Three-dimensional millimeter wave imaging method and system suitable for sparse MIMO array

Abstract

The application discloses a three-dimensional millimeter wave imaging method suitable for a sparse MIMO array, and comprises the following steps: placing an object to be measured in a predetermined imaging range; transmitting a stepping jump millimeter wave signal by a transmitting antenna of a sparse MIMO millimeter wave array; obtaining an electromagnetic wave signal reflected by the object as a return signal data S by a receiving antenna; using an equivalent phase center approximation on the sparse MIMO array, using a fast frequency domain algorithm RMA on a virtual full array obtained, and obtaining an image as an initial value X (0) ; extracting a z value corresponding to a maximum value of a certain pair of x and y to construct an observation matrix Ψ by using a spatial three-dimensional information obtained by the RMA, wherein x, y and z correspond to x, y and z axes in three-dimensional coordinates; introducing an l2 norm in a sparse Bayesian learning framework to construct a minimum iteration model based on a maximum posterior method, stopping iteration after a condition is met, and obtaining an X (i) matrix after taking a modulus, which is a reconstructed image. The application can obtain a high-quality optimized image under the condition of ensuring a high time calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the field of millimeter wave imaging technology, and in particular to a three-dimensional millimeter wave imaging method and system applicable to a sparse MIMO array. Background Art

[0002] For typical millimeter-wave imaging systems, the most direct way to improve resolution and imaging quality is to increase the signal frequency, increase the signal bandwidth, and increase the size of the synthetic aperture by adding more transmit and receive antennas. However, due to the actual system hardware complexity and engineering costs, as well as the inefficiency caused by complex systems and large data volumes, we need to abandon the traditional algorithm's requirement for full sampling in the time domain or frequency domain. Instead, we need to use other methods to reduce data processing while maintaining a larger synthetic aperture, thereby improving imaging efficiency. Summary of the Invention

[0003] The present invention aims to address, at least to some extent, one of the technical problems in the related art. To this end, one object of the present invention is to provide a three-dimensional millimeter-wave imaging method and system suitable for sparse MIMO arrays. This method solves the problems of correcting image distortion and undersampling imaging in sparse MIMO array three-dimensional imaging, shortening computation time while improving imaging quality.

[0004] According to the present invention, a three-dimensional millimeter wave imaging method applicable to a sparse MIMO array is proposed, and the method steps are as follows:

[0005] S1: Place the object to be measured within a predetermined imaging range. The transmitting antenna of the sparse MIMO millimeter wave array transmits a stepped millimeter wave signal. The receiving antenna obtains the electromagnetic wave signal reflected by the object as the echo signal data S, and then executes step S2.

[0006] S2: Use RMA to perform preliminary imaging on the echo signal data S. By using the equivalent phase center approximation for the sparse MIMO array, the fast frequency domain algorithm RMA is used on the obtained virtual full array, and the obtained image is used as the initial value X (0) ,The spatial three-dimensional information obtained by RMA is constructed by extracting the z value corresponding to the maximum value under a certain pair of x, y to construct the observation matrix Ψ, where x, y, and z correspond to the x, y, and z axes in the three-dimensional coordinates;

[0007] S3: In the framework of sparse Bayesian learning, the l2 norm is introduced to construct a minimization iterative model X based on the maximum a posteriori method. (i) , i represents the number of iterations, to limit the upper limit of the number of iterations or X (i) The rate of change is less than a constant as the condition for stopping iteration. When the condition is reached, the iteration is stopped and the obtained X (i) The reconstructed image is obtained by taking the modulus after matrixing.

[0008] Preferably, in step S1:

[0009] The imaging area is divided into three-dimensional grids of x, y, and z dimensions relative to the MIMO array. The number of grids in the three dimensions of x, y, and z is N respectively. x , N y , N z , using N T , N R Represents the number of transmitting antennas and receiving antennas, N k Indicates the number of frequency points, S(x t ,y t , x r ,y r , z0) represents the received echo signal data, x t 、y t 、x r 、y r and z0 represent the array coordinates of the transmitting antenna and receiving antenna in the MIMO sparse array, respectively. According to the propagation theory of electromagnetic waves, the mapping between the echo signal and the imaging grid scattering coefficient is as follows:

[0010]

[0011] Among them, κ(x, y, z) represents the scattering coefficient of each grid point in the spatial imaging area, j represents the imaginary unit, and D t Represents the distance from the spatial grid point to a certain transmitting antenna, D r Represents the distance from a spatial grid point to a receiving antenna.

[0012] Preferably, in step S2:

[0013] S21: Perform equivalent phase center approximation on the sparse MIMO array to obtain the full array signal S′(x m ,y m , k):

[0014]

[0015] Where k represents the wave vector, which is obtained by k = 2πf / c, f represents the frequency of the electromagnetic wave, c represents the speed of light, D m 、x m 、y m Represents the spatial grid point to D t With D r The distance between the equivalent phase centers at the midpoint of the corresponding transmit-receive pair and the coordinates of the midpoint;

[0016] S22: Use the fast frequency domain algorithm RMA. RMA decomposes the spherical wave into a superposition of plane waves according to the stationary phase theory:

[0017]

[0018] Thus we can get the expression of the scattering coefficient κ(x, y, z):

[0019]

[0020] where k x , k y are the Fourier variables relative to x and y, respectively, and their values ​​range from -2k to 2k, FT 2D , They represent 2D Fourier transform and 3D inverse Fourier transform respectively;

[0021] S23: Use the scattering coefficient κ(x, y, z) obtained by RMA as the initial value X (0) At the same time, the obtained three-dimensional spatial information is extracted by extracting the z value corresponding to the maximum value of a certain pair of x and y to construct the observation matrix Ψ.

[0022] Preferably, in step S3:

[0023] S31: According to the theory of compressed sensing, the mapping relationship between the vector Y represented by the echo signal, the spatial grid scattering coefficient X, and the observation matrix Ψ is as follows:

[0024] Y=ΨX+ζ

[0025]

[0026] Where Y is the vectorized echo signal S′(x m ,y m , k), X is the vectorized grid scattering coefficient κ(x, y, z), ζ represents the ambient noise with the same dimension as Y, and the observation matrix in represents complex space;

[0027] S32: The sparse term and penalty term are respectively in accordance with the following probability distribution as the prior probability:

[0028]

[0029] f(Y|X,ζ)∝CN(ΨX,ζI)

[0030] f(ζ)∝1

[0031] Where f(Y|X,ζ) represents the probability density function that obeys the complex Gaussian distribution, ΨX represents the expected value, ζI represents the covariance, ζ represents the environmental noise, I represents the unit matrix, and x n represents the nth element in the vectorized X, and q represents the sparse coefficient;

[0032] S33: Use the maximum a posteriori estimate to estimate X and ζ. After adding the l2 norm, the loss function is:

[0033]

[0034] Among them, M represents the number of elements in Y, N represents the number of elements in X, τ represents the weight coefficient of l2 norm, and X H represents the conjugate transpose of X;

[0035] S24: X H Differentiate and ζ so that Find X H And the iterative form of ζ:

[0036] X (i) =[Ψ H Ψ+ζ (i-1) (Λ (i-1) ) -1 +τζ (i-1) I] -1 Ψ H Y

[0037]

[0038] Where i represents the number of iterations, X (0) Take the value obtained by RMA in step S3, Λ (i-1) Represents a diagonal matrix, which is expressed as follows:

[0039]

[0040] The iteration stop condition is set to ||X (i) -X (i-1) ||2 / ||X (i) When ||2≤η or the number of iterations reaches the preset number, the iteration is stopped when the error of the i-th iteration reaches the preset condition or the number of iterations reaches the upper limit.

[0041] A system for constructing a three-dimensional millimeter wave imaging method suitable for a sparse MIMO array comprises: a frequency signal generating unit, a sparse MIMO array, a computer control unit, and an imaging area for carrying a target to be measured, wherein the signal output end of the frequency signal generating unit is connected to the signal input end of the sparse MIMO array, the signal output end of the computer control unit is connected to the signal input end of the sparse MIMO array, and the signal output end of the sparse MIMO array is connected to the signal input end of the computer control unit.

[0042] The beneficial effects of the present invention are:

[0043] (1) The images obtained by sparse MIMO array with fast frequency domain algorithm have large distortion and low image quality. The present invention uses compressed sensing for the image correction process of sparse MIMO array RMA imaging. The computing time used is greatly reduced compared with the traditional algorithm, and the image quality is greatly improved compared with RMA. At a lower sampling rate, the artifacts and clutter caused by RMA and strong undersampling can be better eliminated, and the computing time is greatly shortened compared with the traditional BP algorithm.

[0044] (2) Compared with the traditional compressed sensing algorithm, the l2 norm introduced in the present invention can give a relatively dense sparse solution, which is consistent with the characteristic that the signal reflection intensity of some areas of the object in the actual imaging area is weak, so that the sparse reconstruction can more completely reconstruct the complete object and edge details. Compared with the traditional compressed sensing algorithm, it can reach the iterative convergence condition faster and improve the computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In the attached figure:

[0046] Figure 1 This is a flow chart of the three-dimensional millimeter wave imaging method applicable to sparse MIMO arrays proposed by the present invention;

[0047] Figure 2 A system block diagram of the three-dimensional millimeter wave imaging method for sparse MIMO arrays proposed in this invention;

[0048] Figure 3 This is the reconstruction diagram of the sparse MIMO array data of the actual tower model using the traditional BP algorithm proposed in this invention;

[0049] Figure 4 This is the reconstruction diagram of the sparse MIMO array data of the actual tower model using the traditional compressed sensing algorithm proposed in this invention;

[0050] Figure 5 This is a reconstruction diagram of the sparse MIMO array data of an actual tower model using the method proposed in this invention.

[0051] In the figure: 21 - frequency signal generating unit, 22 - sparse MIMO array, 23 - computer control unit, 24 - imaging area, 25 - target to be measured. DETAILED DESCRIPTION

[0052] The problem of not significantly reducing the synthetic aperture size can be solved by sparse MIMO arrays. By using multiple transmitters and multiple receivers instead of a single transmitter and receiver, data acquisition speed can be increased while reducing hardware complexity. While traditional algorithms are still applicable to imaging with sparse MIMO arrays, their efficiency is low. Therefore, we prefer to use fast frequency-domain algorithms to achieve imaging goals. Typically, applying fast frequency-domain algorithms to sparse MIMO arrays inevitably results in image blur and distortion. This is due to the phase difference introduced when introducing certain approximations. To address this issue, compressed sensing (CS) can be used to correct the image generated by the fast frequency-domain algorithm. CS algorithms can reconstruct high-dimensional signals from known low-dimensional signals, while allowing image restoration at lower sampling rates. This significantly improves both the accuracy of frequency-domain algorithm image correction and the reduction of data computation and computational efficiency.

[0053] In this embodiment, referring to Figure 1 , a three-dimensional millimeter wave imaging method applicable to sparse MIMO arrays, comprising:

[0054] S1: Place the object to be measured within a predetermined imaging range. The transmitting antenna of the sparse MIMO millimeter wave array transmits a stepped millimeter wave signal. The receiving antenna obtains the electromagnetic wave signal reflected by the object as the echo signal data S, and then executes step S2.

[0055] Specifically, in step S1:

[0056] The imaging area is divided into three-dimensional grids of x, y, and z dimensions relative to the MIMO array. The number of grids in the three dimensions of x, y, and z is N respectively. x , N y , N z , using N T , N R Represents the number of transmitting antennas and receiving antennas, N k Indicates the number of frequency points. In this embodiment, the millimeter wave frequency transmitted by the system is 30-38 GHz, and the method is step frequency hopping. Each hop is 160 MHz, with a total of 51 frequency collection points. According to the propagation theory of electromagnetic waves, S(x t ,y t , x r ,y r , z0) represents the received echo signal data, x t 、y t 、x r 、y r and z0 represent the array coordinates of the transmitting antenna and receiving antenna in the MIMO sparse array, respectively. According to the propagation theory of electromagnetic waves, the mapping between the echo signal and the imaging grid scattering coefficient is as follows:

[0057]

[0058] Among them, κ(x, y, z) represents the scattering coefficient of each grid point in the spatial imaging area, j represents the imaginary unit, and D t Represents the distance from the spatial grid point to a certain transmitting antenna, D r Represents the distance from a spatial grid point to a receiving antenna.

[0059] S2: Use RMA to perform preliminary imaging on the echo signal data S. By using the equivalent phase center approximation for the sparse MIMO array, the fast frequency domain algorithm RMA is used on the obtained virtual full array, and the obtained image is used as the initial value X (0) ,The spatial three-dimensional information obtained by RMA is constructed by extracting the z value corresponding to the maximum value under a certain pair of x, y to construct the observation matrix Ψ, where x, y, and z correspond to the x, y, and z axes in the three-dimensional coordinates;

[0060] In this embodiment:

[0061] S21: Perform equivalent phase center approximation on the sparse MIMO array to obtain the full array signal S′(x m ,y m , k):

[0062]

[0063] Where k represents the wave vector, which is obtained by k = 2πf / c, f represents the frequency of the electromagnetic wave, c represents the speed of light, D m 、x m 、y m Represents the spatial grid point to D t With D r The distance between the equivalent phase centers at the midpoint of the corresponding transmit-receive pair and the coordinates of the midpoint;

[0064] S22: Use the fast frequency domain algorithm RMA. RMA decomposes the spherical wave into a superposition of plane waves according to the stationary phase theory:

[0065]

[0066] Thus we can get the expression of the scattering coefficient κ(x, y, z):

[0067]

[0068] where k x , k y are the Fourier variables relative to x and y, respectively, and their values ​​range from -2k to 2k, FT 2D , They represent 2D Fourier transform and 3D inverse Fourier transform respectively;

[0069] S23: Use the scattering coefficient κ(x, y, z) obtained by RMA as the initial value X (0) At the same time, the obtained three-dimensional spatial information is extracted by extracting the z value corresponding to the maximum value of a certain pair of x and y to construct the observation matrix Ψ.

[0070] S3: In the framework of sparse Bayesian learning, the l2 norm is introduced to construct a minimization iterative model X based on the maximum a posteriori method. (i) , i represents the number of iterations, to limit the upper limit of the number of iterations or X (i) The rate of change is less than a constant as the condition for stopping iteration. When the condition is reached, the iteration is stopped and the obtained X (i) The reconstructed image is obtained by taking the modulus after matrixing.

[0071] In this embodiment:

[0072] S31: According to the theory of compressed sensing, the mapping relationship between the vector Y represented by the echo signal, the spatial grid scattering coefficient X, and the observation matrix Ψ is as follows:

[0073] Y=ΨX+ζ

[0074]

[0075] Where Y is the vectorized echo signal S′(x m ,y m , k), X is the vectorized grid scattering coefficient κ(x, y, z), ζ represents the ambient noise with the same dimension as Y, and the observation matrix in represents complex space;

[0076] S32: The sparse term and penalty term are respectively in accordance with the following probability distribution as the prior probability:

[0077]

[0078] f(Y|X,ζ)∝CN(ΨX,ζI)

[0079] f(ζ)∝1

[0080] Where f(Y|X,ζ) represents the probability density function that obeys the complex Gaussian distribution, ΨX represents the expected value, ζI represents the covariance, ζ represents the environmental noise, I represents the unit matrix, and x n represents the nth element in the vectorized X, and q represents the sparse coefficient;

[0081] S33: Use the maximum a posteriori estimate to estimate X and ζ. After adding the l2 norm, the loss function is:

[0082]

[0083] Among them, M represents the number of elements in Y, N represents the number of elements in X, τ represents the weight coefficient of l2 norm, and X H represents the conjugate transpose of X;

[0084] S34: X H Differentiate and ζ so that Find X H And the iterative form of ζ:

[0085] X (i) =[Ψ H Ψ+ζ (i-1) (Λ (i-1) ) -1 +τζ (i-1) I] -1 Ψ H Y

[0086]

[0087] Where i represents the number of iterations, X (0) Take the value obtained by RMA in step S3, Λ (i-1) Represents a diagonal matrix, which is expressed as follows:

[0088]

[0089] The iteration stop condition is set to ||X (i) -X (i-1) ||2 / ||X (i) || 2≤η or the number of iterations reaches a preset number, which in this embodiment is 6. When the error of the i-th iteration reaches a preset condition or the number of iterations reaches an upper limit, the iteration is stopped.

[0090] In another embodiment, Figure 2 As shown:

[0091] A system for constructing a three-dimensional millimeter wave imaging method suitable for sparse MIMO arrays, comprising:

[0092] The frequency signal generating unit 21 is used to generate a step-hopping millimeter wave signal, which is an agile frequency source in this embodiment;

[0093] The sparse MIMO array 22 is used to transmit electromagnetic waves and receive echo signals of the object to be measured. In this embodiment, it is a boundary sparse antenna array;

[0094] The computer control unit 23 is used to transmit control signals to enable the sparse MIMO array 22 to transmit and receive electromagnetic wave signals, and receive and store echo data;

[0095] The imaging area 24 is used to carry the target 25 to be measured;

[0096] The signal output end of the frequency signal generating unit 21 is connected to the signal input end of the sparse MIMO array 22, the signal output end of the computer control unit 23 is connected to the signal input end of the sparse MIMO array 22, and the signal output end of the sparse MIMO array 22 is connected to the signal input end of the computer control unit 23.

[0097] Experiments have demonstrated the role of this invention in sparse MIMO array imaging:

[0098] Experimental parameters: The system transmits millimeter-wave frequencies between 30 and 38 GHz, using a step-frequency hopping method, with each hop reaching 160 MHz, for a total of 51 frequency acquisition points. The imaging area is 0.4 m × 0.4 m × 0.06 m.

[0099] Figure 3 This is the reconstructed image of the sparse MIMO array of the actual tower model using the traditional BP algorithm. Figure 4 is the reconstructed image of the traditional compressed sensing algorithm, Figure 5 This is the image reconstruction diagram of the algorithm applied in the present invention. All reconstructed images are obtained at a sampling rate of 8.33%. Compared with the traditional BP algorithm, both the traditional compressed sensing algorithm and the algorithm of the present invention have obvious grating lobes caused by undersampling, and the background clutter is also less than that of the BP algorithm. Compared with the reconstructed image of the traditional compressed sensing algorithm, the algorithm proposed in the present invention takes the BP algorithm as the benchmark, and its reconstructed image has higher integrity and more uniform intensity of edge details.

[0100] Table 1 shows the time comparison of the traditional BP algorithm, the traditional compressed sensing algorithm and the algorithm proposed in this invention. The calculation time is only 3.43% of the traditional BP algorithm. Figure 3 、 Figure 4 、 Figure 5 From the comparison, we can see that the image reconstructed by the algorithm proposed in the present invention has higher quality than the traditional compressed sensing algorithm and is closer to the reconstructed image of the traditional BP algorithm, while also significantly improving the computational efficiency.

[0101] Table 1 Comparison of calculation time of different algorithms

[0102]

[0103]

Claims

1. A three-dimensional millimeter wave imaging method suitable for sparse MIMO arrays, characterized in that: The method steps are as follows: S1: Place the object to be measured within a predetermined imaging range. The transmitting antenna of the sparse MIMO millimeter wave array transmits a stepped millimeter wave signal. The receiving antenna obtains the electromagnetic wave signal reflected by the object as the echo signal data S, and then executes step S2. S2: Use RMA to perform preliminary imaging on the echo signal data S. By using the equivalent phase center approximation for the sparse MIMO array, the fast frequency domain algorithm RMA is used on the obtained virtual full array, and the obtained image is used as the initial value X (0) ,The spatial three-dimensional information obtained by RMA is constructed by extracting the z value corresponding to the maximum value under a certain pair of x, y to construct the observation matrix Ψ, where x, y, and z correspond to the x, y, and z axes in the three-dimensional coordinates; S3: In the framework of sparse Bayesian learning, the l2 norm is introduced to construct a minimization iterative model X based on the maximum a posteriori method. (i) , i represents the number of iterations, to limit the upper limit of the number of iterations or X (i) The rate of change is less than a constant as the condition for stopping iteration. When the condition is reached, the iteration is stopped and the obtained X (i) The reconstructed image is obtained by taking the modulus after matrixing.

2. The three-dimensional millimeter wave imaging method applicable to a sparse MIMO array according to claim 1, characterized in that: In step S1: The imaging area is divided into three-dimensional grids of x, y, and z dimensions relative to the MIMO array. The number of grids in the three dimensions of x, y, and z is N respectively. x , N y , N z , using N T , N R Represents the number of transmitting antennas and receiving antennas, N k Indicates the number of frequency points, S(x t ,y t , x r ,y r , z0) represents the received echo signal data, x t 、y t 、x r 、y r and z0 represent the array coordinates of the transmitting antenna and receiving antenna in the MIMO sparse array, respectively. According to the propagation theory of electromagnetic waves, the mapping between the echo signal and the imaging grid scattering coefficient is as follows: Among them, κ(x, y, z) represents the scattering coefficient of each grid point in the spatial imaging area, j represents the imaginary unit, and D t Represents the distance from the spatial grid point to a certain transmitting antenna, D r Represents the distance from a spatial grid point to a receiving antenna.

3. The three-dimensional millimeter wave imaging method applicable to a sparse MIMO array according to claim 2, characterized in that: In step S2: S21: Perform equivalent phase center approximation on the sparse MIMO array to obtain the full array signal S′(x m ,y m , k): Where k represents the wave vector, which is obtained by k = 2πf / c, f represents the frequency of the electromagnetic wave, c represents the speed of light, D m 、x m 、y m Represents the spatial grid point to D t With D r The distance between the equivalent phase centers at the midpoint of the corresponding transmit-receive pair and the coordinates of the midpoint; S22: Use the fast frequency domain algorithm RMA. RMA decomposes the spherical wave into a superposition of plane waves according to the stationary phase theory: Thus we can get the expression of the scattering coefficient κ(x, y, z): where k x , k y are the Fourier variables relative to x and y, respectively, and their values ​​range from -2k to 2k, FT 2D , They represent 2D Fourier transform and 3D inverse Fourier transform respectively; S23: Use the scattering coefficient k(x, y, z) obtained by RMA as the initial value X (0) At the same time, the obtained three-dimensional spatial information is extracted by extracting the z value corresponding to the maximum value of a certain pair of x and y to construct the observation matrix Ψ.

4. The three-dimensional millimeter wave imaging method applicable to a sparse MIMO array according to claim 3, characterized in that: In step S3: S31: According to the theory of compressed sensing, the mapping relationship between the vector Y represented by the echo signal, the spatial grid scattering coefficient X, and the observation matrix Ψ is as follows: Y=ψX+ζ Where Y is the vectorized echo signal S′(x m ,y m , k), X is the vectorized grid scattering coefficient κ(x, y, z), ζ represents the ambient noise with the same dimension as Y, and the observation matrix in represents complex space; S32: The sparse term and penalty term are respectively in accordance with the following probability distribution as the prior probability: f(YX,ζ)∝CN(ψX,ζI) f(ζ)∝1 Where f(Y|X,ζ) represents the probability density function that obeys the complex Gaussian distribution, ΨX represents the expected value, ζI represents the covariance, ζ represents the environmental noise, I represents the unit matrix, and x n represents the nth element in the vectorized X, and q represents the sparse coefficient; S33: Use the maximum a posteriori estimate to estimate X and ζ. After adding the l2 norm, the loss function is: Among them, M represents the number of elements in Y, N represents the number of elements in X, τ represents the weight coefficient of l2 norm, and X H represents the conjugate transpose of X; S34: X H Differentiate and ζ so that Find X H And the iterative form of ζ: X (i) =[Ψ H P+g (i-1) (A (i-1) ) -1 +j (i-1) I] -1 P H Y Where i represents the number of iterations, X (0) Take the value obtained by RMA in step S3, Λ (i-1) Represents a diagonal matrix, which is expressed as follows: The iteration stop condition is set to ||X (i) -X (i-1) ||2 / ||X (i) When ||2≤η or the number of iterations reaches the preset number, the iteration is stopped when the error of the i-th iteration reaches the preset condition or the number of iterations reaches the upper limit.

5. A system for constructing a three-dimensional millimeter wave imaging method suitable for a sparse MIMO array according to any one of claims 1 to 4, characterized in that: include: A frequency signal generating unit (21), a sparse MIMO array (22), a computer control unit (23), and an imaging area (24) for carrying a target to be measured (25), wherein the signal output end of the frequency signal generating unit (21) is connected to the signal input end of the sparse MIMO array (22), the signal output end of the computer control unit (23) is connected to the signal input end of the sparse MIMO array (22), and the signal output end of the sparse MIMO array (22) is connected to the signal input end of the computer control unit (23).

Images