A low-complexity InISAR 3D imaging method based on joint sparse restoration

Abstract

The present invention relates to the field of radar technology, and in particular to a low-complexity InISAR three-dimensional imaging method based on joint sparse recovery, comprising the following steps: establishing the geometric structure of an InISAR imaging system, and establishing an InISAR imaging sparse reconstruction model that conforms to a JSM-2 model according to the geometric structure of the InISAR imaging system; performing unitary transformation on the established InISAR imaging sparse reconstruction model that conforms to the JSM-2 model according to unitary transformation approximate message passing UTAMP, and establishing a Bayesian learning model for joint sparse recovery of InISAR imaging; constructing a factor graph of the InISAR imaging joint sparse recovery Bayesian learning model; designing a message update rule for each variable therein according to the factor graph of the established joint sparse recovery Bayesian learning model; and reconstructing a target three-dimensional image through interference processing and scattering point distance measurement after obtaining two-dimensional images of three channels according to the message update rule. The present invention improves the reconstruction accuracy of three-dimensional images, has better noise suppression suppression capability, and greatly reduces the algorithm calculation complexity.

Description

Technical Field

[0001] The invention relates to the field of radar technology, and in particular to a low-complexity InISAR three-dimensional imaging method based on joint sparse recovery. Background Art

[0002] As an information perception equipment that can image all kinds of moving targets all day and all weather, Inverse Synthetic Aperture Radar (ISAR) has important application value in many fields. ISAR can perform two-dimensional high-resolution imaging of moving targets, and the imaging results can be further used for target recognition. However, the ISAR two-dimensional image is only a projection of the target on the imaging plane, which cannot provide the height information of the target. The imaging plane changes with the movement of the target, and it is difficult to determine when it becomes the image plane, which brings great difficulties to target recognition. Unlike ISAR, Interferometric ISAR (InISAR) can use multiple antennas (usually three) to reconstruct the three-dimensional image of the moving target by interferometric processing of three two-dimensional images. The three-dimensional image can provide richer target information and overcome the influence of the image plane, which is more conducive to target recognition.

[0003] Limited pulse data and sparse aperture data are often encountered in ISAR and InISAR imaging. For InISAR 3D imaging, in the case of limited pulse data or sparse aperture data, traditional Fourier transform-based imaging methods are difficult to obtain high-resolution, well-focused 2D ISAR images, and therefore cannot accurately reconstruct 3D images. In response to this situation, imaging algorithms based on compressed sensing (CS) have been widely studied. Such algorithms can obtain high-resolution, well-focused 2D images, which helps to obtain better 3D imaging results. Sparse Bayesian learning (SBL), as a CS method based on statistical models, has many advantages and has been successfully used in ISAR 2D imaging and InISAR 3D imaging.

[0004] However, the existing SBL-based InISAR imaging algorithms still have some shortcomings. First, SBL algorithms have high computational complexity, especially in InISAR imaging applications where the amount of data is very large, and it is difficult for such algorithms to complete InISAR real-time imaging. Second, the multi-channel joint sparse SBL InISAR three-dimensional imaging algorithm SM-SBL (Sequential Multiple SBL) in the prior art assumes that each channel has the same noise, but in actual InISAR imaging, the noise levels of the three channels may be different, which will cause the SM-SBL model to not match the actual situation, and ultimately lead to algorithm performance loss. Third, the algorithm is not robust enough to noise, especially in low signal-to-noise ratio conditions, and the algorithm's three-dimensional reconstruction accuracy is low. Summary of the invention

[0005] In view of the problems existing in the prior art, the object of the present invention is to propose a low-complexity InISAR three-dimensional imaging method based on joint sparse recovery.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions to achieve it.

[0007] A low-complexity InISAR three-dimensional imaging method based on joint sparse recovery includes the following steps:

[0008] Step 1, establishing the geometric structure of the InISAR imaging system, and establishing an InISAR imaging sparse reconstruction model that conforms to the JSM-2 model according to the geometric structure of the InISAR imaging system;

[0009] Step 2, according to the unitary transformation approximate message passing UTAMP (Approximate Message Passing With Unitary Transformation), the InISAR imaging sparse reconstruction model established in accordance with the JSM-2 model is unitary transformed, and a Bayesian learning model for InISAR imaging joint sparse recovery is established;

[0010] Step 3, constructing a factor graph of the InISAR imaging joint sparse restoration Bayesian learning model;

[0011] Step 4, designing a message update rule for each variable in the established joint sparse recovery Bayesian learning model according to the factor graph;

[0012] Step 5: After obtaining the two-dimensional images of the three channels according to the message update rule, the target three-dimensional image is reconstructed through interference processing and scattering point distance measurement.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] 1. The joint sparsity between different channels is utilized to improve the matching degree between the two-dimensional images of different channels, thereby improving the reconstruction accuracy of the three-dimensional image;

[0015] 2. The two-layer MMV model constructed takes into account that the sparse signal of each channel is a two-dimensional sparse signal and different channels may have different noises. Therefore, the imaging method of the present invention has better noise suppression ability and is more robust to noise processing, and is particularly suitable for the situation where the noises of each channel are different;

[0016] 3. Matrix-vector multiplication is used to replace the matrix inversion operation in the traditional Bayesian learning algorithm, which greatly reduces the computational complexity of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Figure 1 It is a flow chart of the low-complexity InISAR three-dimensional imaging method based on joint sparse recovery of the present invention;

[0019] Figure 2 Schematic diagram of the geometric structure of the InISAR imaging system;

[0020] Figure 3 A factor graph of a joint posterior probability density function of a low-complexity InISAR three-dimensional imaging method based on joint sparse recovery according to the present invention;

[0021] Figure 4 Schematic diagram of the target model used for simulation experiments;

[0022] Figure 5 The two-dimensional imaging results of three channels of the InISAR system obtained by the UTAMP-JSR algorithm of the present invention under the simulation data experiment; Figure 5 (a) is the two-dimensional imaging result of the C channel; Figure 5 (b) is the two-dimensional imaging result of the V channel; Figure 5 (c) is the two-dimensional imaging result of the H channel;

[0023] Figure 6 The two-dimensional imaging results of three channels of the InISAR system obtained by the existing SM-SBL algorithm under the simulation data experiment; Figure 6 (a) is the two-dimensional imaging result of the C channel; Figure 6 (b) is the two-dimensional imaging result of the V channel; Figure 6 (c) is the two-dimensional imaging result of the H channel;

[0024] Figure 7The two-dimensional imaging results of three channels of the InISAR system obtained by the existing SBL algorithm under the simulation data experiment; Figure 7 (a) is the two-dimensional imaging result of the C channel; Figure 7 (b) is the two-dimensional imaging result of the V channel; Figure 7 (c) is the two-dimensional imaging result of the H channel;

[0025] Figure 8 The two-dimensional imaging results of three channels of the InISAR system obtained by the existing RD algorithm under the simulation data experiment; Figure 8 (a) is the two-dimensional imaging result of the C channel; Figure 8 (b) is the two-dimensional imaging result of the V channel; Figure 8 (c) is the two-dimensional imaging result of the H channel;

[0026] Fig. 9 This is the relationship diagram between the correlation coefficient and signal-to-noise ratio of the four algorithms under the simulation data experiment; Fig. 9 (a) is the relationship between the correlation coefficient and signal-to-noise ratio between the C channel and the H channel; Fig. 9 (b) is the relationship between the correlation coefficient and signal-to-noise ratio between the C channel and the V channel;

[0027] Fig.10 This is the relationship between the correlation coefficient and the number of pulses of the four algorithms under the condition of simulating a signal-to-noise ratio of 10dB; Fig.10 (a) is the relationship between the correlation coefficient and the pulse number between the C channel and the H channel; Fig.10 (b) is the relationship between the correlation coefficient between the C channel and the V channel and the pulse number.

[0028] Fig.11 It is the three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention under the simulation data experiment; Fig.11 (a) is a three-dimensional image of the three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention; Fig.11 (b) is a top view of a three-dimensional image of a three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention; Fig.11 (c) is a side view of a three-dimensional image of a three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention; Fig.11 (d) is a front view of a three-dimensional image of a three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention;

[0029] Fig.12 This is the 3D reconstruction result of the SM-SBL algorithm under the simulation data experiment; Fig.12 (a) is the 3D image of the 3D reconstruction result of the SM-SBL algorithm; Fig.12 (b) is a top view of the 3D image of the 3D reconstruction result of the SM-SBL algorithm; Fig.12(c) is the side view of the 3D image of the 3D reconstruction result of the SM-SBL algorithm; Fig.12 (d) is the front view of the 3D image of the 3D reconstruction result of the SM-SBL algorithm;

[0030] Fig.13 This is the 3D reconstruction result of the SBL algorithm under the simulation data experiment; Fig.13 (a) is the 3D image of the 3D reconstruction result of the SBL algorithm; Fig.13 (b) is a top view of the 3D image of the 3D reconstruction result of the SBL algorithm; Fig.13 (c) is the side view of the 3D image of the 3D reconstruction result of the SBL algorithm; Fig.13 (d) is the front view of the 3D image of the 3D reconstruction result of the SBL algorithm;

[0031] Fig.14 This is the 3D reconstruction result of the RD algorithm under the simulation data experiment; Fig.14 (a) is the 3D image of the 3D reconstruction result of the RD algorithm; Fig.14 (b) is a top view of the 3D image of the 3D reconstruction result of the RD algorithm; Fig.14 (c) is the side view of the 3D image of the 3D reconstruction result of the RD algorithm; Fig.14 (d) is the front view of the 3D image of the 3D reconstruction result of the RD algorithm;

[0032] Fig.15 This is the relationship between RMSE and signal-to-noise ratio of the coordinates reconstructed by the four algorithms under the simulation data experiment; Fig.15 (a) is the relationship between RMSE and signal-to-noise ratio of the reconstruction results of the azimuth coordinate ξ of the four algorithms; Fig.15 (b) Four algorithms for height coordinates The relationship between RMSE and signal-to-noise ratio of the reconstruction results;

[0033] Fig.16 This is the relationship between the RMSE and pulse number of the four algorithms for simulating the reconstruction of coordinates under the condition of a simulation signal-to-noise ratio of 10dB; Fig.16 (a) is the relationship between RMSE and pulse number of the reconstruction results of the azimuth coordinate ξ of the four algorithms; Fig.16 (b) Four algorithms for height coordinates The relationship between RMSE and pulse number of the reconstruction result;

[0034] Fig.17 This is a physical picture of PIRAD;

[0035] Fig.18 This is a physical picture of the training ship target Astice;

[0036] Fig.19The two-dimensional imaging results of three channels of the InISAR system obtained by the UTAMP-JSR algorithm of the present invention under the measured data experiment; Fig.19 (a) is the two-dimensional imaging result of the C channel; Fig.19 (b) is the two-dimensional imaging result of the V channel; Fig.19 (c) is the two-dimensional imaging result of the H channel;

[0037] Fig. 20 The two-dimensional imaging results of three channels of the InISAR system obtained by the existing SM-SBL algorithm under the measured data experiment; Fig. 20 (a) is the two-dimensional imaging result of the C channel; Fig. 20 (b) is the two-dimensional imaging result of the V channel; Fig. 20 (c) is the two-dimensional imaging result of the H channel;

[0038] Fig.21 The two-dimensional imaging results of three channels of the InISAR system obtained by the existing SBL algorithm under the measured data experiment; Fig.21 (a) is the two-dimensional imaging result of the C channel; Fig.21 (b) is the two-dimensional imaging result of the V channel; Fig.21 (c) is the two-dimensional imaging result of the H channel;

[0039] Fig. 22 The two-dimensional imaging results of three channels of the InISAR system obtained by the existing RD algorithm under the measured data experiment; Fig. 22 (a) is the two-dimensional imaging result of the C channel; Fig. 22 (b) is the two-dimensional imaging result of the V channel; Fig. 22 (c) is the two-dimensional imaging result of the H channel;

[0040] Fig.23 This is the relationship between the correlation coefficients and pulse numbers of the four algorithms under the measured data experiment; Fig.23 (a) is the relationship between the correlation coefficient and the pulse number between the C channel and the H channel; Fig.23 (b) is the relationship between the correlation coefficient and the pulse number between the C channel and the V channel;

[0041] Fig.24 It is the three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention under the actual data experiment; Fig.24 (a) is a three-dimensional image of the three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention; Fig.24 (b) is a top view of a three-dimensional image of a three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention; Fig.24 (c) is a side view of a three-dimensional image of a three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention; Fig.24(d) is a front view of a three-dimensional image of a three-dimensional reconstruction result of the UTAMP-JSR algorithm of the present invention;

[0042] Fig.25 This is the 3D reconstruction result of the SM-SBL algorithm under the measured data experiment; Fig.25 (a) is the 3D image of the 3D reconstruction result of the SM-SBL algorithm; Fig.25 (b) is a top view of the 3D image of the 3D reconstruction result of the SM-SBL algorithm; Fig.25 (c) is the side view of the 3D image of the 3D reconstruction result of the SM-SBL algorithm; Fig.25 (d) is the front view of the 3D image of the 3D reconstruction result of the SM-SBL algorithm;

[0043] Fig.26 This is the 3D reconstruction result of the SBL algorithm under the measured data experiment; Fig.26 (a) is the 3D image of the 3D reconstruction result of the SBL algorithm; Fig.26 (b) is a top view of the 3D image of the 3D reconstruction result of the SBL algorithm; Fig.26 (c) is the side view of the 3D image of the 3D reconstruction result of the SBL algorithm; Fig.26 (d) is the front view of the 3D image of the 3D reconstruction result of the SBL algorithm;

[0044] Fig. 27 This is the 3D reconstruction result of the RD algorithm under the measured data experiment; Fig. 27 (a) is the 3D image of the 3D reconstruction result of the RD algorithm; Fig. 27 (b) is a top view of the 3D image of the 3D reconstruction result of the RD algorithm; Fig. 27 (c) is the side view of the 3D image of the 3D reconstruction result of the RD algorithm; Fig. 27 (d) is the front view of the 3D image reconstructed by the RD algorithm. DETAILED DESCRIPTION

[0045] The embodiments of the present invention will be described in detail below with reference to examples, but those skilled in the art will understand that the following examples are only used to illustrate the present invention and should not be construed as limiting the scope of the present invention.

[0046] refer to Figure 1 , is a flow chart of a low-complexity InISAR three-dimensional imaging method based on joint sparse recovery of the present invention; the low-complexity InISAR three-dimensional imaging method based on joint sparse recovery comprises the following steps:

[0047] Step 1: Establish the geometric structure of the InISAR imaging system, and establish an InISAR imaging sparse reconstruction model that conforms to the JSM-2 model based on the geometric structure of the InISAR imaging system.

[0048] Specifically, refer to Figure 2 , is a schematic diagram of the geometric structure of the InISAR imaging system;

[0049] Sub-step 1.1, establish the geometry of the InISAR imaging system;

[0050] The InISAR imaging system consists of a transmitting and receiving antenna C, a receiving antenna V and a receiving antenna H. The C antenna is located at the coordinate origin O of the radar coordinate system (O, U, G, W), and the receiving antenna V and the receiving antenna H are located on the W axis and U axis of the radar coordinate system (O, U, G, W), respectively. The baseline lengths of the receiving antenna V and the receiving antenna H are L 1 and L 2 ;

[0051] Take the geometric center O′ of the far-field target as the origin and establish the target coordinate system and a reference coordinate system (O′, X, Y, Z); wherein the geometric center O′ of the target is located on the G axis of the radar coordinate system (O, U, G, W), the X axis and Y axis of the reference coordinate system (O′, X, Y, Z) are respectively parallel to the W axis and U axis of the radar coordinate system (O, U, G, W) and have the same direction, and the Z axis of the reference coordinate system (O′, X, Y, Z) and the G axis of the radar coordinate system (O, U, G, W) are on the same straight line and have the same direction.

[0052] Define the angle between the target speed v and the X-axis in the reference coordinate system (O′, X, Y, Z) as α; define is the rotation parameter of roll motion; is the rotation parameter of pitch motion; is the rotation parameter of yaw motion; defines any scattering point p on the target in the target coordinate system The coordinates on Define R Λp is the distance between antenna Λ and the scattering point p, where Λ represents one of the transmitting and receiving antenna C, the receiving antenna V and the receiving antenna H, that is, (Λ∈{C, V, H}).

[0053] In sub-step 1.2, it is assumed that the linear frequency modulation signal transmitted by the transmitting and receiving antenna C is as shown in equation (1):

[0054]

[0055] In formula (1), rect() is the rectangular window function; T p is the pulse width; Fast time; t m is the slow time, and t m =mT, m=0, ...M-1, where T is the pulse repetition period; fc is the signal carrier frequency, and κ is the modulation frequency.

[0056] Substep 1.3, assuming that the target consists of P scattering points, x p is the scattering intensity of the pth scattering point p. After demodulation and distance compression of the received signal of antenna Λ, it can be expressed as formula (2):

[0057]

[0058] In formula (2), Λ represents one of the transmitting and receiving antennas C, V and H, that is, (Λ∈{C, V, H}); c is the speed of light; B is the signal bandwidth; R Λp (t m ) indicates t m The instantaneous distance from antenna Λ to scattering point p at time t is shown in formula (3):

[0059]

[0060] In formula (3), R o′ Represents the distance from the radar to the geometric center of the target at the initial moment, R o′ +ΔR o′ (t m ) represents the distance between antenna C and the target geometric center O′, ΔR o′ (t m ) is the distance change caused by the target translation, ΔR p (t m ) is the distance change caused by the target rotation; L 1 β p (t m ) and L 2 α p (t m ) is the distance difference caused by antenna position diversity, L 1 , L 2 are the baseline lengths of the receiving antenna V and the receiving antenna H respectively; β p (t m ) represents the instantaneous pitch angle of the scattering point p, α p (t m ) represents the instantaneous azimuth of the scattering point p;

[0061] In the limited imaging time, the target rotation angle is usually small, so ΔR p (t m ) is shown in formula (4):

[0062]

[0063] In formula (4), f pis the Doppler frequency of the scattering point p, ω r is the rotation parameter of rolling motion, ω y is the rotation parameter of yaw motion; and They are ω r and ω y The vector form of ω r and ω y Respectively and are numerically equal.

[0064] During the coherent integration time, β p (t m ) and α p (t m ) is time-varying, β p (t m ) and α p (t m )Taylor expansion is shown in formula (5):

[0065]

[0066] In formula (5), β p，0 With α p，0 is a constant term, and β p，0 ≈Z p / R p , α p，0 ≈X p / R p , where X p , Y p , Z p represents the coordinates of the scattering point p in the reference coordinate system (O′, X, Y, Z) at the initial moment of imaging, R p =R o′ +Y p β p，1 β p (t m )The coefficient of the first-order term after Taylor expansion, β p，2 β p (t m )The coefficient of the quadratic term after Taylor expansion, α p，1 is α p (t m )The coefficient of the first-order term after Taylor expansion, α p，2 is α p (t m )The coefficient of the quadratic term after Taylor expansion, For the remainder of Peano.

[0067] In fact, only the constant term β p，0 and α p，0Helpful for interference handling. p (t m ) and α p (t m ) will cause the two-dimensional ISAR images of different channels to mismatch, so it must be compensated before interferometric processing.

[0068] Substituting equations (4) and (3) into equation (2), after motion compensation and ignoring the influence of cross-distance unit migration, equation (2) can be expressed as equation (6):

[0069]

[0070] In formula (6), T m is the pulse repetition period.

[0071] In order to achieve the registration of ISAR images of different channels, the existing image registration method is used to β p (t m ) and α p (t m ) is compensated, equation (6) can be transformed into equation (7):

[0072]

[0073] Sub-step 1.4, establish a compressed sensing model for ISAR imaging and discretize the imaging scene into P×N grid points, where P is the number of azimuth units and N is the number of range units.

[0074] According to formula (7), the echo of the nth range unit can be expressed as formula (8):

[0075]

[0076] In formula (8), and Represents the scattering point intensity of the nth distance unit and the pth azimuth unit of the two-dimensional image of the C, V and H channels respectively, where w Λn (t m ) represents additive white Gaussian noise.

[0077] Formula (8) can be re-expressed as formula (9):

[0078]

[0079] In formula (9), s Λn =[s Λn (t 1 )…s Λn (t M )]T , w Λn =[w Λn (t 1 )…w Λn (t M )] T , Λ∈{C, V, H}. H is an M×P partial Fourier matrix, whose (m, p)th element is exp(-j4πf c (f p t m ) / c).

[0080] Considering that the ISAR image has a total of N range units, that is, the sparse signal is a matrix rather than a vector, the echo signal of all range units in each channel can be expressed as formula (10), that is, the InISAR imaging sparse reconstruction model:

[0081]

[0082] In formula (10), S Λ =[s Λ1 …s ΛN ], X Λ =[x Λ1 …x ΛN ],W Λ =[w Λ1 …w ΛN ], Λ∈{C, V, H}.

[0083] There is joint sparsity between different channels in InISAR imaging, and the three two-dimensional ISAR images have a common support set. Therefore, the InISAR imaging sparse reconstruction model given by equation (10) conforms to the JSM-2 model.

[0084] Step 2: According to the unitary transform approximate message passing UTAMP, the established InISAR imaging sparse reconstruction model that conforms to the JSM-2 model is unitary transformed, and a Bayesian learning model for InISAR imaging joint sparse recovery is established.

[0085] Sub-step 2.1, according to the unitary transformation approximate message passing UTAMP, it is first necessary to perform unitary transformation on the InISAR imaging sparse reconstruction model of the three channels; since the matrix H has singular values, it is decomposed into H = UΘΞ, where U and Ξ are both unitary matrices, and Θ is a rectangular diagonal matrix.

[0086] Performing unitary transformation on equation (10) yields:

[0087]

[0088] In formula (11), R Λ =UH S Λ , W′ Λ =U H W Λ ,Λ∈{C,V,H}.W′ Λ Still with W Λ Noise matrices with the same mean and variance.

[0089] In sub-step 2.2, according to sparse Bayesian learning (SBL), assuming that the sparse signals of the three channels obey Gaussian distribution and have a common support set, the sparse signal probability distribution function can be obtained as shown in formula (12):

[0090]

[0091] In formula (12): X = [X C , X V , X H ] is the sparse signal of three channels; in, represents the (p, n)th element of the sparse signal matrix of the Λth channel, is the (p, n)th element of the hyperparameter γ, indicating The accuracy of Λ∈{C,V,H}; It obeys the gamma distribution, that is: where ε and η are the shape parameter and rate parameter respectively.

[0092] Since the sparse signals of different channels have a common support set, the three different channels use the same hyperparameter matrix. Since the noise is a zero-mean complex Gaussian distribution, the joint probability density function of the echo of each channel can be obtained, as shown in formula (13):

[0093]

[0094] In formula (13): R = [R C , R V , R H ]; X = [X C , X V , X H ]; λ = [λ C ,λ V ,λ H ] represents the noise accuracy of three different channels, and its prior distribution is in, is the (m, n)th element of the measurement signal matrix of the Λth channel, (ΘΞ) m is the mth row of the matrix ΘΞ, x ΛnRepresents the nth column of the two-dimensional sparse signal matrix of the Λth channel.

[0095] Therefore, the joint posterior probability density function can be expressed as formula (14), which is the Bayesian learning model of InISAR imaging joint sparse recovery:

[0096]

[0097] Step 3: construct the factor graph of the InISAR imaging joint sparse restoration Bayesian learning model.

[0098] Factor graph is a commonly used graph model, which usually uses boxes to represent function nodes and circles to represent variable nodes. The variables represented by the variable nodes connected to a function node are all variables of the function. The information transmitted from one node to another is called a message, and the direction of the message transmission is represented by an arrow. The essence of factor graph is to decompose a multivariable complex function into the product of several local functions, and then represent it in the form of a bidirectional graph.

[0099] Specifically, the specific steps of constructing the factor graph of the Bayesian learning model for InISAR imaging joint sparse recovery are as follows:

[0100] The entire factor graph consists of three outer subgraphs corresponding to the three channels C, V, and H. Each outer subgraph has N inner subgraphs, corresponding to the N distance units in each channel. The entire factor graph has a total of 3N inner subgraphs, and all inner subgraphs have similar structures.

[0101] Node Functions The prior distribution used to describe the noise accuracy of three different channels can be expressed as

[0102] Node variable λ Λ represents the noise accuracy of three different channels, Λ∈{C, V, H};

[0103] Node Functions It can be expressed as in, is the (m, n)th element of the measurement signal matrix of the Λth channel;

[0104] Node variables (ΘΞ) m is the mth row of the matrix ΘΞ, x Λn represents the nth column of the two-dimensional sparse signal matrix of the Λth channel;

[0105] Node Functions Used to describe hard constraints It can be expressed as:

[0106] Node variables represents the (p, n)th element of the sparse signal matrix of the Λth channel;

[0107] Node Functions It can be expressed as

[0108] Node variables is the (p, n)th element of the hyperparameter γ, indicating The accuracy of ;Λ∈{C,V,H};

[0109] Node Functions Representation accuracy The gamma distribution of , which can be expressed as: where ε and η are the shape parameter and rate parameter respectively.

[0110] According to the above description, the above node functions are connected with their corresponding node variables to construct the factor graph of the joint sparse recovery Bayesian learning model, as shown in Figure 3 shown.

[0111] In the entire factor graph, the sparse signals of the three channels have a common support set, that is, they have the same hyperparameters, and the three channels constitute a joint sparse recovery in the form of multiple measurement vectors (MMV). The subgraph corresponding to each channel is a two-dimensional sparse signal recovery problem, which constitutes an MMV problem without a common support set within the subgraph. The entire factor graph models the two-dimensional sparse signal recovery problem of the three channels into a two-layer MMV UTAMP using joint sparse features, namely UTAMP-JSR.

[0112] Step 4: According to the factor graph of the established joint sparse recovery Bayesian learning model, the message update rules of each variable are designed.

[0113] Specifically, use μ x→f (x) represents a message from a variable node x to a function node f, where f is a function of x; μ f→x (x) represents a message from a function node f to a variable node x.

[0114] Because the 3N subgraphs have the same structure, the messages on each subgraph are passed according to the unitary transformation approximation message passing UTAMP, so the message passing on all subgraphs can be executed in parallel.

[0115] Assume that the backward (right to left) input message to each subgraph is Its mean and variance are 0 and

[0116] Combining the unitary transformation approximate message passing UTAMP and variational message passing, the output message of each subgraph can be obtained as shown in formula (15):

[0117]

[0118] In formula (15): in, is the Gaussian message, and denote mean and variance respectively; yes The estimated value in the last iteration of .

[0119] therefore:

[0120]

[0121] In formula (16):

[0122]

[0123]

[0124] Noise accuracy of each channel λ Λ The confidence of can be expressed as formula (17):

[0125]

[0126] Therefore, the estimated value of the noise accuracy of the Λth channel is shown in formula (18):

[0127]

[0128] Using b(λ Λ ) and the variational message passing rule can calculate the forward (from left to right) message of each subgraph as shown in formula (19):

[0129]

[0130] The confidence can be expressed as formula (20):

[0131]

[0132] In formula (20):

[0133] therefore, The confidence can be expressed as formula (21):

[0134]

[0135] In formula (21):

[0136] The confidence of can be expressed as formula (22):

[0137]

[0138] Accuracy The estimated value of can be further expressed as formula (23):

[0139]

[0140] In formula (23), |Λ| represents the number of channels, and the value of |Λ| is 3.

[0141] According to the unitary transformation approximate message passing sparse Bayesian learning UTAMP-SBL, let η = 0, then ε can be updated by formula (24):

[0142]

[0143] Step 5: After obtaining the two-dimensional images of the three channels according to the message update rule, the target three-dimensional image is reconstructed through interference processing and scattering point distance measurement.

[0144] Specifically, by performing azimuth focusing on the one-dimensional range image of equation (7) through Fourier transform, the two-dimensional ISAR image of the target can be obtained as shown in equation (25):

[0145]

[0146] The two-dimensional ISAR image in equation (25) is interferometrically processed, and the interference phase between the image of antenna V, the image of antenna H and the image of antenna C can be expressed as equation (26):

[0147]

[0148] In formula (26), angle(g) represents the phase acquisition operation;

[0149] According to formula (26), the height and azimuth coordinates of the scattering point p in the reference coordinate system (O′, X, Y, Z) can be solved, as shown in formula (27):

[0150]

[0151] The coordinate Y of the scattering point p on the Y axis p It can be obtained through distance measurement.

[0152] Through the above steps, the three-dimensional image reconstruction of the scattering point p is completed.

[0153] Furthermore, in some cases, the target coordinate system When it is not completely consistent with the reference coordinate system (O′, X, Y, Z), use (θ y0 ,θ p0 ,θ r0 ) indicates that at t m = 0, the two coordinate systems have the same direction of rotation angle.

[0154] In order to obtain the scattering point p in the target coordinate system The coordinates in need to be transformed as shown in formula (28):

[0155]

[0156] In formula (28), is the scattering point p in the target coordinate system The initial coordinates in Rot(θ y0 ,θ p0 ,θ r0 ) is the synthetic rotation matrix, as shown in formula (29).

[0157] Rot(θ y0 ,θ p0 ,θ r0 )=roll(θ r0 )·pitch(θ p0 )·yaw(θ y0 ) (29)

[0158] In formula (29):

[0159]

[0160]

[0161]

[0162] The main steps of the UTAMP-JSR algorithm of the present invention are summarized as follows:

[0163]

[0164]

[0165] The effect of the present invention can be further illustrated by the following experiments:

[0166] Simulation data experiment:

[0167] 1. Simulation conditions: The simulation is implemented using Matlab software. All simulation related parameters are shown in Table 1.

[0168] Table 1

[0169]

[0170] The target model used in the simulation is Figure 4 As shown in FIG. 1 , the model is a ship model composed of 64 scattering points. The initial coordinates of the target in the radar coordinate system are (0, 15000, 0), the target speed is v = 20m / s, and the angle between the speed direction and the X axis is α = 15°.

[0171] In addition to translation, the target also has three-dimensional rotation caused by complex sea conditions. Due to the long-term accumulation, the complex three-dimensional rotation will cause nonlinear phase terms of the echo signal. In order to ensure that the echo phase is approximately linear, the simulation selects a shorter CPI (0.4s). By adding Gaussian white noise to the echo signal, the signal-to-noise ratio of the three channels is set to a low value of 5dB.

[0172] It should be pointed out that in this simulation, 128 pulses were randomly selected from 256 continuous pulses to simulate sparse aperture data, and these 128 sparse aperture data were used for imaging.

[0173] 2. Simulation content:

[0174] Simulation 1:

[0175] contrast Figure 5 , Figure 6 , Figure 7 , Figure 8 It can be seen that in the case of sparse aperture data, the imaging result of the RD algorithm will produce serious defocusing, and it is difficult to identify the target from the imaging result; the SBL algorithm obtains a clearer two-dimensional image, but the azimuth focusing is not particularly good; the SM-SBL algorithm utilizes the joint sparsity between images of different channels, so the azimuth focusing effect of its imaging result is better than that of SBL; the UTAMP-JSR algorithm of the present invention not only utilizes the joint sparsity between images of different channels, but also has a good noise parameter learning ability that can effectively suppress noise, so the imaging result of the proposed algorithm not only has the best focus but also has the lowest background noise.

[0176] The correlation coefficients of the two-dimensional imaging results of different algorithms are shown in Table 2.

[0177] Table 2

[0178]

[0179] It can be seen from Table 2 that the multi-channel two-dimensional imaging results reconstructed by the UTAMP-JSR algorithm of the present invention have the largest correlation coefficient, that is, the UTAMP-JSR algorithm has the best reconstruction performance.

[0180] Simulation 2:

[0181] Depend on Fig. 9 It can be seen that the UTAMP-JSR algorithm of the present invention has the best reconstruction performance, especially when the signal-to-noise ratio is low. This is because the UTAMP-JSR algorithm of the present invention has a good learning ability for noise parameters and can better suppress noise. As the signal-to-noise ratio increases, the performance of various algorithms gradually approaches.

[0182] Simulation 3:

[0183] Depend on Fig.10 It can be seen that the correlation coefficient increases with the increase of the number of pulses. Under the same conditions, the correlation coefficient of the imaging result of the UTAMP-JSR algorithm of the present invention is the largest, that is, the UTAMP-JSR algorithm of the present invention has the best reconstruction performance.

[0184] Simulation 4:

[0185] right Figure 5 , Figure 6 , Figure 7 and Figure 8 The two-dimensional image in the image can be interferometrically processed to further reconstruct the three-dimensional image of the target, such as Fig.11 , Fig.12 , Fig.13 and Fig.14 shown.

[0186] refer to Fig.11 , Fig.12 , Fig.13 , Fig.14 ,It can be seen that the UTAMP-JSR algorithm of the present invention has a better 3D reconstruction effect.

[0187] In order to quantitatively evaluate the 3D reconstruction performance, the azimuth coordinate ξ and the height coordinate The RMSE (Root Mean Square Error) of the reconstruction results. The four algorithms are related to the azimuth coordinate ξ and the height coordinate The RMSE of the reconstruction results is shown in Table 3.

[0188] Table 3

[0189]

[0190] It can be seen from Table 3 that the UTAMP-JSR algorithm of the present invention has the smallest RMSE for coordinate reconstruction.

[0191] Simulation 5:

[0192] Depend on Fig.15It can be seen that with the increase of the signal-to-noise ratio, the RMSE of the four algorithms is decreasing; under various signal-to-noise ratio conditions, the UTAMP-JSR algorithm of the present invention has the smallest RMSE, that is, the UTAMP-JSR algorithm of the present invention has the most superior InISAR three-dimensional image reconstruction performance.

[0193] Simulation 6:

[0194] Depend on Fig.16 It can be seen that as the number of pulses increases, the RMSE of the four algorithms decreases; the UTAMP-JSR algorithm of the present invention always has the smallest RMSE, that is, the UTAMP-JSR algorithm of the present invention has better three-dimensional reconstruction performance.

[0195] Measured data experiment:

[0196] 1. Experimental conditions:

[0197] The measured data used in this invention is the data collected by PIRAD (Pisa Radar) when observing the target Astice of the offshore training ship. PIRAD is a ground-based sea-based interferometric three-dimensional imaging radar jointly developed by the University of Pisa, Italy and the National Key Laboratory of Radar and Surveillance System (RASS) of CNIT. The radar consists of a self-transmitting and self-receiving antenna and two receiving antennas, and the three antennas form an L shape. The actual PIRAD is shown in the figure below. Fig.17 The relevant parameters are shown in Table 4. The physical object of the training ship target Astice is shown in Fig.18 Its dimensions are shown in Table 5. It should be noted that due to hardware equipment reasons, the echo signal-to-noise ratio collected by the center antenna C is relatively low, and the signal-to-noise ratios of the three channels are not the same.

[0198] Table 4

[0199]

[0200] Table 5

[0201]

[0202] 2. Experimental content:

[0203] Experiment 1: Randomly extract 128 data from 234 slow-time continuous sampling data to simulate sparse aperture data for three-dimensional interferometric imaging.

[0204] refer to Fig.19 , Fig. 20 , Fig.21 , Fig. 22It can be seen that the RD algorithm cannot achieve azimuth focusing, while the other three algorithms can obtain focused two-dimensional images; the background noise of the imaging results of the SBL algorithm and the SM-SBL algorithm is obvious; the imaging results of the UTAMP-JSR algorithm of the present invention not only have the best focusing but also the lowest noise level.

[0205] It should be noted that the noise in the C channel imaging result is significantly stronger. This is because the noise level of the measured data of each channel is different, not because of the imaging algorithm. The phase of the noise is random. The stronger the noise in the two-dimensional image, the worse the coherence between the two channels. The greater the interference phase error during interference processing, the greater the error in the three-dimensional reconstruction result. In order to quantitatively illustrate the quality of the imaging results of the four algorithms, Table 6 gives the correlation coefficients between the two-dimensional images of each channel.

[0206] It can be seen from Table 6 that the correlation between the two-dimensional images of different channels obtained by the UTAMP-JSR algorithm of the present invention is the strongest.

[0207] Table 6

[0208]

[0209] Experiment 2:

[0210] Depend on Fig.23 It can be seen that under different pulse numbers, the UTAMP-JSR algorithm of the present invention has the largest correlation coefficient, which further proves the superiority of the proposed algorithm.

[0211] Experiment 3:

[0212] In order to better demonstrate the 3D reconstruction effects of different algorithms, we aligned the 3D reconstructed point cloud image with Astice's CAD model, so that the 3D reconstruction effects of different algorithms can be more clearly seen visually.

[0213] refer to Fig.24 , Fig.25 , Fig.26 , Fig. 27 It can be seen that the reconstruction effect of the RD algorithm is the worst, because the two-dimensional image focusing is not well achieved, so there are a large number of false points in the three-dimensional reconstruction results; some weak scattering points are lost in the reconstruction results of the SBL algorithm and the SM-SBL algorithm, and the size and shape of the reconstruction results are less matched with the real target, and the reconstruction effect of SM-SBL is slightly better than that of SBL; the length, width and height of the image reconstructed by the UTAMP-JSR algorithm of the present invention are 28.83m, 6.91m and 11.81m respectively, which are closest to the actual size of the target in Table 5, and the main structure (bow, stern, mast, cab) of the three-dimensional reconstructed image of the UTAMP-JSR algorithm of the present invention has the highest matching degree with the target model.

[0214] The three-dimensional reconstruction experiment of measured data further proves the effectiveness and superiority of the UTAMP-JSR algorithm of the present invention.

[0215] Although the present invention has been described in detail in general terms and in specific embodiments in this specification, it is obvious to those skilled in the art that some modifications or improvements may be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of protection claimed by the present invention.

Claims

1. A low-complexity InISAR three-dimensional imaging method based on joint sparse recovery, characterized in that: The following steps are involved: Step 1, establishing the geometric structure of the InISAR imaging system, and establishing an InISAR imaging sparse reconstruction model that conforms to the JSM-2 model according to the geometric structure of the InISAR imaging system; Step 2, according to the unitary transformation approximate message passing UTAMP, the established InISAR imaging sparse reconstruction model that conforms to the JSM-2 model is unitary transformed, and a Bayesian learning model for InISAR imaging joint sparse recovery is established; Step 3, constructing a factor graph of the InISAR imaging joint sparse restoration Bayesian learning model; Step 4, designing a message update rule for each variable in the established joint sparse recovery Bayesian learning model according to the factor graph; Step 5: After obtaining the two-dimensional images of the three channels according to the message update rule, the target three-dimensional image is reconstructed through interference processing and scattering point distance measurement.

2. The low-complexity InISAR three-dimensional imaging method based on joint sparse recovery according to claim 1, characterized in that: The sub-steps of step 1 are: Sub-step 1.1, establish the geometry of the InISAR imaging system; The InISAR imaging system consists of a transmitting and receiving antenna C, a receiving antenna V and a receiving antenna H; the C antenna is located at the coordinate origin O of the radar coordinate system (O, U, G, W), the receiving antenna V and the receiving antenna H are located on the W axis and U axis of the radar coordinate system (O, U, G, W), and the baseline lengths of the receiving antenna V and the receiving antenna H are L1 and L2 respectively; Take the geometric center O' of the far-field target as the origin and establish the target coordinate system and a reference coordinate system (O', X, Y, Z); wherein the geometric center O' of the target is located on the G axis of the radar coordinate system (O, U, G, W), the X axis and Y axis of the reference coordinate system (O', X, Y, Z) are parallel to the W axis and U axis of the radar coordinate system (O, U, G, W) respectively and have the same direction, and the Z axis of the reference coordinate system (O', X, Y, Z) is on the same straight line and has the same direction as the G axis of the radar coordinate system (O, U, G, W); Define the angle between the target speed v and the X-axis in the reference coordinate system (O', X, Y, Z) as α; define is the rotation parameter of rolling motion; is the rotation parameter of the pitch motion; is the rotation parameter of the yaw motion; defines any scattering point p on the target in the target coordinate system The coordinates on Define R Λp is the distance between antenna Λ and scattering point p, where Λ represents one of the transmitting and receiving antenna C, receiving antenna V and receiving antenna H, that is, Λ∈{C, V, H}; In sub-step 1.2, it is assumed that the linear frequency modulation signal transmitted by the transmitting and receiving antenna C is as shown in equation (1): In formula (1), rect() is the rectangular window function; T p is the pulse width; Fast time; t m is the slow time, and t m =mT, m=0, ...M-1, where T is the pulse repetition period; f c is the signal carrier frequency, κ is the modulation frequency; Substep 1.3, assuming that the target consists of P scattering points, x p is the scattering intensity of the pth scattering point p, and the received signal of antenna Λ is demodulated and distance compressed as shown in formula (2): In formula (2), Λ represents one of the transmitting and receiving antennas C, V and H, that is, Λ∈{C, V, H}; c is the speed of light; B is the signal bandwidth; R Λp (t m ) indicates t m The instantaneous distance from antenna Λ to scattering point p at time t is shown in formula (3): In formula (3), R o' Indicates the distance from the radar to the geometric center of the target at the initial moment, R o' +ΔR o' (t m ) represents the distance between antenna C and the target geometric center O', ΔR o' (t m ) is the distance change caused by the target translation, ΔR p (t m ) is the distance change caused by the target rotation; L1β p (t m ) and L2α p (t m ) is the distance difference caused by antenna position diversity, L1 and L2 are the baseline lengths of receiving antenna V and receiving antenna H respectively; β p (t m ) represents the instantaneous pitch angle of the scattering point p, α p (t m ) represents the instantaneous azimuth of the scattering point p; ΔR p (t m ) is shown in formula (4): In formula (4), f p is the Doppler frequency of the scattering point p, ω r is the rotation parameter of rolling motion, ω y is the rotation parameter of yaw motion; and They are ω r and ω y The vector form of ω r and ω y Respectively and are equal in value; β p (t m ) and α p (t m )Taylor expansion is shown in formula (5): In formula (5), β p,0 With α p,0 is a constant term, and β p,0 ≈Z p / R p , α p,0 ≈X p / R p , where X p , Y p , Z p represents the coordinates of the scattering point p in the reference coordinate system (O', X, Y, Z) at the initial moment of imaging, R p =R o' +Y p β p,1 β p (t m )The first-order coefficient after Taylor expansion, β p,2 β p (t m )The coefficient of the quadratic term after Taylor expansion, α p,1 is α p (t m )The coefficient of the first-order term after Taylor expansion, α p,2 is α p (t m )The coefficient of the quadratic term after Taylor expansion, For the remainder of Peano; Substituting equations (4) and (3) into equation (2), after motion compensation and ignoring the influence of cross-distance unit migration, equation (2) can be expressed as equation (6): In formula (6), T m is the pulse repetition period; Use existing image registration methods to p (t m ) and α p (t m ) is compensated for the time-varying part, and equation (6) is transformed into equation (7): Sub-step 1.4, establish a compressed sensing model for ISAR imaging, discretize the imaging scene into P×N grid points, where P is the number of azimuth units and N is the number of range units; According to formula (7), the echo of the nth range unit is expressed as formula (8): In formula (8), and Represents the scattering point intensity of the nth distance unit and the pth azimuth unit of the two-dimensional image of the C, V and H channels respectively, where w Λn (t m ) represents additive Gaussian white noise; Formula (8) can be reformulated as formula (9): In formula (9), s Λn =[s Λn (t1)…s Λn (t M )] T , w Λn =[w Λn (t1)…w Λn (t M )] T , Λ∈{C, V, H}; H is an M×P partial Fourier matrix, whose (m, p)th element is exp(-j4πf c (f p t m ) / c); The echo signals of all range units of each channel are expressed as formula (10), which is the sparse reconstruction model of InlSAR imaging: In formula (10), S Λ =[s Λ1 …s ΛN ], X Λ =[x Λ1 …x ΛN ],W Λ =[w Λ1 …w ΛN ], Λ∈{C, V, H}; The InlSAR imaging sparse reconstruction model given by formula (10) conforms to the JSM-2 model.

3. The low-complexity lnlSAR three-dimensional imaging method based on joint sparse recovery according to claim 1, characterized in that: The sub-steps of step 2 are: Sub-step 2.1, according to the unitary transformation approximation message passing UTAMP, firstly perform unitary transformation on the InISAR imaging sparse reconstruction model of the three channels; Performing unitary transformation on equation (10) yields equation (11): In formula (11), R Λ =U H S Λ , W' Λ =U H W Λ ,Λ∈{C,V,H};W' Λ Still with W Λ Noise matrices with the same mean and variance; U and Ξ are both unitary matrices; Θ is a rectangular diagonal matrix; In sub-step 2.2, according to sparse Bayesian learning (SBL), assuming that the sparse signals of the three channels obey Gaussian distribution and have a common support set, the sparse signal probability distribution function can be obtained as shown in formula (12): In formula (12): X = [X C ,X V ,X H ] is the sparse signal of three channels; in, represents the (p,n)th element of the sparse signal matrix of the Λth channel, is the (p,n)th element of the hyperparameter γ, indicating The accuracy of Λ∈{C,V,H}; It obeys the gamma distribution, that is: Where ε and η are shape parameters and rate parameters respectively; Then the joint probability density function of each channel echo is as shown in formula (13): In formula (13): R = [R C ,R V ,R H ]; X = [X C ,X V ,X H ]; λ = [λ C ,λ V ,λ H ] represents the noise accuracy of three different channels, and its prior distribution is in, is the (m,n)th element of the measurement signal matrix of the Λth channel, (ΘΞ) m is the mth row of the matrix ΘΞ, x Λn represents the nth column of the two-dimensional sparse signal matrix of the Λth channel; The joint posterior probability density function is expressed as formula (14), which is the Bayesian learning model for InISAR imaging joint sparse recovery.

4. The low-complexity InISAR three-dimensional imaging method based on joint sparse recovery according to claim 1, characterized in that: In step 3, specifically, the specific steps of constructing the factor graph of the Bayesian learning model for InISAR imaging joint sparse recovery are as follows: The entire factor graph consists of three outer subgraphs corresponding to the three channels of antenna C, antenna V and antenna H. Each outer subgraph has N inner subgraphs, corresponding to the N distance units in each channel. The entire factor graph has a total of 3N inner subgraphs. Node Functions It is used to describe the prior distribution of noise accuracy of three different channels, which is expressed as Node variable λ Λ represents the noise accuracy of three different channels, Λ∈{C,V,H}; Node Functions Expressed as in, is the (m,n)th element of the measurement signal matrix of the Λth channel; Node variables (ΘΞ) m is the mth row of the matrix ΘΞ, x Λn represents the nth column of the two-dimensional sparse signal matrix of the Λth channel; Node Functions Used to describe hard constraints It is expressed as: Node variables represents the (p,n)th element of the sparse signal matrix of the Λth channel; Node Functions Expressed as Node variables is the (p,n)th element of the hyperparameter γ, indicating The accuracy of ;Λ∈{C,V,H}; Node Functions Representation accuracy The gamma distribution is expressed as: Where ε and η are shape parameters and rate parameters respectively; According to the above description, the above node functions are connected with their corresponding node variables to construct a factor graph of the joint sparse recovery Bayesian learning model.

5. The low-complexity InISAR three-dimensional imaging method based on joint sparse recovery according to claim 1, characterized in that: In step 4, specifically, use μ x→f (x) represents a message from a variable node x to a function node f, where f is a function of x; μ f→x (x) represents a message from a function node f to a variable node x; Assume that the backward direction to each subgraph, that is, from right to left, the input message is Its mean and variance are 0 and Then the output message of each subgraph is as shown in formula (15): In formula (15): in, is the Gaussian message, and denote mean and variance respectively; yes The estimated value of the last iteration of ; therefore: In formula (16): Noise accuracy of each channel λ Λ The confidence of is expressed as formula (17): Therefore, the estimated value of the noise accuracy of the Λth channel is shown in formula (18): The forward direction of each subgraph, i.e. from left to right, is as shown in formula (19): The confidence can be expressed as formula (20): In formula (20): therefore, The confidence can be expressed as formula (21): In formula (21): The confidence can be expressed as formula (22): Accuracy The estimated value of is expressed as formula (23): In formula (23), |Λ| represents the number of channels, and the value of |Λ| is 3; According to the unitary transformation approximate message passing sparse Bayesian learning UTAMP-SBL, let η = 0, then ε is updated by equation (24), 6. The low-complexity InISAR three-dimensional imaging method based on joint sparse recovery according to claim 1, characterized in that: Step 5, specifically, the one-dimensional range image of equation (7) is azimuthally focused by Fourier transform to obtain a two-dimensional ISAR image of the target as shown in equation (25): The two-dimensional ISAR image in equation (25) is interferometrically processed, and the interference phase between the image of antenna V, the image of antenna H and the image of antenna C can be expressed as equation (26): In formula (26), angle(g) represents the phase acquisition operation; According to formula (26), the height and azimuth coordinates of the scattering point p in the reference coordinate system (O', X, Y, Z) can be solved, as shown in formula (27): The coordinate Y of the scattering point p on the Y axis p It can be obtained through distance measurement; Through the above steps, the three-dimensional image reconstruction of the scattering point p is completed.

7. The low-complexity InISAR three-dimensional imaging method based on joint sparse recovery according to claim 6, characterized in that: When the target coordinate system When it is not completely consistent with the reference coordinate system (O', X, Y, Z), use (θ y0 ,θ p0 ,θ r0 ) indicates that at t m = 0, the two coordinate systems have the same direction of rotation angle; In order to obtain the scattering point p in the target coordinate system The coordinates in need to be transformed as shown in formula (28): In formula (28), is the scattering point p in the target coordinate system The initial coordinates of Rot(θ y0 ,θ p0 ,θ r0 ) is the synthetic rotation matrix, as shown in formula (29); Rot(θ y0 ,i p0 ,i r0 )=roll(θ r0 )·pitch(θ p0 )·yaw(θ y0 (29) In formula (29):

Images