Ck(j) | ＞ tkσk, wherein
2≤t of threshold parameterk≤3；CkJ () represents interim index set CkIn j-th element；rk-1It is residual values；M is calculation matrix
The line number of Φ；
Coefficients of Approximation vector is calculated, residual values are updated, reconstruction signal s is returned4。
Wherein, in step 103 according to optimal sparse base, ultrasonic phase array signal is entered using compression sampling match tracing
The step of line reconstruction, is specially：,
α K column vectors are chosen from matrix A, makes it that there is highest correlation, recording indexes Ω with residual error；α is tuning
Parameter, K is sparse angle value；
Supported collection merges；Calculate the optimal approximation coefficient under current column vector；Preserve maximum preceding K coefficient, iteration weight
It is multiple, residual values are updated, return to reconstruction signal s5。
Wherein, the above-mentioned five kinds ultrasonic phase arrays of greedy restructing algorithm are used under the different compression ratios of calculating in step 104
Signal reconstruction error is simultaneously specially according to the step of result selection optimal algorithm：
It the ratio between is the signal length compressed with original signal strength to define compression ratio, chooses percentage mean square error and quantifies
Evaluate the precision of restructing algorithm；Part primary signal is removed by random, it is 20%~80% to set compression ratio scope, every
5% 1 grade, calculate the A under different compression ratios and sweep signal reconstruction error and optimal algorithm is selected according to result.
Wherein, the result by optimal algorithm in step 105 compares with traditional wavelet compression result, verification algorithm
The step of applicability, is specially：
By the compression ratio for setting different threshold values to adjust wavelet compression, all defect signal is entered using wavelet compression
Row is decomposed and reconstituted, and the result of compressed sensing algorithm and wavelet compression, the usability of verification algorithm are compared under identical compression ratio.
In sum, the invention provides a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm, this
Invention is compressed to signal using compressed sensing algorithm and reconstructs and determine optimal greedy algorithm by experimental result, and the present invention is also
Contrasted come the quality reconstruction and applicability of verification algorithm by with what Traditional Wavelet compressed.
Embodiment 2
The scheme in embodiment 1 is described in detail with reference to specific computing formula, example, it is as detailed below to retouch
State：
201：Ultrasonic phase array defect detecting system is built, the ultrasound reflected via the defective locations of test specimen 4 is obtained
Echo, and extract A and sweep signal；
The detailed operation of the step is：
1) ultrasonic phase array defect detecting system is built, the system includes：It is host computer 1, ultrasonic phase array detector 2, super
Sound phased array probe 3 and test specimen 4, detecting system are as shown in Fig. 2 defect sets and numbering is as shown in Figure 3.
2) first in the surface smear couplant of test specimen 4, all defect detection is finished, and extracts the A of each defective locations
Sweeping signal carries out data processing.
In order to improve detection coverage rate, the embodiment of the present invention carries out defects detection, sample frequency using sector scan mode
It is 100MHz.Test specimen 4 can be containing 9 aluminum test blocks of the different-diameter different depth flat-bottom hole of artificial.
The embodiment of the present invention is with 2,36 degree of resin glass of ultrasonic phase array detector of the MULTI2000 models of M2M companies
Illustrated as a example by the ultrasonic phase array probe 3 of glass voussoir.When implementing, the embodiment of the present invention is to ultrasonic phase array detector
2nd, the model of ultrasonic phase array probe 3 is not limited, as long as the device of above-mentioned functions can be completed.
202：Signal is swept to A using orthogonal basis carries out sparse transformation, and optimal sparse base is chosen by calculating degree of rarefication；
To be that signal will have openness for important priori conditions in compression sensing algorithm, therefore this step takes common
Orthogonal basis sweeps signal to A and carries out sparse transformation, and optimal sparse base is chosen by calculating degree of rarefication, the detailed operation of the step
For：
1) the degree of rarefication computational methods of definition signal, embodiment of the present invention selection one kind is between L1 norms and L2 norms
Formula carry out the degree of rarefication of each sparse transformation of quantitative description：
In the embodiment of the present invention, N represents the length of signal, θiIt is each coefficient after conversion.
2) signal x (n) is swept to selected A carry out discrete Fourier transform and obtain X (k), and calculate its degree of rarefication.
WN=e-j2π/N
3) discrete cosine transform is carried out to x (n) and obtains D (k), and calculate its degree of rarefication.
4) wavelet transform is carried out to x (n) using the sym4 wavelet basis of four layers of decomposition and obtains WTf(m, n), and calculate it
Degree of rarefication.
Wherein, wavelet transform can be obtained by the scale parameter a and translation parameters b in discretization continuous wavelet.
Takem,n∈Z,a0≠ 1, a0、b0It is initial coefficients, typically takes a0>1、b0>0；M, n are respectively scale factor
And shift factor；Z is set of integers.
By wavelet basis functionObtain It is mother
Small echo.
Corresponding discrete wavelet transformer is changed to：
Wherein, ψ * (a0 -mt-nb0) it is the wavelet function generated by morther wavelet；* it is conjugate of symbol.
5) result of wavelet transformation is different and different with wavelet basis and Decomposition order, chooses common db, sym,
Totally 54 kinds of wavelet basis are swept signal and are decomposed to A in 2) for bior, rbio and coif family, and Decomposition order is set as 2 to 6 layers, root
Optimal sparse base is chosen according to degree of rarefication result of calculation.
203：Ultrasonic phase array signal is reconstructed using match tracing, reconstruction signal is designated as s1；
The embodiment of the present invention is calculation matrix using gaussian random matrix in subsequent reconstructIn selection
State analysis and show that optimal sparse base is designated asUltrasonic phase array signal is designated as x, and its nonlinear measurement value is y=Ax, its
Middle A=Φ Ψ.Ultrasonic phase array signal is reconstructed first by match tracing (MP) algorithm, reconstruction signal is designated as s1；
The detailed operation of the step is：
1) initialize：Make s1=0, residual values r0=y, approximation x0=0, iteration count k=1.
2) the coefficient n of corresponding column vector in A is obtainedk.Column vector a is chosen from matrix An, make it that there is highest with residual error
Correlation：
Wherein,<>It is inner product operation symbol；rk-1It is current residue.
3) update and rebuild echo signal：
Wherein, xkIt is current approximation value；xk-1It is previous step approximation；For the column vector that previous step is selected.
4) residual error is updated：
5) k=k+1, repeat the above steps 2)~4), until meeting end condition.
6) s is made1=xk, s1Reconstruction signal obtained by as.
204：Ultrasonic phase array signal is reconstructed using orthogonal matching pursuit (OMP) algorithm, reconstruction signal is designated as s2；
The detailed operation of the step is：
1) initialize：Make indexed setResidual values r0=y, iteration count k=1；It is empty set.
2) search identification：Column vector a is chosen from matrix An, make it that there is highest correlation with residual error, record is related
Coefficient nk：
Ωk=Ωk-1∪{nk}
Wherein,<rk-1,an>It is current residue rk-1With column vector anInner product；Ωk-1It is indexed set before；ΩkFor new
Indexed set.
3) parameter Estimation：Calculate the optimal approximation coefficient x under current column vectork：
Wherein,For the column vector that previous step is selected.
4) it is iteratively repeated：Update residual values：
K=k+1, repeat the above steps 2)~4), until meeting end condition.
5) reconstruction signal s is returned2=xk, s2Reconstruction signal obtained by as.
205：Ultrasonic phase array signal is reconstructed using orthogonal matching pursuit (ROMP) algorithm of regularization, reconstruct letter
Number it is designated as s3；
The detailed operation of the step is：
1) initialize：Residual error r0=y, indexes value setIndex value set Represent empty set.Estimate letter
Number degree of rarefication is K=68, iteration count k=1.
2) coefficient correlation u is calculated：U={ un|un=|<rk-1,an>|, n=1,2 ..., N }, wherein rk-1It is current residue；
anThe column vector of representing matrix A；unIt is the element in u；<>It is inner product operation symbol.
3) index position corresponding to K maximum is found from u, is deposited into J.
4) carry out postsearch screening using regularization method, the coefficient correlation of the corresponding atom of index value in J is divided into it is some,
So that | u (i) |≤2 | u (j) |, i, j ∈ J, then select the corresponding atom index value of one group of coefficient correlation of energy maximum to be stored in
J0In, J0It is first element of set J.
5) Ω=Ω ∪ J are made0。
6) carry out Signal approximation using least square method and residual error updates：
xk=arg minx||y-AΩx||2
rk=y-AΩxk
Wherein, AΩFor the column vector that previous step is selected；xkIt is current approximation value.
7) k=k+1, repeat the above steps 2)~6), until | Ω | >=2K.
8) s is made3=xk, s3Reconstruction signal obtained by as.
206：Ultrasonic phase array signal is reconstructed using progressively orthogonal matching pursuit (StOMP) algorithm, reconstruction signal
It is designated as s4；
The detailed operation of the step is：
1) initialize：Residual error r0=y, indexes value setIndex value set Represent empty set.Estimate letter
Number degree of rarefication is K=68, iteration count k=1.
2) C is calculatedk=<A,rk-1>, wherein CkIt is interim indexed set, rk-1It is current residue；<>It is inner product operation symbol.
3) soft-threshold h=t is set upkσk, calculate the atom set J under the threshold valuek={ j:|Ck(j) | ＞ tkσk, wherein2≤t of threshold parameterk≤3；CkJ () represents set CkIn j-th element；rk-1It is current residue；M is
The line number of calculation matrix Φ.
4) Ω=Ω ∪ J are made0, calculate Coefficients of Approximation xk：
xk=(AΩ TAΩ)-1AΩ Ty
Wherein AΩIt is the column vector selected；AΩ TRepresent AΩTransposition.
5) updating residual values is：rk=y-Axk。
6) k=k+1, repeat the above steps 2)~5), until meeting end condition.
7) s is made4=xk, s4Reconstruction signal obtained by as.
207：Ultrasonic phase array signal is reconstructed using compression sampling match tracing (CoSaMP) algorithm, reconstruction signal
It is designated as s5；
The detailed operation of the step is：
1) initialize：Make residual values r0=y, indexed setApproximation x0=0, estimate that signal degree of rarefication is K=68,
Iteration count k=1, tuning parameter is α.
2) search identification：α K column vectors a is chosen from matrix An, make it that there is highest correlation with residual error, record
Index Ω：
Ω∈arg min|P|≤αK∑n∈P|<rk-1,an>|
Wherein, P is indexed set；rk-1It is current residue；<>It is inner product operation symbol.
3) supported collection merges：P=supp (xk-1)∪Ω；Supp is supported collection symbol, xk-1Represent previous step approximation collection
Close.
4) parameter Estimation：Calculate the optimal approximation coefficient under current column vector：
uk=arg minu||rk-1-APu||2
Wherein, APFor the column vector that previous step determines.
5) screening retains：Preserve maximum preceding K coefficient, xk=[u]K。
6) it is iteratively repeated：Update residual values, rk=y-Axk
7) k=k+1, repeat the above steps 2)~6), until meeting end condition.
8) s is made5=xk, s5Reconstruction signal obtained by as.
208：Calculate the ultrasonic phase array signal reconstruction errors that above-mentioned five kinds greedy restructing algorithms are used under different compression ratios
And optimal algorithm is selected according to result；
The detailed operation of the step is：
1) it the ratio between is the signal length compressed with original signal strength to define compression ratio (CR)：
Wherein, M is the length of measured value.
2) embodiment of the present invention chooses the precision of percentage mean square error (PRD) quantitative assessment restructing algorithm：
It follows that PRD values are smaller, represent that reconstruction accuracy is higher.
3) part primary signal is removed by random, it is 20%~80% to set compression ratio scope, every 5% 1 grade.Make
The A under different compression ratios is calculated with foregoing five kinds of greedy algorithms sweep signal reconstruction error.
4) according to result, selection optimal algorithm is considered.
209：All defect signal is compressed using traditional wavelet algorithm and calculates reconstruction accuracy, by optimal algorithm
The result of reconstruct compared with wavelet compression result, the applicability of verification algorithm.
The detailed operation of the step is：
1) compression ratio is adjusted in wavelet compression by setting different threshold values, soft-threshold mode is used in the present invention.
2) all defect signal is carried out using wavelet compression it is decomposed and reconstituted,
3) result of compressed sensing algorithm and wavelet compression is compared under identical compression ratio.
In sum, the invention provides a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm, this
Invention is compressed to signal using compressed sensing algorithm and reconstructs and determine optimal greedy algorithm by experimental result, and the present invention is also
Contrasted come the quality reconstruction and applicability of verification algorithm by with what Traditional Wavelet compressed.
Embodiment 3
Feasibility checking is carried out to the scheme in embodiment 1 and 2 with reference to specific test data, it is as detailed below to retouch
State：
Device parameters used in the present embodiment are：Centre frequency is popped one's head in for the 64 array element ultrasonic phase arrays of 5MHz, battle array
First centre-to-centre spacing is 0.6mm, and material for test to be measured is aluminium, and AD sample frequencys are 100MHz.Host computer CPU is AMD Athlon X4
Four cores, 4GB internal memories, operating system is the 64bit of Windows 7.
1) subsequent analysis are carried out as a example by No. 8 flat-bottom holes of selection first, a diameter of 5mm of the flat-bottom hole, depth is 2mm.Defect
Echo A is swept shown in signal such as Fig. 4 (a), signal length N=1024.
2) discrete Fourier transform, discrete cosine transform and wavelet transform are carried out respectively to above-mentioned signal, change is got in return
The result for arriving is respectively as shown in Fig. 4 (b), (c), (d).The degree of rarefication calculated using formula described in step 202 is respectively
0.8140th, 0.7559 and 0.8438.By comparing, it is evident that the degree of rarefication of wavelet transformation is higher.
3) carry out Its Sparse Decomposition using other wavelet basis described in step 202 and calculate degree of rarefication, the result for obtaining shows 4
The bior3.1 small echos that layer is decomposed have best degree of rarefication, are 0.8973.
4) to other 8 flat-bottom hole flaw indications also using it is above-mentioned 2)~3) step be analyzed, wherein 5 at 4 layers
There is best degree of rarefication under bior3.1 wavelet decompositions, 3 degree of rarefications under the decomposition are also highly desirable in addition.For unified point
Analysis, selects 4 layers of bior3.1 small echos of decomposition as the sparse base of whole ultrasonic phase array signals in embodiments of the present invention.
5) using step 203 to five kinds of restructing algorithms described in step 207 to signal described in 1) under all compression ratios
It is reconstructed, obtains result as shown in Figure 5.Special instruction, due to the randomness of Gauss measurement matrix, each run knot
Fruit has small difference, and the data point in Fig. 5 is 100 average values of computing.
6) by Fig. 5 it will be evident that OMP algorithms all show very low reconstructed error in each compression ratio level, say
Understand superiority of the algorithm in the perception of ultrasonic phase array Signal Compression.Particularly when compression ratio reaches 70%, reconstruct is missed
Difference is only 3.0901%.
7) using OMP algorithms and wavelet compression all defect signal is carried out respectively it is decomposed and reconstituted, from greedy algorithm
4 layers of bior3.1 small echos of identical are used as wavelet basis.When compression ratio is 70%, OMP algorithms and the weight of wavelet compression algorithm are used
Application condition result is as shown in Figure 6.
8) contrast understands that the reconstruction accuracy that OMP algorithms reach can compare favourably with classical wavelet compression, further demonstrates
Applicability of the algorithm in ultrasonic phase array Signal Compression.It is noted that the compressed sensing algorithm based on OMP can be by
Sampling and compression are carried out simultaneously, and wavelet compression still follows traditional mode.
The foregoing is only preferable preferable example of the invention, be not intended to limit the invention, it is all it is of the invention spirit and
Within principle, any modification, equivalent substitution and improvements made etc. should be included within the scope of the present invention.
To the model of each device in addition to specified otherwise is done, the model of other devices is not limited the embodiment of the present invention,
As long as the device of above-mentioned functions can be completed.
It will be appreciated by those skilled in the art that accompanying drawing is a schematic diagram for preferred embodiment, the embodiments of the present invention
Sequence number is for illustration only, and the quality of embodiment is not represented.
The foregoing is only presently preferred embodiments of the present invention, be not intended to limit the invention, it is all it is of the invention spirit and
Within principle, any modification, equivalent substitution and improvements made etc. should be included within the scope of the present invention.
Claims (10)
1. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm, it is characterised in that the signal reconstruction is excellent
Change method is comprised the following steps：
Ultrasonic phase array defect detecting system is built, the ultrasonic echo reflected via the defective locations of test specimen is obtained, and carry
Take A and sweep signal；
Signal is swept to A using orthogonal basis carries out sparse transformation, and optimal sparse base is chosen by calculating degree of rarefication；
According to optimal sparse base, using match tracing, orthogonal matching pursuit, the orthogonal matching pursuit of regularization, progressively orthogonal
Ultrasonic phase array signal is reconstructed respectively with tracking, compression sampling match tracing；
Calculate and the above-mentioned five kinds ultrasonic phase array signal reconstruction errors of greedy restructing algorithm are used under different compression ratios and according to knot
Fruit selection optimal algorithm；
The result of optimal algorithm is compared with traditional wavelet compression result, the applicability of verification algorithm.
2. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is that the ultrasonic phase array defect detecting system includes：The host computer that is sequentially connected electrically, ultrasonic phase array detector and
Ultrasonic phase array is popped one's head in.
3. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is that the use orthogonal basis sweeps signal to A and carries out sparse transformation, and the step of optimal sparse base is chosen by calculating degree of rarefication
It is rapid to be specially：
Using the degree of rarefication of each sparse transformation of formula quantitative description between L1 norms and L2 norms；
Signal is swept to A carry out discrete Fourier transform and obtain X (k), carry out discrete cosine transform and obtain D (k), and calculate corresponding
Degree of rarefication；Wavelet transform is carried out to x (n) using the sym4 wavelet basis of four layers of decomposition and obtains WTf(m, n), and it is dilute to calculate its
Dredge degree；
Choose common db, totally 54 kinds of wavelet basis are swept signal and decomposed to A for sym, bior, rbio and coif family, decomposition layer
Number is set as 2 to 6 layers, and optimal sparse base is chosen according to degree of rarefication result of calculation.
4. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is, it is described according to optimal sparse base, it is specially the step of be reconstructed to ultrasonic phase array signal using match tracing：
Obtain the coefficient n of corresponding column vector in matrix Ak, column vector a is chosen from matrix An, make it that there is highest phase with residual error
Guan Xing；
Update and rebuild echo signal；Residual error is updated, is iteratively repeated, update residual values；Return to reconstruction signal s1。
5. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is, it is described according to optimal sparse base, it is specially the step of be reconstructed to ultrasonic phase array signal using orthogonal matching pursuit：
Column vector a is chosen from matrix An, make it that there is highest correlation, record coefficient correlation n with residual errork；Prostatitis is worked as in calculating
Optimal approximation coefficient under vector；
It is iteratively repeated, updates residual values, returns to reconstruction signal s2。
6. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is, it is described according to optimal sparse base, the step being reconstructed to ultrasonic phase array signal using the orthogonal matching pursuit of regularization
It is rapid to be specially：
Coefficient correlation u is calculated, the index position corresponding to K maximum is found from u, be deposited into indexed set J；K is dilute
Dredge angle value；
Postsearch screening is carried out using regularization method, the maximum corresponding atom index value of one group of coefficient correlation of selection energy is stored in
J0In, J0It is first element of set J；
Make Ω=Ω ∪ J0, update supported collection AΩ；Signal approximation is carried out using least square method and residual error updates；Ω is indexed set；
| Ω | >=2K is steps be repeated alternatively until, reconstruction signal s is returned3。
7. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is, it is described according to optimal sparse base, have the step of be reconstructed to ultrasonic phase array signal using progressively orthogonal matching pursuit
Body is：
Set up soft-threshold and calculate the atom set J under the threshold valuek={ j:|Ck(j) | ＞ tkσk, wherein
2≤t of threshold parameterk≤3；CkJ () represents interim index set CkIn j-th element；rk-1It is residual values；M is calculation matrix
The line number of Φ；
Coefficients of Approximation vector is calculated, residual values are updated, reconstruction signal s is returned4。
8. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is, it is described according to optimal sparse base, have the step of be reconstructed to ultrasonic phase array signal using compression sampling match tracing
Body is：
α K column vectors are chosen from matrix A, makes it that there is highest correlation, recording indexes Ω with residual error；α joins for tuning
Number, K is sparse angle value；
Supported collection merges；Calculate the optimal approximation coefficient under current column vector；Maximum preceding K coefficient is preserved, is iteratively repeated, more
New residual values, return to reconstruction signal s5。
9. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is that described calculating use the above-mentioned five kinds ultrasonic phase array signal reconstruction errors of greedy restructing algorithm and root under different compression ratios
The step of selecting optimal algorithm according to result is specially：
It the ratio between is the signal length compressed with original signal strength to define compression ratio, chooses percentage mean square error quantitative assessment
The precision of restructing algorithm；Part primary signal is removed by random, it is 20%~80% to set compression ratio scope, every 5% 1
Shelves, calculate the A under different compression ratios and sweep signal reconstruction error and select optimal algorithm according to result.
10. a kind of phased array supersonic signal reconstruction optimization method based on greedy algorithm according to claim 1, its feature
It is that the result by optimal algorithm compares with traditional wavelet compression result, has the step of the applicability of verification algorithm
Body is：
By the compression ratio for setting different threshold values to adjust wavelet compression, all defect signal is divided using wavelet compression
Solution reconstruct, compares the result of compressed sensing algorithm and wavelet compression, the usability of verification algorithm under identical compression ratio.
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