A one-station fixed bistatic SAR sparse imaging method based on a back-projection operator

Abstract

The application discloses a one-station fixed dual-station SAR sparse imaging method based on a back-projection operator, and comprises the following steps: constructing a one-station fixed dual-station SAR imaging geometric model and designing a BP imaging processing flow; constructing a sparse SAR imaging model based on the SAR imaging geometric model and the BP imaging processing flow; designing an echo simulation operator required by the sparse SAR imaging model based on the BP imaging processing flow; and realizing sparse reconstruction of an observation scene through iteration recovery based on the sparse SAR imaging model and the echo simulation operator, and outputting a reconstructed image. The application solves the two-dimensional space variability problem of dual-station data, realizes high-precision imaging processing by utilizing the characteristic that the BP algorithm does not have any approximate processing, combines dual-station SAR imaging with sparse imaging, realizes sparse microwave imaging reconstruction without approximate observation, improves the quality of an image, provides a new idea for dual-station SAR imaging, and can realize accurate imaging of dual-station data.

Description

Technical Field

[0001] This invention belongs to the fields of sparse signal processing and microwave imaging, and relates to sparse imaging of bistatic synthetic aperture radar (SAR). Specifically, it relates to a one-station fixed bistatic SAR sparse imaging method based on a back projection operator. Background Technology

[0002] Synthetic Aperture Radar (SAR) is a high-resolution microwave remote sensing imaging radar. It is not limited by extreme weather conditions and can perform high-resolution imaging of the observation area around the clock and in all weather conditions. It is widely used in economic construction and national defense fields: topographic mapping, monitoring of high mountain glaciers, monitoring of vegetation coverage, crop yield assessment, monitoring of natural disasters such as landslides and floods, military reconnaissance, target identification and monitoring, and many other applications.

[0003] Unlike traditional SAR, bistatic SAR uses two separate platforms for transmitting and receiving antennas, allowing for a degree of freedom in their movement. Bistatic SAR can utilize a "long-range transmission, near-range reception" approach, placing the transmitting platform far from the battlefield while the receiving platform operates in a "silent" state (passive reception). This allows for better concealment, and enemy interference with the transmitting platform does not affect the continued operation of the receiving platform, giving bistatic SAR excellent anti-jamming capabilities. This reduces vulnerability in military applications while improving imaging efficiency.

[0004] Sparse signal processing techniques utilize as little effective information as possible from the original signal to recover and approximate it. Sparse microwave imaging is a novel method that systematically introduces and organically combines sparse signal processing theory into microwave imaging. In 2007, Baraniuk used compressed sensing theory to reconstruct the original signal using less observation data. The essence of signal reconstruction in this theory is solving underdetermined equations. If the signal is sparse, it can be sampled at a sampling rate far lower than that required by the Nyquist sampling theorem and perfectly reconstructed. A SAR image enhancement method based on Lq regularization solves the optimization problem through a threshold iteration algorithm and a complex approximation information transfer algorithm, achieving sidelobe suppression and target clutter ratio improvement in SAR images. This method can be used to improve the image quality of reconstruction results from existing matched filtering algorithms. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the existing technology, a one-station fixed bistatic SAR sparse imaging method based on the back projection operator (BP) is provided. The method utilizes the characteristic of the BP algorithm that it does not have any approximation processing to achieve high-precision imaging processing, and combines bistatic SAR imaging with sparse imaging to improve image quality.

[0006] Technical Solution: To achieve the above objectives, this invention provides a one-station fixed bistatic SAR sparse imaging method based on a back projection operator, comprising the following steps:

[0007] S1: Construct a one-station fixed dual-station SAR imaging geometric model and design the BP imaging processing flow;

[0008] S2: Construct a sparse SAR imaging model based on the SAR imaging geometric model and BP imaging processing flow;

[0009] S3: Based on the BP imaging processing flow, design the echo simulation operator required for the sparse SAR imaging model;

[0010] S4: Based on the sparse SAR imaging model and echo simulation operator, sparse reconstruction of the observed scene is achieved through iterative recovery, and the reconstructed image is output.

[0011] Furthermore, the method for constructing the geometric model of a single-station fixed bistatic SAR imaging in step S1 is as follows:

[0012] For a single point target P(x,y) with a range and azimuth position of (x,y), the received signal after orthogonal demodulation by the SAR system is:

[0013]

[0014] Where σ(x,y) is the target backscattering coefficient, ω r (τ) is the envelope of the transmitted pulse, ω a (η) represents the azimuth antenna pattern, K r τ is the range pulse modulation frequency, f0 is the carrier frequency, τ is the range time, and η is the azimuth time. c At the moment of beam center crossing, R(η) = R T (x, y; η) + R R (x,y) is the two-way slant distance, R T (x, y; η) represents the instantaneous slant range between the launch platform and the point target, R. R (x,y) represents the distance between the receiving platform and the target point, which is independent of the azimuth time η. r This is the equivalent radar velocity.

[0015] Furthermore, the design method for the BP imaging processing flow in step S1 is as follows:

[0016] Construct a range-directed matched filter function:

[0017]

[0018] Perform a range-direction Fourier transform on s0(τ, η), multiply it with the range-direction matched filter function H(f), and complete the range-direction processing through an inverse range-direction Fourier transform. Ignoring the constant term, we obtain the time-domain result of the range-direction pulse compression:

[0019]

[0020] in, Wavelength;

[0021] The target region within the slant range plane is meshed with reference to the range and azimuth resolutions, and η is calculated. i The slant range value of the radar reaching each grid point at any given time is calculated in the distance pulse compression result s1(τ, η). i The slant range R(x) of the grid points within the interpolation beam illumination range is calculated. m y n η i The echo value corresponding to )

[0022] The interpolated s1(R(x) m y n η i ) / c,η i Phase compensation is performed and coherently accumulated. The compensated phase is exp{j2π(R(x)}. m y n η i )- xm Finally, the scattering information of the target is obtained by scattering λ / λ.

[0023]

[0024] Furthermore, the method for constructing the sparse SAR imaging model in step S2 is as follows:

[0025] The two-dimensional sparse SAR imaging model is represented as:

[0026] Y = ΞX

[0027] in, It is two-dimensional echo data. Let Ξ be the backscattering coefficient of the target region, and Ξ be the system observation matrix;

[0028] make This represents the BP imaging algorithm process, therefore the reconstructed observation area is:

[0029]

[0030] The concept of azimuth-range decoupling originates from the formation of SAR echo data from the reflectivity image X of the observation area. The radar system observation matrix Ξ can simulate the transformation from the observation scene to the echo data; it includes an azimuth-directed convolution operation Ξ on the reflectivity image. a To generate phase history, the range-azimuth migration operator Generate two-dimensional bending and distance-oriented convolution operators Ξ r Therefore, based on the above-mentioned idea of ​​azimuth-distance decoupling, the imaging model is rewritten as follows:

[0031]

[0032] in, For echo simulation operators, the inverse process of MF imaging;

[0033] After random downsampling of the echo data, the imaging model is as follows:

[0034]

[0035] Where Y becomes two-dimensional downsampled echo data, Φ a and Φ r Let N0 represent the azimuth and range descent sampling matrices of the sparse sampling, respectively, and N0 be the noise matrix.

[0036] Scene reconstruction is performed by iteratively solving the following optimal problem using a threshold:

[0037]

[0038] in, This represents the reconstructed two-dimensional image, where δ is the regularization parameter.

[0039] Furthermore, the design method for the echo simulation operator required for the sparse SAR imaging model in step S3 is as follows:

[0040] The range-direction matched filter function H(f) and the range-frequency signal S0(f) constructed in step S1 τ The process of obtaining s1(τ,η) by inverse Fourier transform after multiplying τ and η is expressed as:

[0041] s1=C r (s0)

[0042] Among them, C r (·) represents the operator used to implement range pulse compression;

[0043] In s1(τ, η i The slope distance R(x) of the interpolated grid points in )m y n η i The echo value corresponding to ) is expressed as:

[0044]

[0045] in, This is an operator used to implement echo interpolation;

[0046] The interpolated s1(R(x) m y n η i ) / c,η i Phase compensation and coherent accumulation are represented as follows:

[0047]

[0048] Where ⊙ represents the Hadamard product, S a (·) is an operator that coherently accumulates the sub-images of the target region along the azimuth direction, and Ψ is a phase compensation vector that performs phase correction on the sub-images of the target region after interpolation.

[0049] Therefore, the mathematical expression for the back projection imaging operator is obtained as follows:

[0050]

[0051] Based on the concept of inverse imaging echo simulation, the back projection echo simulation operator is obtained as follows:

[0052]

[0053] Furthermore, the method for sparse reconstruction of the observation scene through iterative recovery in step S4 is as follows:

[0054] The threshold iterative algorithm takes echo data Y as input and an operator as input. Let X be the target scene for sparse reconstruction. (0) The initial value is 0, its iteration parameter is ξ, its error parameter is ε, and its maximum number of iterations is I. max When the condition i≤I is satisfied max And when the residual Residual > s, perform the following steps:

[0055] A1: Estimated residual data values:

[0056] Input echo data Y, range and azimuth downsampling matrices Φ a and Φ r Calculate the residual data values:

[0057]

[0058] Substituting the residual data values ​​into the imaging operator yields:

[0059]

[0060] A2: Calculate the iteration parameters:

[0061]

[0062] in, In support set X (i-1) The value at that location is ΔX (i) The remaining positions are zero;

[0063] A3: Calculate the parameters that control sparsity:

[0064] Among them, |X (i) + μ ΔX (i) | k+1 Represents the image |X (i) +μΔX (i) |The (k+1)th largest element value in the scene, where k represents the sparsity of the scene;

[0065] A4: Update the target scene value for sparse reconstruction:

[0066] X (i+1) =F(X) (i) +μ (i) ΔX (i) μ (i) δ (i) )

[0067] Where F(·) is the threshold operator, μ and δ are two key parameters that control the iteration process, and their values ​​are adaptively set according to the iteration; the normalization parameter μ controls the convergence speed of the iterative algorithm, and the regularization parameter δ controls the reconstruction accuracy;

[0068] A5: Update the residuals of the restored image:

[0069] Residual = ||X (i+1 )-X (i) || F

[0070] A6: Output the reconstructed image.

[0071] This invention solves the two-dimensional spatial variability problem of bistatic data by employing a one-station fixed bistatic SAR sparse imaging method based on back projection operators. It utilizes the characteristic of the BP algorithm that it does not require any approximation processing to achieve high-precision imaging processing. Furthermore, it combines bistatic SAR imaging with sparse imaging to achieve sparse microwave imaging reconstruction without approximation observations, thereby improving image quality. This invention provides a new approach to bistatic SAR imaging and enables accurate imaging of bistatic data.

[0072] In this invention, the BP algorithm calculates the slant range by taking the target position and radar position at each azimuth time. The calculation process has no approximations. It uses slant range information for interpolation imaging and instantaneous slant range imaging at each time, making it applicable to SAR imaging with any known motion trajectory. The calculation process has no geometric approximations, resulting in high imaging accuracy.

[0073] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0074] 1. The BP algorithm provided by this invention performs interpolation by calculating the two-way slant range of the radar from the target at each azimuth time. It is applicable to SAR imaging with any known motion trajectory and has no geometric approximation, thus achieving high-precision imaging.

[0075] 2. Compared with existing sparse microwave imaging algorithms, this invention constructs an echo simulation operator based on the BP algorithm, i.e. scene observation. Because it utilizes the BP imaging operator and the BP-based echo simulation operator for sparse imaging, the geometric approximation-free nature of BP can achieve sparse microwave imaging reconstruction without approximation, further improving image quality. Attached Figure Description

[0076] Figure 1 This is a flowchart of the method of the present invention;

[0077] Figure 2 A geometric model for a single-station fixed dual-station SAR imaging system;

[0078] Figure 3 The flowchart is shown below for a one-station fixed bi-station SAR sparse imaging algorithm based on the back projection algorithm.

[0079] Figure 4 Design diagram for point target imaging scene;

[0080] Figure 5 The images show the one-station fixed bi-station SARBP and sparse BP imaging results under full sampling conditions; where (a) is the BP imaging result and (b) is the BP-based sparse SAR imaging result.

[0081] Figure 6 The images show the 1-station fixed bi-station SARBP and sparse BP imaging results under 70% random downsampling; where (a) is the BP imaging result and (b) is the BP-based sparse SAR imaging result. Detailed Implementation

[0082] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0083] like Figure 1 As shown, this invention provides a one-station fixed bistatic SAR sparse imaging method based on a back projection operator, comprising the following steps:

[0084] S1: Construct a one-station fixed bistatic SAR imaging geometric model and design the BP imaging processing flow:

[0085] Reference Figure 2 The geometric model of a fixed bistatic SAR imaging system shown below, for a single point target P(x,y) with positions (x,y) in both range and azimuth directions, the received signal after orthogonal demodulation by the SAR system is as follows:

[0086]

[0087] Where σ(x,y) is the target backscattering coefficient, ω r (τ) is the envelope of the transmitted pulse, ω a (η) represents the azimuth antenna pattern, K r τ is the range pulse modulation frequency, f0 is the carrier frequency, τ is the range time, and η is the azimuth time. c At the moment of beam center crossing, R(η) = R T (x, y; η) + R R (x,y) is the two-way slant distance, R T (x, y; η) represents the instantaneous slant range between the launch platform and the point target, R. R (x,y) represents the distance between the receiving platform and the target point, which is independent of the azimuth time η. r Equivalent radar velocity;

[0088] Construct a range-directed matched filter function:

[0089]

[0090] Performing a range-to-Fourier transform on s0(τ,η) yields the range-frequency signal S0(f). τ The function η is multiplied by the range-direction matched filter function H(f), and the range-direction processing is completed by the inverse range-direction Fourier transform. Ignoring the constant term, the time-domain result of the range-direction pulse compression is obtained:

[0091]

[0092] in, Wavelength;

[0093] The target region within the slant range plane is meshed with reference to the range and azimuth resolutions, and η is calculated. i The slant range value of the radar reaching each grid point at any given time is calculated in the distance pulse compression result s1(τ, η). i The slant range R(x) of the grid points within the interpolation beam illumination range is calculated. m y n η i The echo value corresponding to )

[0094] The interpolated s1(R(x) m y n η i ) / c,η i Phase compensation is performed and coherently accumulated. The compensated phase is exp{j2π(R(x)}. m y n η i )-x m Finally, the scattering information of the target is obtained by scattering λ / λ.

[0095]

[0096] S2: Constructing a sparse SAR imaging model based on the SAR imaging geometric model and BP imaging processing workflow:

[0097] The two-dimensional sparse SAR imaging model is represented as:

[0098] Y = ΞX

[0099] in, It is two-dimensional echo data. Let Ξ be the backscattering coefficient of the target region, and Ξ be the system observation matrix;

[0100] make This represents the BP imaging algorithm process, therefore the reconstructed observation area is:

[0101]

[0102] The concept of azimuth-range decoupling originates from the formation of SAR echo data from the reflectivity image X of the observation area. The radar system observation matrix Ξ can simulate the transformation from the observation scene to the echo data; it includes an azimuth-directed convolution operation Ξ on the reflectivity image. a To generate phase history, the range-azimuth migration operator Generate two-dimensional bending and distance-oriented convolution operators Ξ r Therefore, based on the above-mentioned idea of ​​azimuth-distance decoupling, the imaging model is rewritten as follows:

[0103]

[0104] in, For echo simulation operators, the inverse process of MF imaging;

[0105] After random downsampling of the echo data, the imaging model is as follows:

[0106]

[0107] Where Y becomes two-dimensional downsampled echo data, Φ a and Φ r Let N0 represent the azimuth and range descent sampling matrices of the sparse sampling, respectively, and N0 be the noise matrix.

[0108] Scene reconstruction is performed by iteratively solving the following optimal problem using a threshold:

[0109]

[0110] in, This represents the reconstructed two-dimensional image, where δ is the regularization parameter.

[0111] S3: Based on the BP imaging processing flow, design the echo simulation operator required for the sparse SAR imaging model:

[0112] According to step S1, the back projection imaging algorithm process is mainly divided into three steps: range pulse compression, echo interpolation, and coherent accumulation.

[0113] The range-direction matched filter function H(f) and the range-frequency signal S0(f) constructed in step S1 τ The process of obtaining s1(τ,η) by inverse Fourier transform after multiplying τ and η is expressed as:

[0114] s1=C r (s0)

[0115] Among them, C r (·) represents the operator used to implement range pulse compression;

[0116] In s1(τ, η i The slope distance R(x) of the interpolated grid points in ) m y n η i The echo value corresponding to ) is expressed as:

[0117]

[0118] in, This is an operator used to implement echo interpolation;

[0119] The interpolated s1(R(x) m yn η i ) / c,η i Phase compensation and coherent accumulation are represented as follows:

[0120]

[0121] Where ⊙ represents the Hadamard product, Sa(·) is the operator that coherently accumulates the sub-images of the target region along the azimuth direction, and Ψ is the phase compensation vector that performs phase correction on the sub-images of the target region after interpolation.

[0122] Therefore, the mathematical expression for the back projection imaging operator is obtained as follows:

[0123]

[0124] Based on the concept of inverse imaging echo simulation, the back projection echo simulation operator is obtained as follows:

[0125]

[0126] in, This is the inverse interpolation operator, i.e., image interpolation. It is an inverse distance pulse compression operator. It is the inverse coherent accumulation operator.

[0127] S4: Based on the sparse SAR imaging model and echo simulation operator, sparse reconstruction of the observed scene is achieved through iterative recovery. The algorithm flow is as follows: Figure 3 As shown, the final output is the reconstructed image:

[0128] The threshold iterative algorithm takes echo data Y as input and an operator as input. Let X be the target scene for sparse reconstruction. (0) The initial value is 0, its iteration parameter is ξ, its error parameter is ε, and its maximum number of iterations is I. max When the condition i≤I is satisfied max And if the residual Residual > ε, perform the following steps:

[0129] A1: Estimated residual data values:

[0130] Input echo data Y, range and azimuth downsampling matrices Φ a and Φ r Calculate the residual data values:

[0131]

[0132] Substituting the residual data values ​​into the imaging operator yields:

[0133]

[0134] A2: Calculate the iteration parameters:

[0135]

[0136] in, In support set X (i-1) The value at that location is ΔX (i) The remaining positions are zero;

[0137] A3: Calculate the parameters that control sparsity:

[0138] Among them, |X (i) +μΔX (i) | k+1 Represents the image |X (i) +μΔX (i) |The (k+1)th largest element value in the scene, where k represents the sparsity of the scene;

[0139] A4: Update the target scene value for sparse reconstruction:

[0140] X (i+1) =F(X) (i) +μ (i) ΔX (i) ,μ (i) δ (i) )

[0141] Where F(·) is the threshold operator, μ and δ are two key parameters that control the iteration process, and their values ​​are adaptively set according to the iteration; the normalization parameter μ controls the convergence speed of the iterative algorithm, and the regularization parameter δ controls the reconstruction accuracy;

[0142] A5: Update the residuals of the restored image:

[0143] Residual = ||X (i+1) -X (i) || F

[0144] A6: Output the reconstructed image.

[0145] Based on the above, in order to verify the effectiveness and practical effect of the present invention, this embodiment analyzes and compares the imaging performance of the method of the present invention, as follows:

[0146] The method of the present invention was verified by point target simulation according to the parameters shown in Table 1.

[0147] Table 1 Simulation parameters of SAR system

[0148]

[0149] Design as Figure 4The rectangular imaging scene is shown, with three point targets set at near, far, and center of the scene for imaging. Under full sampling, the BP imaging and sparse BP results are as follows: Figure 5 As shown in (a) and (b) above, under 70% random downsampling, the results of BP imaging and sparse BP are as follows: Figure 6 As shown in (a) and (b) in the figure. The imaging results show that the method of the present invention not only achieves accurate focusing on a single-station fixed bistatic SAR based on the BP algorithm, but also, compared with the imaging results of traditional BP, can achieve sparse microwave imaging reconstruction without approximate observations, significantly remove or suppress clutter and sidelobes, and further improve the image quality.

Claims

1. A one-station fixed bistatic SAR sparse imaging method based on a backward projection operator, characterized in that, The method comprises the following steps: S1: constructing a one-station fixed two-station SAR imaging geometry model and designing a BP imaging processing flow; S2: constructing a sparse SAR imaging model based on the SAR imaging geometry model and the BP imaging processing flow; S3: designing an echo simulation operator required by the sparse SAR imaging model based on the BP imaging processing flow; S4: realizing sparse reconstruction of an observed scene through iterative recovery based on the sparse SAR imaging model and the echo simulation operator and outputting a reconstructed image; The construction method of the sparse SAR imaging model in step S2 is as follows: The two-dimensional sparse SAR imaging model is expressed as: wherein is two-dimensional echo data, is a backscatter coefficient of the target region, is a system observation matrix; Let denotes the BP imaging algorithm process, so the observation region reconstruction is: According to the idea of azimuth-range decoupling, the imaging model is rewritten as: wherein, is the echo simulation operator, the inverse of MF imaging; After random down-sampling of echo data, the imaging model is: where Y becomes the two-dimensional down-sampled echo data, Φ a and Φ r represent the azimuth and range down-sampling matrices of sparse sampling, respectively, and N0 is the noise matrix. Scene reconstruction is performed through threshold iterative solving of the following optimal problem: wherein, denotes the reconstructed two-dimensional image, and δ is a regularization parameter.

2. The one-station fixed bistatic SAR sparse imaging method based on a backward projection operator according to claim 1, characterized in that, The construction method of the one-station fixed two-station SAR imaging geometry model in step S1 is as follows: For a single point target P(x, y) with a position of (x, y) in the range direction and the azimuth direction, the received signal after orthogonal demodulation operation of the SAR system is: where σ(x, y) is the target backscattering coefficient, ω r (τ) is the transmit pulse envelope, ω a (η) is the azimuth antenna pattern, K r is the range rate of the range pulse, f0 is the carrier frequency, τ is the range time, η is the azimuth time, η c is the beam center crossing time, R(η) = R T (x, y; η) + R R (x, y) is the two-way slant range, R T (x, y; η) is the instantaneous slant range from the transmitting platform to the point target, R R (x, y) is the range from the receiving platform to the point target, independent of the azimuth time η.

3. The one-station fixed bistatic SAR sparse imaging method based on a back-projection operator according to claim 2, characterized in that, The design method of the BP imaging processing flow in step S1 is as follows: A range direction matched filter function is constructed: The range direction Fourier transform is performed on s0(τ, η), multiplied by the range direction matched filter function H(f), and the range direction processing is completed through the range direction inverse Fourier transform, ignoring the constant term, to obtain the range direction pulse compression time domain result: wherein is the wavelength; The target area in the slant range plane is gridded with reference to the range and azimuth resolution, and η is calculated i The slant range value of each grid point is reached at the moment of lightning, and the echo value corresponding to the slant range value R(x m ,y n ; η i ) of the grid point in the beam irradiation range is interpolated in the range pulse compression result s1(τ,η i ). s1(R(x m ,y n ; η i ) / c,η i ) is phase compensated and coherently added, the compensation phase is esp{j2π(R(x m ,y n ; η i )-x m ) / λ}, and finally the scattering information of the target is obtained:

4. The one-station fixed bistatic SAR sparse imaging method based on a back-projection operator according to claim 3, characterized in that, The design method of the echo simulation operator required by the sparse SAR imaging model in step S3 is as follows: The range-direction matched filter function H(f) and the range-frequency signal S0(f) constructed in step S1 τ The process of obtaining s1(τ,η) by inverse Fourier transform after multiplying τ and η is expressed as follows: s1 = C r (s0) wherein C r (·) is an operator for implementing range pulse compression; The echo value corresponding to the slant range value R(x m ,y n ; η i ) of the interpolated grid point in s1(τ, η i ) is represented as: wherein is an operator for implementing echo interpolation; The phase compensated and coherently accumulated s1(R(x m ,y n ; η i ) / c,η i ) is represented as: wherein, ⊙ represents Hadamard product, S a (·) is an operator for coherently accumulating the sub-images of the target region in the azimuth direction, and Ψ is a phase compensation vector for phase correction of the sub-images of the target region after interpolation. Therefore, the mathematical expression of the back-projection imaging operator is obtained as follows: According to the inverse imaging echo simulation idea, the back-projection echo simulation operator is obtained as follows:

5. The one-station fixed bistatic SAR sparse imaging method based on the back-projection operator of claim 4, wherein, The method for realizing sparse reconstruction of an observed scene through iterative recovery in step S4 is as follows: A1: estimating residual data values; A2: calculating iterative parameters; A3: calculating parameters for controlling sparsity; A4: updating target scene values of sparse reconstruction; A5: updating residual errors of a recovered image; A6: outputting a reconstructed image.

6. The one-station fixed bistatic SAR sparse imaging method based on the back-projection operator of claim 5, wherein, The threshold iterative algorithm in the step S4 inputs the echo data Y and the operator Let the target scene X of sparse reconstruction (0) be initialized as 0, the iteration parameter is ξ, the error parameter is ε, and the maximum iteration step is I max ; when the condition i≤I max and the residual error Residual>ε are met, the following steps are performed: A1: estimating residual data values: Input echo data Y, range and azimuth down-sampling matrix Φ a and Φ r , compute residual data values: The residual data values are substituted into the imaging operator to obtain: A2: calculating iterative parameters: wherein at the support set X (i-1) the value is ΔX (i) the remaining positions are zero; A3: calculating parameters for controlling sparsity: where |X (i) + μΔX (i) | k+1 denotes the image |X (i) + μΔX (i) | the k+1th largest element value, k represents the sparsity of the scene; A4: updating target scene values of sparse reconstruction: X (i+1) = F(X (i) + μ (i) ΔX (i) , μ (i) ) Wherein, F(·) is a threshold operator, and μ and δ values are two key parameters for controlling the iterative process; the normalization parameter μ controls the convergence speed of the iterative algorithm, and the regularization parameter δ controls the reconstruction precision; A5: updating residual errors of a recovered image: Residual = ||X (i+1) - X (i) || F A6: outputting a reconstructed image.

Images