CN109188409A

CN109188409A - An Orthogonal Sparse Dictionary Design Method Based on Chirp Codes

Info

Publication number: CN109188409A
Application number: CN201811243842.4A
Authority: CN
Inventors: 王平; 孔露; 罗汉武; 李昉; 李猛克; 崔士刚; 陈师宽; 赵振东; 刘斌; 薛枫; 杜婷婷; 孔美娅; 李锡涛; 柳学功; 杨飞; 石轶哲; 李佳琦; 姜佳昕
Original assignee: Chongqing University; Maintenance Co of State Grid East Inner Mongolia Electric Power Co Ltd
Current assignee: Chongqing University; Maintenance Co of State Grid East Inner Mongolia Electric Power Co Ltd
Priority date: 2018-10-24
Filing date: 2018-10-24
Publication date: 2019-01-11

Abstract

The invention relates to a Chirp code-based orthogonal sparse dictionary design method, belonging to the technical field of ultrasonic imaging; the method comprises the following steps: s1: a Chirp code excitation signal processed by a windowing function is adopted in an ultrasonic emission signal; s2: processing the received ultrasonic echo signals and re-describing the signals in a matrix form; s3: combining the sparse representation of the frequency domain sparse signal to construct an orthogonal dictionary for sparse representation of the ultrasonic echo; s4: measuring the thinned signals by using a measurement matrix, and projecting the original signals from a high-dimensional space to a low-dimensional space; s5: solving an optimization problem through a reconstruction algorithm to obtain a coefficient vector of an original signal; s6: and restoring the original signal by using the coefficient vector, thereby carrying out ultrasonic imaging. The invention can reconstruct high-precision original signals under the condition of lower sampling rate, thereby reducing the complexity of the storage space and hardware realization of the ultrasonic system.

Description

Chirp code-based orthogonal sparse dictionary design method

Technical Field

The invention belongs to the technical field of ultrasonic imaging, and relates to a Chirp code-based orthogonal sparse dictionary design method.

Background

In the ultrasonic imaging process, a large amount of echo data can be generated, which brings great trouble to the storage and transmission of the data and increases the complexity of hardware implementation. In 2006, the compressed sensing theory proposed by Candes and Donoho is just one solution proposed for high-speed data acquisition and large data storage, and this theory shows that if the signal itself is sparse or sparse over some transform domain, the original signal can be accurately recovered from a small amount of sampled data through a reconstruction algorithm. Since compressed sensing firstly transforms a signal to be recovered into a certain sparse domain, a common reconstruction algorithm is to reconstruct a sparse representation coefficient in the sparse domain and then recover an original signal. The data volume measured by the compressed sensing theory is far smaller than that obtained by the Nyquist sampling theorem, but the reconstruction effect of the original signal is not obviously influenced. Under the same reconstruction condition, the more sparse the sparse coefficient is, i.e. the signal is represented by the least coefficient, the better the effect of the sparse dictionary is. However, in the conventional sparse representation-based reconstruction, the process of sparse representation does not take into account the structural features of the data. Therefore, the common sparse matrix lacks pertinence, and particularly when the sparse matrix is applied to a signal with repeated superposition characteristics such as ultrasonic echoes, the signal cannot be well represented sparsely, so that the quality of a reconstructed image is poor.

When the data volume of the compressed sensing sample is smaller than the full sample data volume, a reconstruction algorithm is used for restoring the original ultrasonic echo signal, so that a larger error is brought. The ultrasonic encoding transmission technology can improve the energy of the ultrasonic transmission signal on the premise of not increasing the power of the ultrasonic transmission signal, effectively improve the robustness of an ultrasonic echo signal, inhibit side lobes and improve the imaging contrast. Therefore, in order to obtain better reconstructed ultrasonic imaging quality under the condition of low sampling rate, the invention combines the coding technology with the compressive sensing theory and provides the compressive sensing ultrasonic imaging algorithm fused with Chirp coding. However, as is readily known from the frequency spectrum of the Chirp code signal, the Chirp code echo signal is not sparse in the frequency domain.

In summary, there is an urgent need to provide a sparse dictionary capable of sparsely representing ultrasonic echo signals, and reconstruct original signals with high precision at a low sampling rate, so as to ensure the quality of ultrasonic imaging.

Disclosure of Invention

In view of this, the present invention aims to provide a method for designing an orthogonal sparse dictionary based on a Chirp code, where the orthogonal sparse dictionary can perform a good sparse representation on an ultrasonic signal, effectively overcome the defect of insufficient sparse capability of a traditional sparse dictionary on the ultrasonic signal, and reconstruct an original signal at a low sampling rate and with a very high precision, so as to ensure ultrasonic imaging quality.

In order to achieve the purpose, the invention provides the following technical scheme:

a Chirp code-based orthogonal sparse dictionary design method comprises the following steps:

s1: a Chirp code excitation signal processed by a windowing function is adopted in an ultrasonic transmitting signal, and the energy of the transmitting signal is increased;

s2: processing the received echo signals and re-describing the processed echo signals in a matrix form;

s3: combining the sparse representation of the frequency domain sparse signal to construct an orthogonal dictionary for sparse representation of the ultrasonic echo;

s4: measuring the thinned signals by using a measurement matrix, and projecting the original signals from a high-dimensional space to a low-dimensional space;

s5: solving an optimization problem through a reconstruction algorithm to obtain a coefficient vector of an original signal;

s6: and restoring the original signal by using the coefficient vector, thereby carrying out ultrasonic imaging.

Further, in step S1, the window function w (k) is expressed as:

wherein K is the width of the windowing function, and K is the processing position of the kth windowing function; and (5) processing the Chirp signal by using a window function w (k) to obtain an ultrasonic transmitting signal.

Further, the step S2 specifically includes the following steps:

s21: echo signal s of Chirp signal under scattering point model_r(t) is expressed as:

wherein f is₀Is the central frequency of the signal, T is the duration of the signal transmitted by the ultrasonic system, T is the sampling time, gamma is the frequency modulation rate, P is the number of scattering points, A_iAnd t_diRespectively representing the scattering intensity and the time delay of the ith scattering point; t is t_di＝2r_i/c，r_iThe distance from the ith point to the array element is shown, and c is the sound velocity;

s22: the signal data processing adopts a time width fixed signal, and a signal with the same frequency and modulation frequency as a Chirp code transmitting signal is used as a reference signal, and the reference signal and an echo signal are subjected to difference frequency processing and then are digitized and subjected to orthogonal detection; processing a Chirp code signal transmitted by an ultrasonic system to obtain a reference signal s_ref(t) is expressed as:

wherein f is₀Is the center frequency of the signal, t is the sampling time, gamma is the frequency modulation rate, t_ref＝2R_refC is a reference delay, R_refIs a reference distance;

s23: the processed difference frequency output signal is:and s_ref(t) conjugation, then s_IF(t) is expressed as:

wherein s is_IF(t) is a linear combination of P point frequency signals, sparse in the frequency domain;

s24: to pairSampling to obtain time vectorWherein:n is a sampling time dimension; let s_r(t)、s_ref(t) and s_IF(t) at a sampling frequency f_sThe lower sampling results are respectively s_r、s_refAnd s_IF，t＝[t₁,t₂,…,t_N]^TThen s_r、s_refAnd s_IFWritten in vector form are:

further, the step S3 specifically includes the following steps:

s31: from s_refStructure of the deviceDimension N × N matrix S, whose elements satisfy:

wherein m and n are row and column serial numbers of elements in the matrix S, S_ref(m) represents s_refThe mth element, m is more than or equal to 1, and N is more than or equal to N;

s32: calculating a matrix of the frequency domain sparse signal constructed by the fast fourier transform as:

wherein,represents the nth column vector of the matrix D,denotes d_nThe size of the mth element is not less than 1 and not more than m, and N is not less than N;

s33: described in matrix formThe matrix after data processing is obtained by the construction process of S:

s_IF＝S^H×s_r

wherein S is^HIs a conjugate transpose of S, S^H×s_rDenotes S^HAnd s_rA vector product of (a);

S34：s_IFis formed by linear combination of dot frequency signals, P is finite value, s_IFWhen the matrix D is sparse and its sparse vector is α, there is s_IFD α, thus yielding:

s_IF＝S^H×s_r＝Dα；

s35: s is easily obtained from the constitution of S^HI is an N × N identity matrix, i.e. S is invertible, and S is^-1＝S^H，S^-1Being the inverse matrix of S, we can obtain:

s_r＝SDα

wherein α is a sparse coefficient vector, Ψ ═ SD is a sparse matrix, and then s is present_rPsi α, i.e. s_rSparse over the matrix Ψ;

s36: from the constitution of D in S32, it can be obtained:

Ψ^HΨ＝(D^HS^H)SD＝I

therein, Ψ^H、D^HRespectively, conjugate transposes of Ψ, D.

Further, the step S4 specifically includes the following steps:

s41: a sparse random measurement matrix is adopted as a measurement matrix phi, and the construction method of the sparse random measurement matrix is as follows: firstly, generating an all-zero matrix phi with the size of M multiplied by N, wherein M is less than N; then selecting q positions for each column of the matrix phi and setting 1 at the selected positions, wherein q is less than M; the value of q is generally {4,8,10,16}, where q is selected to be 8;

s42: using measuring matrix phi to pair signals s_rThe measurement is carried out, and the measurement signal y is obtained as follows: y ═ Φ s_r。

Further, the step S5 specifically includes the following steps:

and S51, solving a coefficient vector α by using the measurement signal y:

y＝Φs_r＝ΦΨα＝Θα

wherein Θ ═ Φ Ψ is a sensing matrix;

and S52, solving α through y ═ theta α, namely converting into solving an optimization problem:

by a 1₁And (5) solving by using a norm minimum method, and solving by using a reconstruction algorithm to obtain an approximate value α' of α.

Further, the step S6 is to recover the original signal S by approximating α' to the coefficient vector α_rComprises the following steps:

s_r＝Ψα′

wherein the matrix Ψ is the orthogonal sparse dictionary, and the original signal s is recovered_rThen ultrasonic imaging processing is carried out.

The invention has the beneficial effects that: the invention describes the linear frequency modulation signal Stretch processing again in a matrix form, and constructs an Orthogonal Sparse Dictionary (OSD) for Chirp code echo sparse representation by combining the sparse representation of frequency domain sparse signals, thereby providing the orthogonal sparse representation of the Chirp code echo. Compared with the traditional sparse dictionaries DFT, DCT and DWT, the OSD has better sparse representation capability on ultrasonic echoes, the reconstruction error is far smaller than that of the traditional sparse transform under the same compression rate and reconstruction algorithm, and good reconstructed image quality can be ensured under the low compression rate.

Drawings

In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:

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

FIG. 2 shows DAS imaging before and after Chirp encoding;

FIG. 3 is a sparse representation of 4 sparse dictionaries;

FIG. 4 is a single-row echo reconstructed image under 4 kinds of sparse transformations;

FIG. 5 is a point target reconstructed image under 4 kinds of sparse transform;

FIG. 6 is a point target reconstructed image under 5 different sampling rates;

FIG. 7 is a sound absorption spot reconstruction image under 4 kinds of sparse transform;

FIG. 8 is a reconstructed image of the sound absorption spots at 5 different sampling rates;

FIG. 9 is a reconstructed image of the geobr _0 experimental data under 4 sparse transforms.

Detailed Description

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

Fig. 1 is a flowchart of an algorithm of the present invention, and as shown in the figure, the present invention provides a method for designing an orthogonal sparse dictionary based on a Chirp code, which includes the following steps:

step S1: in the ultrasonic emission signal, a Chirp code excitation signal processed by a windowing function is adopted, the energy of the emission signal is increased, and a required window function w (k) is expressed as:

Step S2: the method comprises the following steps of processing the received echo signals and re-describing the processed echo signals in a matrix form:

step S3: combining the sparse representation of the frequency domain sparse signal to construct an orthogonal dictionary for sparse representation of the ultrasonic echo, specifically comprising the following steps:

s31: from s_refConstructing a dimension NxN matrix S, the elements of which satisfy:

s_IF＝S^H×s_r

s_IF＝S^H×s_r＝Dα；

s35: s is easily obtained from the constitution of S^HS ═ I, I is an NxN identity matrix, i.e., S is reversible, and S-¹＝S^H，S-¹Being the inverse matrix of S, we can obtain:

s_r＝SDα

s36: from the constitution of D in S32, it can be obtained:

Ψ^HΨ＝(D^HS^H)SD＝I

therein, Ψ^H、D^HRespectively, conjugate transposes of Ψ, D.

Step S4: measuring the thinned signals by using a measurement matrix, and projecting the original signals from a high-dimensional space to a low-dimensional space, wherein the method specifically comprises the following steps:

Step S5: solving an optimization problem through a reconstruction algorithm to obtain a coefficient vector of an original signal, and specifically comprising the following steps of:

and S51, solving a coefficient vector α by using the measurement signal y:

y＝Φs_r＝ΦΨα＝Θα

wherein Θ ═ Φ Ψ is a sensing matrix;

s52 solving α by y Θ α can translate into solving the optimization problem:

Step S6:recovery of the original signal s using the approximated value α' of the coefficient vector α_rComprises the following steps:

s_r＝Ψα′

Field II is an ultrasonic experimental simulation platform developed by Denmark university of Engineers based on acoustic principle, and has been widely accepted and used in theoretical research. In order to verify the effectiveness of the algorithm, a point scattering target and a sound absorption spot target which are commonly used in ultrasonic imaging are imaged by using Field II, and an imaging contrast experiment is carried out by using the data of the geobr _0 experiment. In the point target simulation experiment, two lines of 20 point targets with the transverse interval of 4mm and the longitudinal interval of 10mm are arranged, the depth is distributed between 30mm and 120mm, and the imaging dynamic range of the image is set to be 50 dB. In a sound absorption spot target simulation experiment, 5 scattering dark spots with different sizes, 5 scattering bright spots with different sizes and 5 scattering points are arranged, the scattering spots and the scattering points are divided into three rows which are uniformly distributed between 30mm and 90mm, the distance is 10mm, and the imaging dynamic range is set to be 50 dB. The central frequency of the array elements adopted by the geobr _0 experiment is 3.33MHz, the number of the array elements is 64, the spacing is 0.2413mm, the sampling frequency is 17.76MHz, the sound velocity is 1500m/s, and the imaging dynamic range is set to be 50 dB. For the three experimental targets, reconstruction imaging experiments are performed by using an Orthogonal Sparse Dictionary (OSD) based on Chirp echoes, Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT). And selecting 5 different sampling rates to carry out a reconstruction imaging experiment on the first two experimental targets under OSD conversion. Meanwhile, the image recovery quality is evaluated from Mean Square Error (MSE) and Reconstruction Time (RT), and the quality of different sparse dictionaries and the reconstruction difference under different sampling rates are judged.

Fig. 2 shows a comparison of conventional DAS imaging with an addition of Chirp encoding signals. As can be seen from fig. 2, the DAS imaging effect with the increased Chirp encoded signal is significantly better than that of the conventional DAS imaging, the side lobe is improved well, and the resolution and contrast are higher. DAS imaging added with Chirp coding signals is used as an original image of subsequent simulation analysis, and therefore the orthogonal sparse dictionary provided by the invention is superior to a traditional sparse dictionary.

Fig. 3 shows sparse representation of a single-column Chirp echo signal under 4 different sparse transformations, and it can be visually seen from fig. 3 that the sparse representation capability of the orthogonal sparse dictionary provided by the present invention is obviously superior to that of the other 3 sparse transformations, the sparse coefficient is mainly concentrated at a target point, and the sparsity is exactly close to the interval number 10 of the target point.

Fig. 4 shows that when the same reconstruction algorithm is adopted, the original image of a single-column Chirp echo signal and the reconstructed signal under 4 different sparse transformations have a sampling rate of 50%. Comparing the 4 reconstructed images with the original image, the reconstruction effect under DFT conversion is the worst, and the target point cannot be distinguished. Although the original image can be well reconstructed under the DWT transformation and the DCT transformation, partial distortion occurs under the DWT transformation, and a plurality of clutter is generated at non-target points under the DCT transformation. The reconstruction effect at the OSD conversion is best, closest to the original signal. Table 1 lists the mean square error of the reconstructed images under different sparse dictionaries. It can be seen from table 1 that the mean square error under the OSD transform is minimum, which is about 1/1154, 1/17, 1/178 times of that of the three conventional dictionaries. As can be seen from fig. 3 and 4, the stronger the sparse representation capability of the echo signal under the sparse dictionary is, the better the reconstructed image effect is, and the smaller the error is.

Mean square error of reconstructed image under table 14 sparse dictionaries

Sparse dictionary	OSD	DFT	DCT	DWT
					MSE	3.3e-05	0.0381	5.6e-04	0.0059

Fig. 5 shows a point target image reconstruction simulation experiment under 4 different sparse transformations, with a sampling rate of 50%. As can be seen from fig. 5, the quality of the point target reconstructed image under DFT transform is the worst, and serious artifacts are generated, while the resolution of the point target reconstructed image under DWT transform is poor, and distortion occurs. The original image can be well reconstructed under the DCT and OSD transformation, but the point target image reconstructed under the DCT transformation generates a small amount of artifacts in a near area. Table 2 lists the mean square error and reconstruction time for the reconstructed images under different sparse transforms. It can be clearly found by combining table 2 that the MSE of the point target image reconstructed under the OSD conversion is the minimum, which indicates that the reconstructed image is closest to the original image and the corresponding reconstruction time is also the shortest.

Mean square error and reconstruction time of reconstructed image under 24 sparse dictionaries in table

Sparse dictionary	OSD	DFT	DCT	DWT
					MSE	2.1e-04	0.0319	0.0011	0.0042
RT(s)	148.37	276.12	165.59	194.81

Fig. 6 shows simulation results of different sampling rates under the orthogonal sparse dictionary OSD transform. As can be seen from fig. 6, the quality of the reconstructed image at 50% and 40% sampling rates is the best, while the reconstructed image at 30% sampling rate is closer to the reconstructed image under DCT transform, and the reconstructed image at 20% sampling rate is similar to the reconstructed image under DWT transform. The reconstructed image at the sampling rate of 10% has artifacts in a near area and has distortion at other target points, and the imaging quality is poor. As can be seen from fig. 6 and table 3, under the same sparse dictionary transformation, the higher the data sampling rate is, the better the quality of the point target reconstructed image is, and the smaller the MSE is, but the longer the reconstruction time is.

TABLE 35 reconstructed image mean square error and reconstruction time at different sampling rates

Sampling rate	50％	40％	30％	20％	10％
						MSE	2.1e-04	3.4e-04	8.7e-04	0.0017	0.0063
RT(s)	148.37	113.75	71.78	35.65	20.44

FIG. 7 shows simulation results of the sound absorption spot target under different sparse transformations at a sampling rate of 50%. As can be seen from fig. 7, the reconstructed image under the OSD conversion is closest to the original image, and the imaging quality is the best. The original image can be accurately reconstructed even by DCT transformation, but the reconstruction quality is inferior to OSD transformation. The reconstructed image has the worst quality under the DFT and DWT conversion, and the original image cannot be accurately reconstructed. In order to more intuitively display the quality of the reconstructed image, the mean square error and the reconstruction time of the reconstructed image under different sparse transformations are listed in table 4. As is clear from table 4, the mean square error MSE under the OSD transform is minimum, and the reconstruction time is also minimum. In contrast, the mean square error MSE under DFT and DWT transforms is larger, and the reconstruction time is also relatively longer. As can be seen from fig. 7 and table 4, the quality of the reconstructed images obtained by the different sparse transformations is consistent with the image evaluation index value.

Mean square error and reconstruction time of reconstructed image under table 44 sparse dictionaries

Sparse dictionary	OSD	DFT	DCT	DWT
					MSE	6.8e-04	0.0148	0.0025	0.0125
RT(s)	15750.38	24166.47	21392.24	22601.59

Fig. 8 shows reconstructed images of the sound absorption spot target when different sampling rates are selected under the OSD conversion. The original image can be accurately reconstructed at the sampling rates of 50%, 40% and 30%, the scattering dark spots at the depths of the reconstructed image at the sampling rate of 20% cannot be well reconstructed, and the reconstructed image at the sampling rate of 10% has the worst quality and serious distortion, so that the scattering dark spots cannot be clearly distinguished. Comparing fig. 7 and 8, it is found that the quality of the reconstructed image at the DCT transform is close to that at the 30% sampling rate, and the quality of the reconstructed image at the DFT and DWT transforms is close to that at the 10% sampling rate. Table 5 lists the mean square error and reconstruction time for the reconstructed images at 5 different sampling rates. As can be seen from table 5, the mean square error MSE at 50% sampling rate is the smallest, but the reconstruction time is the longest. With the reduction of the sampling rate, the mean square error MSE increases, and the reconstruction time correspondingly decreases. As can be seen from fig. 8 and table 5, the higher the data sampling rate, the closer the reconstructed image is to the original image, the smaller the error, but the longer the reconstruction time.

TABLE 55 mean square error and reconstruction time for reconstructed images at different sampling rates

Sampling rate	50％	40％	30％	20％	10％
						MSE	6.8e-04	0.0012	0.0031	0.0064	0.0128
RT(s)	15750.38	10107.26	6987.73	4285.09	2206.18

Fig. 9 shows reconstructed images of imaging data geabr _0 provided by biomedical ultrasound laboratory of Michigan university under different sparse transforms, with a sampling rate of 30%. As is clear from fig. 9, the reconstructed image quality under OSD transform is the best, scattering spots and scattering points can be clearly distinguished, and the reconstructed image quality under DWT transform is inferior, while the reconstructed image quality under DCT transform is poor, especially the imaging quality at black dark spots is poor, the reconstructed image quality under DFT transform is the worst, and the image distortion is the most serious. Table 6 lists the mean square error and reconstruction time of the reconstructed image under different sparse transforms, and it can be seen from table 6 that the mean square error MSE is minimum and the reconstruction time is also minimum under OSD transform. The experimental result is similar to the previous simulation result, and the superiority of the sparse dictionary OSD provided by the invention is verified.

Mean square error and reconstruction time of reconstructed image under 64 sparse dictionaries in table

Sparse dictionary	OSD	DFT	DCT	DWT
					MSE	0.0069	0.0505	0.0235	0.0210
RT(s)	8379.68	17878.82	12795.05	11250.47

Finally, it is noted that the above-mentioned preferred embodiments illustrate rather than limit the invention, and that, although the invention has been described in detail with reference to the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.

Claims

1. an orthogonal sparse dictionary design method based on Chirp code, is characterized in that, this method may further comprise the steps:

S1: use the Chirp code excitation signal processed by the windowing function in the ultrasonic transmission signal;

S2: Process the received ultrasonic echo signal and re-describe it in matrix form;

S3: Combine the sparse representation of the sparse signal in the frequency domain to construct an orthogonal dictionary for the sparse representation of ultrasonic echoes;

S4: Use the measurement matrix to measure the sparse signal, and project the original signal from the high-dimensional space to the low-dimensional space;

S5: Solve the optimization problem through the reconstruction algorithm, and obtain the coefficient vector of the original signal;

S6: Restore the original signal by using the coefficient vector, so as to perform ultrasound imaging.

2. a kind of orthogonal sparse dictionary design method based on Chirp code according to claim 1, is characterized in that, in step S1, described window function w (k) is expressed as:

Wherein, K is the width of the added window function, and k is the position of the kth windowed function; the Chirp signal processed by the window function w(k) is used as the ultrasonic transmission signal.

3. a kind of orthogonal sparse dictionary design method based on Chirp code according to claim 1, is characterized in that, described step S2 specifically comprises the following steps:

S21: Under the scattering point model, the echo signal s _r (t) of the Chirp signal is expressed as:

Among them, f ₀ is the center frequency of the signal, T is the duration of the transmitted signal of the ultrasound system, t is the sampling time, γ is the frequency modulation rate, P is the number of scattering points, A _i and t _di represent the ith scattering point, respectively The scattering intensity and delay time; t _di =2r _i /c, _ri represents the distance from the ith point to the array element, and c is the speed of sound;

S22: The signal data processing adopts a fixed time width, and the signal with the same frequency and frequency modulation frequency as the Chirp code transmission signal is used as the reference signal, and it is subjected to frequency difference processing with the echo signal, and then digitized and quadrature detection; The Chirp code signal is processed, the reference signal s _ref (t) is expressed as:

Where f ₀ is the center frequency of the signal, t is the sampling time, γ is the frequency modulation rate, t _ref =2R _ref /c is the reference delay, and R _ref is the reference distance;

S23: The processed difference frequency output signal is: Conjugated with s _ref (t), then s _IF (t) is expressed as:

Among them, s _IF (t) is a linear combination of P point-frequency signals, which is sparse in the frequency domain;

S24: yes Sampling to get a time vector in: N is the sampling time dimension; let the sampling results of s _r (t), s _ref (t) and s _IF (t) at the sampling frequency f _s be respectively s _r , s _ref and s _IF , t=[t ₁ , t ₂ ,…,t _N ] ^T , then s _r , s _ref and s _IF are written in vector form as:

4. a kind of orthogonal sparse dictionary design method based on Chirp code according to claim 3, is characterized in that, described step S3 specifically comprises the following steps:

S31: Construct a dimension N×N matrix S from s _ref , and its elements satisfy:

Among them, m and n are the row and column numbers of elements in matrix S, respectively, s _ref (m) represents the mth element of s _ref , 1≤m, n≤N;

S32: Calculate the matrix of the frequency-domain sparse signal constructed by the fast Fourier transform as:

in, represents the nth column vector of matrix D, Indicates the size of the mth element in d _n , 1≤m, n≤N;

S33: Describe in matrix form From the construction process of S, the matrix after data processing is:

s _IF = S ^H ×s _r

Among them, ^SH is the conjugate transpose of S, and ^SH ×s _r represents the vector product of ^SH and s _r ;

S34: s _IF is formed by a linear combination of point-frequency signals, P is a finite value, and s _IF is sparse in matrix D, if its sparse vector is α, then s _IF = Dα, so we get:

s _IF = ^SH ×s _r =Dα;

S35: It is easy to obtain S ^H S=I from the structure of S, where I is an N×N unit matrix, that is, S is invertible, and S ⁻¹ = ^SH , S ⁻¹ is the inverse matrix of S, we can obtain:

s _r = SDα

Among them, α is a sparse coefficient vector, Ψ=SD is a sparse matrix, then s _r = Ψα, that is, s _r is sparse on the matrix Ψ;

S36: According to the composition of D in S32, it can be obtained:

Ψ ^H Ψ=(D ^H S ^H )SD=I

Among them, Ψ ^H and ^DH are the conjugate transposes of Ψ and D, respectively.

5. a kind of orthogonal sparse dictionary design method based on Chirp code according to claim 4, is characterized in that, described step S4 specifically comprises the following steps:

S41: take the sparse random measurement matrix as the measurement matrix Φ, and the construction method of the sparse random measurement matrix is as follows: first generate an all-zero matrix Φ of size M×N, and M<<N; then select q for each column of the matrix Φ position and set 1 at the selected position, and q<M;

S42: Measure the signal s _r with the measurement matrix Φ, and obtain the measured signal y as: y=Φs _r .

6. a kind of orthogonal sparse dictionary design method based on Chirp code according to claim 5, is characterized in that, described step S5 specifically comprises the following steps:

S51: Use the measurement signal y to solve the coefficient vector α:

y=Φs _r =ΦΨα=Θα

Among them, Θ=ΦΨ is the perception matrix;

S52: Solve α by y=Θα, that is, convert it into solving the optimization problem:

It is solved by the minimum l ₁ norm method, and the approximate value α' of α is obtained by the reconstruction algorithm.

7. A kind of orthogonal sparse dictionary design method based on Chirp code according to claim 6, it is characterized in that, described step S6 is specifically: restore original signal s _r by approximation value α' of coefficient vector α as:

s _r =Ψα′

The matrix Ψ is the orthogonal sparse dictionary, and ultrasonic imaging processing is performed after the original signal s _r is recovered.