CN106802418A - A kind of method for designing of the high-effect sparse dictionary in synthetic aperture compressed sensing ultrasonic imaging - Google Patents

Abstract

The invention discloses a method for designing a high-efficiency sparse dictionary in synthetic aperture compressed sensing ultrasonic imaging, and belongs to the technical field of ultrasonic imaging. The method includes the following steps: the continuous echo signal received by the ultrasonic array is amplified and processed and A/D converted to obtain the echo signal x required for ultrasonic imaging; the delta matrix is selected as the measurement matrix for synthetic aperture compressive sensing ultrasonic imaging, and the echo The wave signal x is subjected to non-uniform compression sampling to obtain the measurement signal y; the transmitted pulse is used as the basis function to construct a high-performance sparse dictionary Ψ; according to the delta matrix, the measurement signal y and the high-performance sparse dictionary Ψ, a mathematical model of synthetic aperture compressive sensing ultrasound imaging is constructed , the reconstructed original echo signal is obtained through the model and the reconstruction algorithm Reconstructing the original echo signal by using Carrying out beam synthesis and final imaging; the present invention enables echo signals to achieve the same restoration effect with a higher compression rate, further reduces the amount of stored data required for synthetic aperture imaging, and reduces the complexity of the ultrasonic imaging system.

Description

Design of a High Performance Sparse Dictionary for Synthetic Aperture Compressive Sensing Ultrasound Imaging method

technical field

The invention belongs to the technical field of ultrasonic imaging, and in particular relates to a method for designing a high-efficiency sparse dictionary in synthetic aperture compressed sensing ultrasonic imaging.

Background technique

Synthetic aperture imaging is a method used to improve image resolution and image quality in ultrasound imaging. This technology was first proposed by Passman in 1996. The basic idea is that a single array element transmits pulse signals sequentially, and all array elements receive scattered signals from the detection area at the same time, and then process all array element data to obtain the final medical image. The amount of echo data to be stored is huge, which increases the complexity of hardware implementation. Compressed sensing is a solution proposed for high-speed data acquisition and large-capacity data storage in recent years. The theory believes that when the signal itself or in a certain transform domain is sparse, the reconstruction algorithm can be used to sample data from a small amount. Reconstruct the original signal with extremely high precision, reduce the amount of data that needs to be stored, and reduce the complexity of hardware implementation.

Since compressed sensing needs to transform the signal to be restored into a certain sparse domain first, the common reconstruction algorithm first reconstructs the sparse representation coefficients in the sparse domain and then restores the original signal, so the sparse coefficients of the signal in the sparse domain are directly Determines the effect of refactoring. Under the same reconstruction conditions, the sparser the sparse coefficients, that is, the fewer non-zero elements, the higher the reconstruction accuracy, and the better the performance of the sparse dictionary. Currently commonly used sparse transformation matrices are: Discrete Fourier Transform (DFT) matrix, discrete orthogonal cosine transform (Discrete cosine transform, DCT) matrix, wavelet transform (Discrete Wavelet Transform, DWT) matrix, discrete Walsh-Ha Discrete Walsh-Hadamard Transform (DWHT) matrix, etc. However, the common sparse matrix lacks pertinence, especially when it is applied to a signal with repeated superposition characteristics such as ultrasonic echo signal, it does not make full use of the characteristics of the signal itself, so its sparse representation ability is limited and the reconstruction accuracy is low. It is difficult to guarantee the effect of reconstructed image under low compression rate. Therefore, designing a high-efficiency sparse dictionary is a hotspot in the application research of synthetic aperture compressive sensing ultrasound imaging.

Contents of the invention

In view of this, the object of the present invention is to provide a method for designing a high-efficiency sparse dictionary in synthetic aperture compressive sensing ultrasound imaging.

To achieve the above object, the present invention provides the following technical solutions:

A method for designing a high-efficiency sparse dictionary in synthetic aperture compressive sensing ultrasound imaging, the method comprising the following steps:

1) The continuous echo signal x(t) received by the acoustic array is amplified and A/D converted to obtain the echo signal x required for ultrasonic imaging;

2) Select the delta matrix as the measurement matrix of synthetic aperture compressive sensing ultrasound imaging, perform a certain proportion of non-uniform compression sampling on the echo signal x, and obtain the measurement signal y;

3) Use the transmitted pulse s(t) as the basis function to construct a high-performance sparse dictionary Ψ;

4) Construct a mathematical model of synthetic aperture compressive sensing ultrasound imaging according to the delta matrix, measurement signal y and high-performance sparse dictionary Ψ;

5) Reconstruct the original echo signal through the mathematical model and reconstruction algorithm of synthetic aperture compressive sensing ultrasound imaging

6) Using reconstructed original echo signal Perform beamforming and final imaging;

Further, in step 2), specifically include:

21) Calculate the length M=p N of the measurement signal y according to the length N of the echo signal x and the selected compression sampling rate p;

22) Randomly select the M×N-dimensional delta matrix Φ as the measurement matrix for synthetic aperture compressed sensing ultrasound imaging, where the sampling signal corresponding to the element "1" in the delta matrix Φ is stored, and the sampling signal corresponding to the element "0" is not stored give up.

23) Compressively sample the echo signal x with the delta matrix Φ to obtain the measurement signal y=Φx.

Further, in step 3), specifically include:

31) Using the continuous echo signal x(t) as the superposition characteristic of the transmitted pulse s(t) after different delay attenuation, the mathematical expression of the echo signal x can be expressed as:

Where T is the period of the transmitted pulse, n is the number of pulse signals received by reflection, t is the time from the first pulse sent by the ultrasonic array, t _m and α _m are the delay time and amplitude of the mth reflected echo . If the sampling frequency of the system is f _s , then the sampling period T _S =1/f _s , the continuous echo signal x(t) can be re-expressed as:

where n _m =t _m /T _s .

32) Utilize the transmitted pulse signal s(t) to construct a sparse basis function and a sparse dictionary:

ψ _i (t)=s(t-iT _s )

Ψ={ψ _i (t)|ψ _i (t)=s(t-iT _s )} i=1,2,…,N

Using the frequency f _s to discretize the sparse basis function to obtain a vector:

ψ _i =[0,…,0,s(T _s ),s(2T _s ),s(3T _s ),…,s(kT _s ),0,…,0]

=[0,...0,ψ,0,...,0]

Where k=T/T _s , ψ=[s(T _s ), s(2T _s ), s(3T _s ), . . . , s(kT _s )].

Substitute ψ _i into Ψ to get a high-performance sparse dictionary Ψ∈C ^N×N :

33) Select the sparse dictionary Ψ as the sparse matrix, and the sparse transformation of the echo signal x on Ψ is:

Where α is the sparse coefficient of the echo signal x on Ψ.

Further, in step 4), a mathematical model of synthetic aperture compressive sensing ultrasound imaging is constructed according to the delta matrix Φ, the measurement signal y, and the high-performance sparse dictionary Ψ:

y=Φx=ΦΨα

Further, in step 5), specifically include:

51) By solving the optimization problem arg min||α|| ₁ stΦΨα=Φx=y, the actual sparse representation of the echo signal x is obtained

52) Through high-performance sparse dictionary Ψ and actual sparse representation Reconstruct the original echo signal in

Further, in step 6), the original echo signal is reconstructed through the traditional time-delay stacking beamforming algorithm Perform weighted summation to calculate the beamforming signal:

where s _DAS represents the calculated beamforming signal, Represents the reconstructed original echo signal on the i-th array element, and N ₁ represents the total number of ultrasonic arrays.

Owing to adopting above-mentioned technical scheme, the present invention has following advantage:

The invention discloses a method for designing a high-efficiency sparse dictionary in synthetic aperture compressed sensing ultrasonic imaging; the method designs a high-efficiency sparse dictionary by using transmitted pulses according to the attenuation and superposition characteristics of ultrasonic echo signals. The dictionary can theoretically make the sparsity of the echo signal sparse coefficient equal to the number of reflected echoes received by the array element, so that the echo signal has good sparsity. Under the same reconstruction conditions, the sparse dictionary of this patent has higher reconstruction accuracy and smaller reconstruction error, which further reduces the amount of data stored for synthetic aperture ultrasonic imaging and reduces the complexity of the system.

Description of drawings

In order to make the purpose, technical scheme and beneficial effect of the present invention clearer, the present invention provides the following drawings for illustration:

Fig. 1 is a technical flow chart of the method of the present invention;

Figure 2 is the original single row echo signal;

Fig. 3 is the sparse representation of the single column echo signal under 4 kinds of sparse dictionaries;

Figure 4 is the reconstructed signal of the single column echo signal under 4 kinds of sparse dictionaries when the compression rate is 50%;

Figure 5 is the reconstructed image under different sparse transformations at 50% compression rate;

Figure 6 is the cross-section analysis at 60mm of different sparse transformation imaging;

Figure 7 shows the original image and the reconstructed image under 4 different sparse transformations at 50% compression rate;

Figure 8 is the reconstructed image of 4 different compression ratios under the sparse dictionary;

Figure 9 shows the mean absolute error analysis of four sparse transformations under different compression ratios;

Figure 10 shows the original phantom image and the reconstructed images under 4 different sparse transformations at 30% compression rate.

detailed description

The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

Fig. 1 is a technical flow chart of the present invention, as shown in the figure, the present invention provides a kind of design method of high-efficiency sparse dictionary in synthetic aperture compressive sensing ultrasonic imaging, comprising the following steps:

1) The continuous echo signal x(t) received by the acoustic array is amplified and A/D converted to obtain the echo signal x required for ultrasonic imaging;

2) The delta matrix is selected as the measurement matrix of synthetic aperture compressive sensing ultrasound imaging, and a certain proportion of non-uniform compression sampling is performed on the echo signal x to obtain the measurement signal y. Specifically include the following steps:

21) Calculate the length M=p N of the measurement signal y according to the length N of the echo signal x and the selected compression sampling rate p;

22) Randomly select the M×N-dimensional delta matrix Φ as the measurement matrix for synthetic aperture compressed sensing ultrasound imaging, where the sampling signal corresponding to the element "1" in the delta matrix Φ is stored, and the sampling signal corresponding to the element "0" is not stored give up.

23) Compressively sample the echo signal x with the delta matrix Φ to obtain the measurement signal y=Φx.

3) Use the transmitted pulse s(t) as the basis function to construct a high-performance sparse dictionary Ψ. Specifically include the following steps:

31) Using the continuous echo signal x(t) as the superposition characteristic of the transmitted pulse s(t) after different delay attenuation, the mathematical expression of the echo signal x can be expressed as:

Where T is the period of the transmitted pulse, n is the number of pulse signals received by reflection, t is the time from the first pulse sent by the ultrasonic array, t _m and α _m are the delay time and amplitude of the mth reflected echo . If the sampling frequency of the system is f _s , then the sampling period T _S =1/f _s , the continuous echo signal x(t) can be re-expressed as:

where n _m =t _m /T _s .

32) Utilize the transmitted pulse signal s(t) to construct a sparse basis function and a sparse dictionary:

ψ _i (t)=s(t-iT _s )

Ψ={ψ _i (t)|ψ _i (t)=s(t-iT _s )} i=1,2,…,N

Using the frequency f _s to discretize the sparse basis function to obtain a vector:

ψ _i =[0,…,0,s(T _s ),s(2T _s ),s(3T _s ),…,s(kT _s ),0,…,0]

=[0,...0,ψ,0,...,0]

Where k=T/T _s , ψ=[s(T _s ), s(2T _s ), s(3T _s ), . . . , s(kT _s )].

Substitute ψ _i into Ψ to get a high-performance sparse dictionary Ψ∈C ^N×N :

33) Select the sparse dictionary Ψ as the sparse matrix, and the sparse transformation of the echo signal x on Ψ is:

Where α is the sparse coefficient of the echo signal x on Ψ.

4) Construct a mathematical model of synthetic aperture compressive sensing ultrasound imaging according to delta matrix, measurement signal y and high-performance sparse dictionary Ψ. The specific mathematical expression is:

y=Φx=ΦΨα

5) Reconstruct the original echo signal through the mathematical model and reconstruction algorithm of synthetic aperture compressive sensing ultrasound imaging Specifically include the following steps:

51) By solving the optimization problem arg min||α|| ₁ stΦΨα=Φx=y, the actual sparse representation of the echo signal x is obtained

52) Through high-performance sparse dictionary Ψ and actual sparse representation Reconstruct the original echo signal in

6) Using reconstructed original echo signal Perform beamforming and final imaging. Reconstruction of the original echo signal using the traditional time-delay and stacking beamforming algorithm Perform weighted summation to calculate the beam signal:

where s _DAS represents the calculated beam signal, Represents the reconstructed original echo signal on the i-th array element, and N ₁ represents the total number of ultrasonic arrays.

In order to verify the effectiveness of the present invention, in this embodiment, Field II is used to image point scattering objects and speckle scattering objects commonly used in medical imaging, and to collect actual data on body membranes. In the simulation, a total of 10 scattering point targets are set up, which are evenly distributed in the area of 30-120mm, and the spacing is 10mm. Simultaneously set 10 scattering spots and 5 scattering points, and the scattering spots are divided into two columns and evenly distributed between 30 and 90 mm, with a spacing of 10 mm. Four kinds of sparse dictionaries are used for reconstruction under different compression ratios, and the resolution, contrast and mean absolute error of various sparse dictionaries are compared. The central frequency of phantom data acquisition is f ₀ =3.5MHz, and the sampling frequency is f _s =25MHz. The number of array elements is N=16, the spacing between array elements is 0.78mm, and the dynamic range of the resulting image is 50dB. Four kinds of sparse dictionaries are used to reconstruct and compare the effects.

Figure 2 shows the single-column echo signal received by the array element during synthetic aperture imaging. It can also be seen from Figure 2 that the echo signal is the superposition of the attenuated reflection signals of the transmitted pulse signal at different target points. As the depth increases, the attenuation of the reflected signal increases, but the shape of the signal remains basically unchanged. Fig. 3 is the sparse representation of single row echo signals under 4 different sparse transformations. It can be seen intuitively from Fig. 3 that the sparse representation ability of the sparse dictionary proposed by this patent is obviously stronger than that of the other 3 sparse transformations. The sparsity is approximately equal to the number of target points 10 set by the simulation. Fig. 4 shows the recovered signals of the single column echo signal under four different sparse transformations when the YALL1_group reconstruction algorithm is used. The reconstruction uses 50% of the original data volume. Compared with the four reconstructed images, the sparse dictionary proposed in this patent has the best reconstruction effect and does not generate additional clutter. Although the DCT transformation can accurately restore the signal at the target point, it introduces some Clutter, so the reconstruction effect is slightly worse than the sparse dictionary, and the restored signal at the far-field target point under DWT transformation has some distortion, and its reconstruction effect is slightly better than DFT. The reconstruction effect in Figure 4 is consistent with the sparse representation in Figure 3. The higher the sparsity of the sparse coefficients, the better the reconstruction effect under the same conditions.

A single row of echo signals cannot reflect the influence of the four sparse transformations on the overall reconstructed image. Figure 5 shows the reconstructed image of the four different sparse transformations at the same compression rate. In order to facilitate the calculation and comparison, all the original echo data are normalized in this paper. It can be seen from Figure 5 that the restored image of the sparse dictionary and DCT is basically the same as the original image, and the image quality is not distorted, while some artifacts that are not in the original image appear in the restored image of DFT and DWT, and the image quality has declined. . Figure 6 shows the cross-sectional comparison results of four sparse transformation images at 60mm. From Figure 6, it can be seen that the cross-sectional curve of the sparse dictionary completely coincides with the original data, the cross-sectional curve of DCT basically coincides with the original data, and the reconstruction effect of DWT It is slightly worse than DCT, and the DFT curve has some distortions at both ends. In comparison, the resolution of the reconstructed image under the sparse dictionary is the closest to the resolution of the original image, and it has basically no effect on the side lobes. The restoration effect best.

In order to more accurately measure the restoration effects of the four sparse transformations, this patent uses mean absolute error (themean absolute error, MAE) as an evaluation standard. Table 1 shows the average absolute error between the reconstructed data and the original echo data under 4 different sparse transformations, because this patent reconstructs each row of echo signals separately, and the echo signal in the synthetic transmit aperture There are thousands of columns in , so the mean absolute error can rule out chance results. From the data in Table 1, the effects of the four sparse transformations can be seen more intuitively. The average absolute error between the reconstructed data of the sparse dictionary and the original data is much lower than that of the other three sparse transformations, followed by DCT and slightly better by DWT. Based on DFT, it shows that the reconstruction accuracy is the highest and the reconstruction effect is the best under the sparse dictionary.

Table 1 Mean absolute error between reconstructed data and original echo data under 4 different sparse transformations

sparse transformation DFT DWT DCT sparse dictionary mean absolute error 0.0153 0.0049 0.0015 2.71e-06

Figure 7 shows the reconstructed images of complex targets with 4 different sparse transformations at 50% compression rate. From Figure 7, we can see that the recovery effect of the sparse dictionary proposed by this patent is significantly better than that of DFT and DWT. Compared with sparse dictionary and It is found that the recovery quality of scattered spots under the sparse dictionary is better, which shows that the restoration effect of the sparse dictionary proposed in this patent is slightly better than that of DCT, and it proves that the dictionary can also be well applied to complex target echoes. A sparse representation of a signal.

In order to distinguish the effects of the four sparse transformations more intuitively, the average absolute error is also used as the evaluation standard. Table 2 shows the average absolute error of the four different sparse transformations reconstructed under 50% compression rate in Figure 7. The data in the table can be It can be seen that under the same compression rate, the reconstruction error of the sparse dictionary proposed by this patent is the smallest, and it is much lower than the other three sparse transformations. The contrast analysis of the area marked by the black box and the white circle box in Figure 7 is performed, and the results are shown in Table 3. The center average power and background average power of the marked area of the reconstructed image under the sparse dictionary are the closest to the original image, so the contrast of the restored image is the highest, the restoration effect on the original image is the best, and the imaging quality is better than DFT, DWT and DCT.

Table 2 The average absolute error of reconstruction under 50% compression ratio of 4 different sparse transformations in complex target simulation

sparse transformation DFT DWT DCT sparse dictionary mean absolute error 0.0754 0.0347 0.0039 9.15e-04

Table 3 Contrast analysis of reconstructed images under 50% compression ratio of 4 different sparse transformations in complex target simulation

sparse transformation The original image DFT DWT DCT sparse dictionary Center average power/dB 51.72 35.18 34.04 50.61 51.29 Background average power/dB 26.7 25.86 26.18 26.53 26.69 Contrast/dB 25.02 9.32 7.86 24.08 24.60

The purpose of compressive sensing in the application of synthetic aperture ultrasound imaging is to minimize the amount of data storage and reduce the complexity of the system. In order to verify the reconstruction of the sparse dictionary of this patent under low compression rates, 30%, 20%, 10% and 5% compression rates are selected for signal reconstruction. Figure 8 shows the reconstructed images of these 4 compression ratios under the sparse dictionary. It can be seen from the figure that as the compression rate decreases, although the restoration quality of the image decreases, the reconstruction effect of the patented sparse dictionary at a low compression rate is still comparable to that of other sparse transformations at a high compression rate. Table 4 shows the average absolute error of sparse dictionary reconstruction under 4 different compression ratios. According to the data in Table 4, it can also be seen that the average absolute error of 30% data recovery under sparse dictionary and the average absolute error of 50% data recovery under DCT transformation The errors are similar, the average absolute error of 5% data recovery is similar to the average absolute error of 50% data recovery under DFT and DWT transformation. Figure 9 shows the relationship curves between the compression rate and the mean absolute error under different sparse representation methods. The trend of each curve also shows that the reconstruction effect of the sparse dictionary at each compression rate is far better than other sparse transformations.

Table 4 Mean absolute error of reconstruction under 4 different compression ratios under sparse dictionary

Compression ratio 30% 20% 10% 5% mean absolute error 0.0027 0.0093 0.0284 0.0422

The experiment randomly selects 30% of the actual data, and uses four different sparse transformations for reconstruction. When the imaging dynamic range is set to 60dB, the DAS imaging results of the reconstructed data are shown in Figure 10. Comparing the images in Figure 10, it can be seen that the overall effect of reconstructing the image under the sparse dictionary is the best when the compression rate is 30%, and its image resolution is obviously better than DFT and DWT, which is basically equivalent to DCT, and the original image is relatively complete. Image resolution for data DAS imaging. From the perspective of contrast, although the contrast of the sparse dictionary reconstructed image is lower than that of DWT with the highest reconstruction contrast, due to the reconstruction clutter, the reconstructed image of DWT has large noise and low imaging quality. Therefore, from all aspects, the quality of the reconstructed image under the sparse dictionary is the best, and the reconstruction quality can still be guaranteed under low compression ratio. In order to more intuitively characterize the performance of the sparse dictionary, the average absolute error is also used as the verification standard. Table 5 shows the average absolute error between the reconstruction data of four different sparse transformations and the original phantom experimental data at 30% compression rate. According to the data in Table 5, it can be seen that the average absolute error of the sparse dictionary is the smallest, only about half of DCT, 1/7 of DWT, and 1/16 of DFT, which also proves the superiority of the sparse dictionary proposed in this patent. Therefore, the reconstruction error of the sparse dictionary proposed in this patent is smaller, and the resolution and contrast of the reconstructed image are closer to the original image.

Table 5. Mean absolute error of 4 different sparse transformations reconstructed under 30% compression ratio

sparse transformation DFT DWT DCT sparse dictionary mean absolute error 0.0516 0.0229 0.0058 0.0032

Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that it can be described in terms of form and Various changes may be made in the details without departing from the scope of the invention defined by the claims.

Claims (6)

1. a design method of high-efficiency sparse dictionary in synthetic aperture compressed sensing ultrasonic imaging, it is characterized in that, the method comprises the steps: 1) The continuous echo signal x(t) received by the ultrasonic array is amplified and A/D converted to obtain the echo signal x required for ultrasonic imaging; 2) Select the delta matrix as the measurement matrix of synthetic aperture compressive sensing ultrasonic imaging, and perform non-uniform compression sampling on the echo signal x to obtain the measurement signal y; 3) Use the transmitted pulse s(t) as the basis function to construct a high-performance sparse dictionary Ψ; 4) Construct a mathematical model of synthetic aperture compressive sensing ultrasound imaging according to the delta matrix, measurement signal y and high-performance sparse dictionary Ψ; 5) Reconstruct the original echo signal through the mathematical model and reconstruction algorithm of synthetic aperture compressive sensing ultrasound imaging 6) Using reconstructed original echo signal Perform beamforming and final imaging. 2. the design method of the high-efficiency sparse dictionary in a kind of synthetic aperture compressive sensing ultrasonic imaging according to claim 1, it is characterized in that: in step 2), specifically comprise: 21) Calculate the length M=p N of the measurement signal y according to the length N of the echo signal x and the selected compression sampling rate p; 22) Randomly select the M×N-dimensional delta matrix Φ as the measurement matrix for synthetic aperture compressed sensing ultrasound imaging, where the sampling signal corresponding to the element "1" in the delta matrix Φ is stored, and the sampling signal corresponding to the element "0" is not stored give up; 23) Compressively sample the echo signal x with the delta matrix Φ to obtain the measurement signal y=Φx. 3. the design method of the high-efficiency sparse dictionary in a kind of synthetic aperture compressive sensing ultrasonic imaging according to claim 1, it is characterized in that: in step 3), specifically comprise: 31) The continuous echo signal x(t) is the superposition of the transmitted pulse s(t) after different delay attenuation. The mathematical expression of the echo signal x is expressed as: $\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&NotElement;</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>$ Where T is the period of the transmitted pulse, n is the number of pulse signals received by reflection, t is the time from the first pulse sent by the ultrasonic array, t _m and α _m are the delay time and amplitude of the mth reflected echo ; If the sampling frequency of the system is f _s , Then the sampling period T _S =1/f _s , the continuous echo signal x(t) can be re-expressed as: $\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>$ where n _m =t _m /T _s ; 32) Utilize the transmitted pulse signal s(t) to construct a sparse basis function and a sparse dictionary: ψ _i (t)=s(t-iT _s ) Ψ={ψ _i (t)|ψ _i (t)=s(t-iT _s )}i=1,2,…,N Using the frequency f _s to discretize the sparse basis function to obtain a vector: ψ _i =[0,…,0,s(T _s ),s(2T _s ),s(3T _s ),…,s(kT _s ),0,…,0] =[0,...0,ψ,0,...,0] Where k=T/T _S , ψ=[s(T _s ),s(2T _s ),s(3T _s ),…,s(kT _s )]; Substitute ψ _i into Ψ to get a high-performance sparse dictionary Ψ∈C ^N×N : 33) Select the sparse dictionary Ψ as the sparse matrix, and the sparse transformation of the echo signal x on Ψ is: Where α is the sparse coefficient of the echo signal x on Ψ. 4. the design method of the high-efficiency sparse dictionary in a kind of synthetic aperture compressive sensing ultrasonic imaging according to claim 1, is characterized in that: in step 4), specifically comprise: 41) Construct a mathematical model of synthetic aperture compressive sensing ultrasound imaging according to delta matrix Φ, measurement signal y and high-performance sparse dictionary Ψ: y = Φx = ΦΨα. 5. the design method of the high-efficiency sparse dictionary in a kind of synthetic aperture compressive sensing ultrasonic imaging according to claim 1, it is characterized in that: in step 5), specifically comprise: 51) By solving the optimization problem arg min||α|| ₁ stΦΨα=Φx=y, the actual sparse representation of the echo signal x is obtained 52) Through high-performance sparse dictionary Ψ and actual sparse representation Reconstruct the original echo signal in 6. the design method of the high-efficiency sparse dictionary in a kind of synthetic aperture compressive sensing ultrasonic imaging according to claim 1, it is characterized in that: in step 6), specifically comprise: using traditional time-delay stacking beamforming algorithm to Reconstruct the original echo signal Perform weighted summation to calculate the beam signal: ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; A</span>}\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$ where s _DAS represents the calculated beam signal, Represents the reconstructed original echo signal on the i-th array element, and N ₁ represents the total number of ultrasonic arrays.