CN106841401A - A kind of phased array supersonic signal reconstruction optimization method based on sensing matrix - Google Patents
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Abstract
The invention discloses a kind of phased array supersonic signal reconstruction optimization method based on sensing matrix, 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；Using random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and binary sparse matrix as sensing matrix, according to optimal sparse base, ultrasonic phase array signal is reconstructed using orthogonal matching pursuit；The ultrasonic phase array signal reconstruction error that above-mentioned four kinds of sensing matrixs are used under different compression ratios is calculated, and Optimal matrix is selected according to result.Compressed sensing is applied to ultrasonic phase array Signal Compression field by the present invention, and reconstruction accuracy is further increased by the selection of sensing matrix, achieves good effect.
Description
Technical field
Field, more particularly to a kind of phased array based on sensing matrix are perceived the present invention relates to ultrasonic phase array Signal Compression
Ultrasonic signal reconstruction and optimization method.
Background technology
Since the sixties in last century, ultrasonic phased array technology starts to be applied in medical imaging, is shortly introduced into afterwards
Industrial nondestructive testing field, and be used widely in the detection such as communications and transportation, oil-gas pipeline, aviation composite.It is phased
The unique array type ultrasonic probe of battle array ultrasound can make sound wave be superimposed interference in order by controlling exomonental time delay, be formed
Focus on and deflection acoustic beam.Therefore, detected compared to conventional ultrasound, phased array supersonic has that scanning scope is big, detection speed fast, differentiates
Rate is high, the advantages of detected suitable for complex component.
In recent years, with detection speed and the raising of required precision, phased array probe array number is continuously increased, two-dimensional array
Also begin to be applied in industrial detection etc. more complicated array, bring the big problem of data volume, increased signal acquisition and place
The difficulty of reason.Researcher proposes many algorithms and solves this problem, wherein being most typically based on wavelet transformation or lifting
The compression method of wavelet transformation.These methods all achieve good compression effectiveness, but still to follow traditional Nyquist
Sampling thheorem, it is impossible to fundamentally reduce sampled data output.
Compressed sensing is a kind of new signal processing theory for growing up in recent years, Candes, Romberg, Donoho
With Tao et al.[1][2][3]Establish the sampling system of whole compressed sensing.The theory is pointed out sparse or with sparse expression
Signal can use the linear non-self-adapting measured value accurate reconstruction far below nyquist sampling quantity, and sampling and compression are closed into two
It is one.Compressive sensing theory once proposition, just in information theory, image procossing, imaging of medical, pattern-recognition, optical imagery, radio
The numerous areas such as astronomy, channel coding cause the extensive concern of researcher, but, at present in the phased array signals processing of industrial ultrasonic
The application of aspect is also little.
The content of the invention
The invention provides a kind of phased array supersonic signal reconstruction optimization method based on sensing matrix, the present invention uses pressure
Contracting perception algorithm is compressed the selection reconstructed and by sensing matrix to signal and further increases reconstruction accuracy, as detailed below
Description：
A kind of phased array supersonic signal reconstruction optimization method based on sensing matrix, 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；
Using random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and binary sparse matrix as sensing matrix, root
According to optimal sparse base, ultrasonic phase array signal is reconstructed using orthogonal matching pursuit；
Calculate and use under different compression ratios the ultrasonic phase array signal reconstruction error of above-mentioned four kinds of sensing matrixs and according to knot
Fruit selection Optimal matrix.
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；Signal is swept to A carry out wavelet transform using the db6 wavelet basis of four layers of decomposition and obtain WTf(m, n), and count
Calculate its degree of rarefication；
Using common db, totally 54 kinds of wavelet basis are swept signal and are 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 using random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and binary sparse matrix as sensing square
Battle array, is specially according to optimal sparse base, the step of be reconstructed to ultrasonic phase array signal using orthogonal matching pursuit：
Above-mentioned four kinds of matrixes are used successively as sensing matrix, the optimal sparse base for selecting above-mentioned analysis to draw；
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 is returned.
The ultrasonic phase array signal reconstruction error and root calculated under different compression ratios using above-mentioned four kinds of sensing matrixs
The step of selecting Optimal matrix according to result is specially：
The ratio between signal length and original signal strength that compression ratio is defined as having compressed；It is original by random removal part
Signal, it is 20%~70% to set compression ratio scope, every 10% 1 grade, respectively using four kinds of matrix computations in different compression ratios
Under A sweep signal reconstruction error and according to result select Optimal matrix.
The beneficial effect of technical scheme that the present invention is provided is：
1st, compressed sensing is the study hotspot of field of signal processing in recent years, and the algorithm is applied to ultrasound phase-control by the present invention
Battle array Signal Compression field, achieves good effect；
2nd, the present invention is using random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and binary sparse matrix conduct
Sensing matrix, is reconstructed using orthogonal matching pursuit (OMP) algorithm to ultrasonic phase array flaw echo, is compared in different pressures
Reconstructed error and standard deviation under shrinkage, have selected the optimal sensing matrix of suitable such signal；
3rd, the present invention is tested using multigroup flaw indication, is as a result shown, when compression ratio reaches 70%, uses part
The average percent reconstructed error of Hadamard sensing matrix is only 2.6577%, 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 sensing matrix；
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. 2 defect A sweep signal；
Fig. 4 (b) is No. 2 schematic diagrames of defect discrete Fourier transform result；
Fig. 4 (c) is No. 2 schematic diagrames of defect discrete cosine transform result；
Fig. 4 (d) is No. 2 schematic diagrames of defect wavelet transform result；
Fig. 5 is the schematic diagram of the error mean comparing result of different matrixes；
Fig. 6 is the schematic diagram of the error to standard deviation comparing result of different matrixes.
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.
Embodiment 1
A kind of phased array supersonic signal reconstruction optimization method based on sensing matrix is the embodiment of the invention provides, referring to figure
1, the optimization method is comprised the 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：Using random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and binary sparse matrix as sensing square
Battle array, according to optimal sparse base, is reconstructed using orthogonal matching pursuit to ultrasonic phase array signal；
104：Calculate the ultrasonic phase array signal reconstruction error and root that above-mentioned four kinds of sensing matrixs are used under different compression ratios
Optimal matrix is selected according to result.
Ultrasonic phase array defect detecting system includes：Host computer, ultrasonic phase array detector, the Yi Jichao being sequentially connected electrically
Sound phased array probe.
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；Signal is swept to A carry out wavelet transform using the db6 wavelet basis of four layers of decomposition and obtain WTf(m, n), and count
Calculate its degree of rarefication；
Using common db, totally 54 kinds of wavelet basis are swept signal and are 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 by random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and the sparse square of binary
Battle array as sensing matrix, according to optimal sparse base, the step of being reconstructed to ultrasonic phase array signal using orthogonal matching pursuit
Specially：
Above-mentioned four kinds of matrixes are used successively as sensing matrix, the optimal sparse base for selecting above-mentioned analysis to draw；
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 is returned.
Wherein, the ultrasonic phase array signal of above-mentioned four kinds of sensing matrixs is used under the different compression ratios of calculating in step 104
Reconstructed error, and be specially according to the step of result selection Optimal matrix：
The ratio between signal length and original signal strength that compression ratio is defined as having compressed；It is original by random removal part
Signal, it is 20%~70% to set compression ratio scope, every 10% 1 grade, respectively using four kinds of matrix computations in different compression ratios
Under A sweep signal reconstruction error and according to result select Optimal matrix.
In sum, a series of random sensing matrixs are applied to ultrasonic phase array Signal Compression and perceived by the embodiment of the present invention
In, signal is reconstructed using orthogonal matching pursuit algorithm, above-mentioned four kinds sensings are used under different compression ratios by comparing
The average reconstruct root-mean-square error and corresponding standard deviation of matrix select Optimal matrix, there is provided a kind of based on sensing matrix
Ultrasonic phase array signal reconstruction optimization method.
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 6 aluminum test blocks of a diameter of 1mm through holes 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) definition of signal degree of rarefication is the number of the nonzero element after certain conversion, but in actual application, is passed through
There are many coefficients after conversion close to 0 but for 0, so the degree of rarefication for selecting a kind of mode to carry out quantificational expression signal is needed, this
Inventive embodiments select a kind of formula between L1 norms and L2 norms to 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 db6 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 ψm,n(t)=| a0|-m/2ψ(a0 -mt-nb0),For
Morther wavelet.
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：Build random Gaussian sensing matrix；
The detailed operation of the step is：
To matrixMake its each elementFor the average being independently distributed is 0, variance is the Gaussian Profile of 1/M,
I.e.
Wherein, M is the line number of matrix Φ.
204：Build random Bernoulli Jacob's matrix；
The detailed operation of the step is：
To matrixMake its each elementIt is independent to obey Bernoulli Jacob's distribution, i.e.,
Or its correlation distribution
Wherein, M is the line number of matrix Φ.
205：The local hadamard matrix of construction；
The detailed operation of the step is：
1) N × N hadamard matrix is firstly generated.
2) it is random that t row vectors are chosen from the matrix of above-mentioned generation, constitute a local hadamard matrix of t × N.
3) because the structure of hadamard matrix itself is limited, the value of N must is fulfilled for N=2k, k=1,2,3 ....
206：The construction sparse random matrix of binary；
The detailed operation of the step is：
1) matrix is firstly generatedBy its all elements zero setting；
2) in each column vector of matrix, randomly choose d position and the element on the position is put the value of 1, d
It is little on the influence of compressed sensing result.
207：Ultrasonic phase array signal is reconstructed using orthogonal matching pursuit (OMP) algorithm；
Use above-mentioned four kinds of matrixes (unified to use as sensing matrix successivelyRepresent), select above-mentioned analysis to draw
Optimal sparse base be designated asUltrasonic phase array signal is designated as x, and its nonlinear measurement value is y=Ax, wherein matrix A
=Φ Ψ.
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 3)~5), until meeting end condition.
5) as n ∈ Ωk, return to reconstruction signal s (n)=xk(n), otherwise s (n)=0.S is gained reconstruction signal.
208：Calculate the ultrasonic phase array signal reconstruction error and root that above-mentioned four kinds of sensing matrixs are used under different compression ratios
Optimal matrix 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, n is the length of measured value.
2) precision of percentage mean square error (PRD) quantitative assessment restructing algorithm is chosen：
It follows that PRD values are smaller, represent that reconstruction accuracy is higher.
3) part primary signal is removed by random, it is 20%~70% to set compression ratio scope, every 10% 1 grade.
4) ultrasonic phase array signal is reconstructed under all compression ratio levels using above-mentioned four kinds of sensing matrixs, is compared
Error simultaneously selects Optimal matrix according to result.
In sum, a series of random sensing matrixs are applied to ultrasonic phase array Signal Compression and perceived by the embodiment of the present invention
In, signal is reconstructed using orthogonal matching pursuit algorithm, above-mentioned four kinds sensings are used under different compression ratios by comparing
The average reconstruct root-mean-square error and corresponding standard deviation of matrix select Optimal matrix, there is provided a kind of based on sensing matrix
Ultrasonic phase array signal reconstruction optimization method.
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. 2 through holes of selection first.Shown in signal such as Fig. 4 (a), next flaw echo A sweeps
A series of sparse transformations are carried out to it, signal length N=1024 is chosen.
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
0.8380th, 0.7881 and 0.8822.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 6
The bior3.1 small echos that layer is decomposed have best degree of rarefication, are 0.9028.
4) to other five defective hole signals also using it is above-mentioned 2)~3) step be analyzed, wherein three at 6 layers points
The bior3.1 small echos of solution have best degree of rarefication, and two other degree of rarefication under the decomposition is also highly desirable.For unified point
Analysis, selects 6 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) ultrasonic phased array echo signal of No. 2 defects is existed to four kinds of sensing matrixs described in step 206 using step 203
It is reconstructed under all compression ratios, each point is calculated 100 times, and results averaged simultaneously calculates corresponding standard deviation.Fig. 5 show
Using the error mean result of different matrixes, Fig. 6 show standard deviation comparing result.
6) as seen from Figure 5, the AME of local Hadamard sensing matrix is significantly lower than other three kinds of sensing matrixs,
And the performance of random Gaussian matrix, Bernoulli Jacob's matrix and binary sparse matrix is then difficult to distinguish.In addition it will be appreciated from fig. 6 that local breathe out
Up to agate sensing matrix reconstruction of standard difference be also in all sensing matrixs it is minimum, absolutely proved the matrix in ultrasonic phase array
Superiority in Signal Compression perception.Particularly when compression ratio reaches 70%, the reconstructed error of local hadamard matrix is used
Only 2.7871%, standard deviation is 0.1415.
7) other five defective hole echo-signals are carried out with 100 tests using local hadamard matrix, calculates average
Error and respective standard are poor, as a result as shown in table 1.The error result of all defect is held in very low level, illustrates office
Broad applicability of portion's Hadamard sensing matrix in the perception of ultrasonic phase array Signal Compression.
The average PRD (%) and standard deviation of all defect signal of table 1..
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.
Bibliography
[1]Candès EJ,Romberg J,Tao T.Robust uncertainty principles:exact
signal reconstruction from highly incomplete frequency information[J].IEEE
Transactions on Information Theory,2006；52(2):489-509.
[2]Candès EJ,Romberg JK,Tao T.Stable signal recovery from incomplete
and inaccurate measurements[J].Communications on Pure and Applied
Mathematics,2006；59(8):1207-23.
[3]Donoho DL.Compressed sensing[J].IEEE Transactions on Information
Theory,2006；52(4):1289-306.
Claims (5)
1. a kind of phased array supersonic signal reconstruction optimization method based on sensing matrix, 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；
Using random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and binary sparse matrix as sensing matrix, according to most
Excellent sparse base, is reconstructed using orthogonal matching pursuit to ultrasonic phase array signal；
The ultrasonic phase array signal reconstruction error that above-mentioned four kinds of sensing matrixs are used under different compression ratios is calculated, and is selected according to result
Select Optimal matrix.
2. a kind of phased array supersonic signal reconstruction optimization method based on sensing matrix 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 sensing matrix 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；Signal is swept to A carry out wavelet transform using the db6 wavelet basis of four layers of decomposition and obtain WTf(m, n), and calculate it
Degree of rarefication；
Using common db, totally 54 kinds of wavelet basis are swept signal and are 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 sensing matrix according to claim 1, its feature
Be, it is described using random Gaussian matrix, Bernoulli Jacob's matrix, local hadamard matrix and binary sparse matrix as sensing matrix,
It is specially according to optimal sparse base, the step of be reconstructed to ultrasonic phase array signal using orthogonal matching pursuit：
Above-mentioned four kinds of matrixes are used successively as sensing matrix, the optimal sparse base for selecting above-mentioned analysis to draw；
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：Residual values are updated, reconstruction signal is returned.
5. a kind of phased array supersonic signal reconstruction optimization method based on sensing matrix according to claim 1, its feature
It is, the ultrasonic phase array signal reconstruction error calculated under different compression ratios using above-mentioned four kinds of sensing matrixs, and according to
The step of result selection Optimal matrix, is specially：
The ratio between signal length and original signal strength that compression ratio is defined as having compressed；The original letter in part is removed by random
Number, it is 20%~70% to set compression ratio scope, every 10% 1 grade, respectively using four kinds of matrix computations under different compression ratios
A sweep signal reconstruction error and according to result select Optimal matrix.
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