Airborne high squint SAR imaging method based on two-dimensional wave number spectrum resampling

Abstract

The invention discloses an airborne high squint SAR imaging method based on two-dimensional wave number spectrum resampling, and the method comprises the steps: constructing an azimuth ambiguity resolution function, correcting an aliasing azimuth wave number spectrum generated under a PRF limited condition, and providing complete two-dimensional wave number spectrum data for subsequent processing. According to the method, an azimuth ambiguity resolution function is utilized, an aliasing azimuth wave number spectrum is corrected, a two-dimensional wave number spectrum resampling factor is used in subsequent operation, a squint two-dimensional wave number spectrum is subjected to two-dimensional resampling and equivalently converted into a forward side-looking wave number domain signal, and the utilization rate of the wave number spectrum is increased. According to the method, the aliasing azimuth spectrum can be corrected under the condition that the PRF is limited on the airborne large squint SAR, two-dimensional high-resolution imaging of the target area is achieved through the imaging method of two-dimensional wave number spectrum resampling, and the engineering application scene of the method is widened.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, and further relates to an airborne large-slant-look SAR imaging method based on two-dimensional wavenumber spectrum resampling in the field of signal processing and imaging algorithm technology. This invention can be used in airborne large-slant-look synthetic aperture radar (SAR) to suppress azimuth spectrum aliasing under the condition of limited pulse repetition frequency (PRF), and to achieve two-dimensional high-resolution precise focusing imaging of the target area through the two-dimensional wavenumber spectrum resampling imaging method. Background Technology

[0002] Based on the differences in frequency domain mapping models and resampling methods, Omega-K imaging methods under strabismus conditions can be summarized into three categories: strabismus Omega-K algorithms based on traditional Stolt interpolation, strabismus Omega-K algorithms based on extended Stolt interpolation, and strabismus Omega-K algorithms based on interpolation along the line of sight. Among these, the error phase of traditional Stolt interpolation methods is often difficult to explicitly separate, making it difficult to embed motion errors analytically into the imaging process, thus hindering effective integration with conventional motion compensation methods. To address this issue, Naivedya Mishra et al. proposed a strabismus Omega-K method based on extended Stolt interpolation. While maintaining relative independence between range and azimuth processing, this method explicitly retains motion errors in the azimuth modulation phase, facilitating subsequent compensation. On the other hand, the two-dimensional wavenumber spectrum exhibits significant tilting, stretching, and distortion under strabismus imaging: the effective resampling area is significantly reduced when using inner rectangular interpolation; and outer rectangular interpolation requires large-scale interpolation at the edge of the support region, increasing extrapolation errors and computational overhead. As a result, the first two types of methods have relatively low utilization of the two-dimensional wavenumber spectrum support region under strabismus, which inevitably limits the imaging quality. In contrast, the line-of-sight interpolation method transforms the wavenumber spectrum support region under the strabismus coordinate system into an equivalent frontal side view form through two-dimensional rotation resampling, thereby increasing the effective data ratio and improving the focusing effect; however, in order to suppress azimuth blurring under large strabismus conditions and the resulting azimuth wavenumber spectrum aliasing, a higher PRF support is usually required, which puts more stringent constraints on the system parameter configuration.

[0003] The Aerospace Information Research Institute of the Chinese Academy of Sciences discloses a spaceborne large-slant-view multi-mode SAR integrated imaging method and device in its patent application "A Spaceborne Large-Slant-View Multi-Mode SAR Integrated Imaging Method and Device" (Application No. 202510641571.1, Publication No. CN 120161468 A). The method includes: performing Fourier transform on multi-mode SAR data along the range direction, followed by azimuth deslant removal and range compression; eliminating Doppler spectral aliasing based on azimuth sub-bands; performing reference point matched filtering on the data after eliminating Doppler spectral aliasing, and then performing range block segmentation and differential matched filtering on the data after reference point matched filtering; performing two-dimensional frequency domain resampling on the data after range block segmentation and differential matched filtering, and then performing two-dimensional time domain block segmentation and differential matched filtering again to obtain a finely focused imaging result. This method achieves Doppler spectral dealiasing and full-scene fine focusing for large-slant-view multi-mode spaceborne SAR with only a small increase in data volume. However, the method still has shortcomings. It is not adaptable enough to the PRF constraints in handling chain-dependent multiple block division, differential matched filtering and two-dimensional resampling. Under medium and low PRF, the azimuth spectrum aliasing caused by Doppler center shift is more likely to lead to incomplete support domain, which reduces the stability of subsequent two-dimensional resampling and fine focusing processing. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the existing technology by proposing an airborne large-slant-look SAR imaging method based on two-dimensional wavenumber spectrum resampling. This aims to solve the problem that, under PRF constraints, the azimuth wavenumber spectrum of the baseband echo signal in airborne large-slant-look SAR imaging is aliased, making it difficult to obtain a two-dimensional wavenumber domain signal with an effective support domain, thus hindering the accurate imaging of the target area using two-dimensional wavenumber spectrum resampling methods.

[0005] The technical approach to achieving the objective of this invention is to address the azimuth wavenumber spectrum aliasing problem that easily occurs under airborne large squint conditions. It constructs an azimuth de-ambiguity function to correct the aliased azimuth wavenumber spectrum generated under PRF-constrained conditions, thereby providing accurate two-dimensional wavenumber spectrum data for subsequent imaging processing. Based on this, a two-dimensional wavenumber spectrum resampling factor is further constructed to resample the range and azimuth wavenumbers separately, achieving effective decoupling of range and azimuth wavenumbers, thus obtaining accurate two-dimensional focusing results for the target area under airborne large squint conditions. Unlike traditional strategies that rely on increasing PRF to suppress azimuth ambiguity, this invention can complete azimuth wavenumber spectrum aliasing suppression and two-dimensional resampling processing without increasing PRF. This not only avoids the range ambiguity risk that may be introduced under high PRF conditions but also reduces the system's data rate requirements and real-time processing computational burden. The process of this invention is clear and easy to implement, enabling more full utilization of the two-dimensional wavenumber spectrum support area and improving imaging quality. It also exhibits good applicability and robustness under high-mobility platform large squint imaging conditions.

[0006] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0007] Step 1: Perform range dimension transformation on the acquired airborne large-slant-look SAR baseband echo signal to obtain the range wavenumber domain signal;

[0008] Step 2: Correct the aliased azimuth wavenumber spectrum generated under PRF-limited conditions to obtain the two-dimensional wavenumber domain signal that recovers the effective support domain;

[0009] Step 3: Perform range-direction matched filtering and unified phase compensation on the two-dimensional wavenumber domain signal to compensate for the range-azimuth coupling phase and obtain the compensated two-dimensional wavenumber domain signal.

[0010] Step 4: Based on the mapping relationship defined by the two-dimensional resampling factor, the two-dimensional wavenumber domain signal is resampled in two dimensions to make it equivalent to the wavenumber domain signal in the front-side view form; the resampled signal is then subjected to a two-dimensional inverse transform to obtain a SAR image focused in the range-azimuth spatial domain.

[0011] Furthermore, the expression for the distance-wavenumber domain signal is as follows: ;

[0012] in, This represents a two-dimensional signal where the range dimension is in the wavenumber domain and the azimuth dimension is in the spatial domain. The first character represents the range dimension and the second character represents the azimuth dimension, both in uppercase. Represents the wavenumber field, lowercase. Represents the spatial domain; Represents the range wavenumber variable. The wavenumber domain representation of the distance-to-envelope. This indicates the azimuth sampling location of the carrier platform. This represents the spatial domain representation of the orientation envelope. Indicates the slant distance from the scene center. Represented by natural constant an exponential function with base 0. The symbol representing the imaginary unit. Represents pi (π). Represents the speed of light. Indicates the range-directed frequency modulation. Indicates the distance to the wavenumber center. Indicates the carrier frequency of the transmitted signal. , Indicates the range of values ​​for the range wavenumber. Indicates the transmit pulse width. Indicates instantaneous slant distance. Indicates location and time.

[0013] Furthermore, the correction of the aliased azimuth wavenumber spectrum generated under PRF-constrained conditions refers to multiplying the range wavenumber domain signal with the azimuth deambiguation function to obtain the preprocessed azimuth phase; then, using the same azimuth transformation method as the range transformation, the two-dimensional wavenumber domain signal that recovers the effective support domain is obtained.

[0014] The orientation defuzzification function is as follows:

[0015] ;

[0016] in, This represents the orientation unambiguity function. This indicates the angle of view of the beam center.

[0017] The preprocessed azimuth phase is obtained by multiplying the range wavenumber domain signal by the azimuth deambiguity function, and its expression is as follows: ;

[0018] in, This indicates the slant range when the beam center sweeps across the target.

[0019] The orientation dimension transformation is obtained by the following equation: ;

[0020] Furthermore, the range-directed matched filtering refers to multiplying the two-dimensional wavenumber domain signal with a range-directed matched filter function to obtain a range-directed pulse-compressed two-dimensional wavenumber domain signal, the expression of which is as follows:

[0021] ; ;

[0022] in, This represents the distance-matched filter function. This represents a two-dimensional signal where the distance dimension is in the wavenumber domain and the azimuth dimension is in the wavenumber domain. Represents the azimuth wavenumber vector. The wavenumber domain representation of the azimuth envelope. This indicates the azimuthal distance of the target relative to the center of the scene.

[0023] Furthermore, the unified phase compensation refers to multiplying the compressed signal by the unified phase compensation function to obtain the phase-compensated two-dimensional wavenumber domain signal, the expression of which is as follows:

[0024] ;

[0025] ;

[0026] in, Represents the unified phase compensation function. Indicates the slant distance from the scene center. This indicates the cosine operation. This represents the two-dimensional wavenumber domain signal after phase compensation.

[0027] Furthermore, the two-dimensional wavenumber spectrum resampling of the two-dimensional wavenumber domain signal based on the mapping relationship defined by the two-dimensional resampling factor is expressed as follows:

[0028] ;

[0029] ;

[0030] ;

[0031] in, This represents the range wavenumber vector after two-dimensional resampling. This represents the azimuth wavenumber vector after two-dimensional resampling. This represents the wavenumber domain signal after two-dimensional resampling.

[0032] Furthermore, the two-dimensional inverse transform of the resampled signal is obtained by the following equation:

[0033] ;

[0034] in, This represents a two-dimensional signal where the distance dimension is in the spatial domain and the orientation dimension is in the spatial domain. The sinc function .

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] First, this invention corrects the aliased azimuth wavenumber spectrum by constructing an azimuth deambiguity function, enabling the two-dimensional wavenumber spectrum resampling method to be stably implemented under low to medium PRF conditions, thereby avoiding the distance ambiguity risk easily caused by high PRF. This breaks through the dependence of the two-dimensional wavenumber spectrum resampling method on high PRF, achieves focusing under low to medium PRF conditions, and improves the engineering feasibility of the algorithm.

[0037] Secondly, this invention transforms the tilted and stretched wavenumber spectrum support region under oblique viewing conditions into an equivalent frontal side-view form through two-dimensional wavenumber spectrum resampling, allowing subsequent resampling to be performed within a more regular support domain. Whether using inset interpolation for a larger effective rectangular area or outward expansion for a smaller boundary extrapolation range, it reduces interpolation extrapolation errors and increases the proportion of effective data, overcoming the problems of reduced wavenumber spectrum utilization and limited imaging quality caused by spectral support domain distortion under oblique viewing conditions in existing technologies. Attached Figure Description

[0038] Figure 1 This is a flowchart of the present invention;

[0039] Figure 2 This is a geometric configuration diagram of the oblique-view strip SAR imaging of the present invention, wherein, Figure 2 (a) shows the SAR imaging geometry of a highly maneuverable platform. Figure 2 (b) is the slant range plane geometry configuration for linear trajectory sub-aperture SAR imaging;

[0040] Figure 3 This is a schematic diagram of the azimuth wavenumber spectrum center correction of the present invention;

[0041] Figure 4 This is a schematic diagram of two-dimensional wavenumber spectrum resampling according to the present invention;

[0042] Figure 5 This is a schematic diagram of a dot matrix model according to an embodiment of the present invention;

[0043] Figure 6 This is a focusing result diagram of an embodiment of the present invention;

[0044] Figure 7 This is an azimuth cross-sectional view of point targets A, B, C, and D in an embodiment of the present invention;

[0045] Figure 8 This is a two-dimensional contour map of point targets A, B, C, and D in an embodiment of the present invention; Detailed Implementation

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0047] Reference Figure 1 The specific implementation steps of the embodiments of the present invention will be described in further detail below.

[0048] Step 1: Perform range-dimensional transformation on the acquired airborne large-slant-look SAR baseband echo signal to obtain the range-wavenumber domain signal; First, construct a geometric model for airborne SAR imaging to obtain the SAR slant-range history expression, construct the fundamental frequency echo signal based on the slant-range history, and perform range-dimensional transformation on the obtained fundamental frequency echo signal to obtain the range-wavenumber domain signal.

[0049] The large squint SAR imaging geometric model of this invention is as follows: Figure 2 As shown in (a), the projection of the airborne platform's location onto the ground. Establish a spatial rectangular coordinate system with point as the origin. During the echo acquisition process, the radar operates in strip mode, and the carrier aircraft flies at a horizontal speed v along the X-axis. The angle of view at the beam center. The azimuth beamwidth, The platform's flight altitude is [value], and the closest distance between the target and the aircraft's flight path is [value]. , The slant range from the beam center to the target is the point. The center point of the scene.

[0050] To facilitate subsequent analysis of the echo model, Figure 2 (b) The slant range plane geometry for straight-track SAR imaging is given, where point B is the azimuth starting position of the antenna phase center, i.e. At this time, point P is the position illuminated by the beam center, and the azimuth distance between point target P and point B is... ,go through After a certain time, the carrier platform moves to point C. The instantaneous slant distance between the carrier platform and point C at this moment is... It can be represented as:

[0051] ;

[0052] Assuming the radar transmit signal is a linear frequency modulated (LFM) signal, the baseband echo signal can be expressed as:

[0053] ;

[0054] in, The range sampling position of the transmitted signal. At the speed of light, For the linear frequency modulation of the transmitted signal, For carrier wavelength, and These are the spatial domain expressions for the range and azimuth window function envelopes, respectively. For subsequent two-dimensional wavenumber spectrum analysis, an accurate two-dimensional wavenumber spectrum expression for the echo signal is needed. This is achieved by performing a range-dimensional transform on the baseband echo signal, transforming it to the range-wavenumber domain, resulting in the range-wavenumber domain expression:

[0055] ;

[0056] in, For the range wavenumber variable, This is the wavenumber domain representation of the distance-oriented envelope. Indicates the distance to the wavenumber center. For transmitting signal carrier frequency, , , This represents the width of the transmitted pulse.

[0057] Step 2 involves correcting the aliased azimuth wavenumber spectrum generated under PRF-constrained conditions to obtain a two-dimensional wavenumber domain signal that recovers the effective support domain. First, an azimuth deambiguity function is introduced in the range wavenumber domain to correct the aliased azimuth wavenumber spectrum, thereby recovering the two-dimensional wavenumber domain signal of the effective support domain and ensuring stable implementation of two-dimensional resampling under low to medium PRF conditions. Subsequently, an azimuth-dimensional Fourier transform is performed on the deambigued data to obtain the preprocessed two-dimensional wavenumber domain signal.

[0058] A deambiguity function is constructed to eliminate the aliasing of the local wavenumber spectrum introduced by the large-viewing-angle platform, restoring the effective support domain of the two-dimensional wavenumber spectrum. This allows two-dimensional resampling to be stably implemented under medium-low PRF conditions. The deambiguity function is as follows:

[0059] ;

[0060] Multiplying the range wavenumber domain expression by the deambiguity function and performing a fast Fourier transform in the azimuth direction yields the two-dimensional wavenumber domain signal expression:

[0061] ;

[0062] After deblurring, the azimuth wavenumber spectrum center is shifted back to zero, eliminating azimuth wavenumber spectrum aliasing and providing an aliasing-free two-dimensional wavenumber spectrum for subsequent signal processing. A schematic diagram of azimuth wavenumber spectrum center correction is shown below. Figure 3 As shown.

[0063] Step 3: Perform range-direction matched filtering and unified phase compensation on the two-dimensional wavenumber domain signal to compensate for the range-azimuth coupling phase and obtain the compensated two-dimensional wavenumber domain signal.

[0064] Range-matched filtering is applied to a two-dimensional wavenumber spectrum signal to achieve range pulse compression. The range-matched filtering function is as follows:

[0065] ;

[0066] The new two-dimensional wavenumber spectrum expression is obtained as follows:

[0067] ;

[0068] Then, a unified phase compensation function is introduced in the two-dimensional wavenumber domain to compensate for most of the range-azimuth coupling terms, and the phase-compensated signal is obtained.

[0069] Multiply the two-dimensional wavenumber spectrum signal by a uniform phase compensation function:

[0070] ;

[0071] in, For reference distance, typically the slant distance from the scene center, we obtain:

[0072] ;

[0073] It can be seen that after unified phase compensation, most of the mid-ground range-azimuth coupling terms in the above formula are compensated, while the target at the reference range is fully compensated.

[0074] Step 4: Based on the mapping relationship defined by the two-dimensional resampling factor, perform two-dimensional wavenumber spectrum resampling on the two-dimensional wavenumber domain signal to make it equivalently represent the wavenumber domain signal in the front-side-looking form; perform a two-dimensional inverse transform on the resampled signal to obtain a SAR image focused in the range-azimuth spatial domain. First, to eliminate the residual range-azimuth coupling term, Stolt resampling is used for decoupling. First, a range dimension mapping operation is performed, with the interpolation mapping relationship as follows:

[0075] ;

[0076] To perform two-dimensional resampling along an oblique viewpoint, the original coordinate axes need to be rotated, i.e., the original coordinate system needs to be rotated. Rotate to an equivalent frontal and side view coordinate system The mapping relationship defined for two-dimensional resampling is as follows:

[0077] ;

[0078] ;

[0079] in, This represents the range wavenumber vector after two-dimensional resampling. This represents the azimuth wavenumber vector after two-dimensional resampling. This resampling method is equivalent to diagonal pulling along the support region of the two-dimensional wavenumber spectrum, which is basically equivalent to the direction of interpolation for a fixed scene viewed from the front, improving data utilization and accuracy. A schematic diagram of two-dimensional wavenumber spectrum resampling is shown below. Figure 4 As shown.

[0080] To simplify the process, the two interpolation operations are combined to obtain the two-dimensional wavenumber domain expression in the equivalent frontal and side-view conditional coordinate system:

[0081] ;

[0082] Simplifying, we get:

[0083] ;

[0084] Performing a two-dimensional inverse transform on the above equation yields a SAR image focused in the range-azimuth spatial domain, with the signal expression being:

[0085]

[0086] The target focus position is The first coordinate term is the distance-oriented focusing position, and the second term is the azimuth-oriented focusing position.

[0087] The effects of this invention will be further illustrated below with simulation experiments:

[0088] 1. Simulation experimental conditions:

[0089] The hardware platform for the simulation experiment of this invention is: Intel(R) Core(TM) i5-7300HQ processor with a main frequency of 2.40GHz and 16.00GB of memory.

[0090] The software platform for the simulation experiment of this invention is: Windows 11 operating system and MATLAB R2023a.

[0091] The system simulation parameters are shown in Table 1 below.

[0092] Table 1. Airborne SAR Simulation Parameters

[0093]

[0094] 2. Simulation content and result analysis:

[0095] The simulation experiment of this invention uses the method of this invention to simulate a point target array using typical airborne SAR imaging parameters, and verifies the effectiveness of the proposed algorithm. For a swath width of... The dot matrix is ​​used for simulation, and the dot matrix model is as follows: Figure 5 As shown. The simulation imaging results of the point target array are as follows. Figure 6 As shown. To further verify the effectiveness of the proposed method, Figure 7 The corresponding azimuth profile curves are given. Figure 8 A contour map of the point target is provided.

[0096] The following is combined with Figure 5 , Figure 6 , Figure 7 The simulation results further illustrate the effects of the present invention.

[0097] An excessively high PRF can lead to distance blurring, so the PRF needs to be less than [a certain value]. A low PRF (Positioning Frequency Filter) results in azimuth blurring, so the PRF needs to be greater than the echo Doppler bandwidth. The echo Doppler center is Therefore, the original imaging parameters cannot simultaneously meet the imaging requirements of range and azimuth. Thus, based on the existing algorithm, a deblurring function is constructed to eliminate the azimuth spectrum aliasing problem. Now, the system's PRF only needs to be greater than the Doppler accumulation bandwidth. That's all.

[0098] In the simulation implementation, the number of sampling points is taken as... The initial number of azimuth sampling points is The image was upsampled by 2x to 8192 in subsequent processing. The image is referenced to the data center. For consistency, this paper uses pixel index pairs. Indicates the position of the point target in the imaging plane, where For azimuth sampling index, This is the range sampling index. Therefore, the focus index of the lattice center point A should be located at... . Figure 6 The coordinates of the midpoint C are The imaging result corresponds to a range index offset of 100 range units relative to point A; where the range sampling interval is... The physical distance corresponding to this offset is Relationship with theoretical distance offset The results were consistent. Meanwhile, the azimuth offset of point C relative to point A was 739 azimuth units, where the azimuth sampling interval... The physical distance corresponding to this offset is Relationship with theoretical azimuth offset The results were consistent.

[0099] Figure 6 The coordinates of midpoint B are Points A and B are not on the same equidistant slope line, and the center of the slope distance of B is... The imaging result corresponds to a distance index offset of 152 distance units relative to point A; the physical distance corresponding to this offset is... Relationship with theoretical distance offset The results were consistent. Meanwhile, point B's azimuth offset relative to point A was 373 azimuth units, corresponding to a physical distance of... , This conforms to the interpolation effect along the line of sight.

[0100] Figure 6 midpoint Coordinates are The range index corresponding to its imaging results is relatively The point is offset by 152 distance units; the corresponding physical distance is... Relationship with theoretical distance offset The results were consistent. Meanwhile, the point... relatively The azimuth offset of the point is 364 azimuth units, and the corresponding physical distance is... , This is consistent with the results of two-dimensional resampling.

[0101] The above-mentioned two-dimensional positional relationships in the range and azimuth directions are consistent with the theoretical focusing expression under strabismus geometry, indicating that the proposed two-dimensional wavenumber spectrum resampling strabismus Omega-K imaging processing can achieve correct coordinate mapping and focusing positioning under simulation conditions, demonstrating the correctness of the algorithm.

[0102] like Figure 7 The azimuth profiles of the four selected points are given. It can be seen that the edge points and the center point have similar focusing effects, the first null point is low, and the first side lobe is close to the theoretical value; as shown... Figure 4 The contour maps of the four selected points are given. It can be seen that the contour maps of the four points are basically consistent, and the main and side lobes are clearly separated, which illustrates the effectiveness of the method described in this invention.

[0103] Table 2 Statistical Results of Performance Indicators

[0104]

[0105] Further quantitative evaluation of the indicators was conducted, and the azimuth resolution, peak sidelobe ratio, and integral sidelobe ratio of the selected three points were calculated, as shown in Table 2. It can be seen that the performance index parameters of the algorithm are basically consistent with the theoretical values ​​(azimuth resolution 0.66m, peak sidelobe ratio -13.26dB, integral sidelobe ratio -9.80dB), further demonstrating the effectiveness of the method described in this invention.

Claims

1. An airborne large-slant-look SAR imaging method based on two-dimensional wavenumber spectrum resampling, characterized in that, The specific steps of this imaging method include: Step 1: Perform range dimension transformation on the acquired airborne large-slant-look SAR baseband echo signal to obtain the range wavenumber domain signal; Step 2: Correct the aliased azimuth wavenumber spectrum generated under PRF-limited conditions to obtain the two-dimensional wavenumber domain signal that recovers the effective support domain; Step 3: Perform range-direction matched filtering and unified phase compensation on the two-dimensional wavenumber domain signal to compensate for the range-azimuth coupling phase and obtain the compensated two-dimensional wavenumber domain signal. Step 4: Based on the mapping relationship defined by the two-dimensional resampling factor, the two-dimensional wavenumber domain signal is resampled in two dimensions to make it equivalent to the wavenumber domain signal in the front-side view form; the resampled signal is then subjected to a two-dimensional inverse transform to obtain a SAR image focused in the range-azimuth spatial domain.

2. The airborne large-slant-view SAR imaging method according to claim 1, characterized in that, The expression for the range wavenumber domain signal mentioned in step 1 is as follows: ； in, This represents a two-dimensional signal where the range dimension is in the wavenumber domain and the azimuth dimension is in the spatial domain. The first character represents the range dimension and the second character represents the azimuth dimension, both in uppercase. Represents the wavenumber field, lowercase. Represents the spatial domain; Represents the range wavenumber variable. The wavenumber domain representation of the distance-to-envelope. This indicates the azimuth sampling location of the carrier platform. This represents the spatial domain representation of the orientation envelope. This indicates the slant range when the beam center sweeps across the target. Represented by natural constant an exponential function with base 0. The symbol representing the imaginary unit. Represents pi (π). Represents the speed of light. Indicates the range-directed frequency modulation. Indicates the distance to the wavenumber center. Indicates the carrier frequency of the transmitted signal. , Indicates the range of values ​​for the range wavenumber. Indicates the transmit pulse width. Indicates instantaneous slant distance. Indicates location and time.

3. The airborne large-slant-view SAR imaging method according to claim 2, characterized in that, The step 2 described in the section on correcting the aliased azimuth wavenumber spectrum generated under PRF-constrained conditions refers to multiplying the range wavenumber domain signal with the azimuth deambiguation function to obtain the preprocessed azimuth phase; then, using the same azimuth transformation method as the range transformation, the two-dimensional wavenumber domain signal that recovers the effective support domain is obtained.

4. The airborne large-slant-view SAR imaging method according to claim 3, characterized in that, The orientation defuzzification function is as follows: ； in, This represents the orientation unambiguity function. This indicates the angle of view of the beam center.

5. The airborne large-slant-view SAR imaging method according to claim 4, characterized in that, The preprocessed azimuth phase is obtained by multiplying the range wavenumber domain signal by the azimuth deambiguity function, and its expression is as follows: ； in, This indicates the slant range when the beam center sweeps across the target.

6. The airborne large-slant-view SAR imaging method according to claim 5, characterized in that, The orientation dimension transformation is obtained by the following equation: ； in, This represents a two-dimensional signal where the distance dimension is in the wavenumber domain and the azimuth dimension is in the wavenumber domain. Represents the azimuth wavenumber vector. The wavenumber domain representation of the azimuth envelope. This indicates the azimuthal distance of the target relative to the center of the scene.

7. The airborne large-slant-look SAR imaging method according to claim 6, characterized in that, The range-directed matched filtering mentioned in step 3 refers to multiplying the two-dimensional wavenumber domain signal with the range-directed matched filter function to obtain the range-directed pulse-compressed two-dimensional wavenumber domain signal, the expression of which is as follows: ； ； in, This represents the distance-matched filter function; This represents a two-dimensional signal where the distance dimension is in the wavenumber domain and the azimuth dimension is in the wavenumber domain. Represents the azimuth wavenumber vector. The wavenumber domain representation of the azimuth envelope. This indicates the azimuthal distance of the target relative to the center of the scene.

8. The airborne large-slant-look SAR imaging method according to claim 7, characterized in that, The unified phase compensation mentioned in step 3 refers to multiplying the compressed signal by the unified phase compensation function to obtain the phase-compensated two-dimensional wavenumber domain signal, the expression of which is as follows: ； ； in, Represents the unified phase compensation function. Indicates the slant distance from the scene center. This indicates the cosine operation. This represents the two-dimensional wavenumber domain signal after phase compensation.

9. The airborne large-slant-view SAR imaging method according to claim 8, characterized in that, Step 4 describes the two-dimensional wavenumber spectrum resampling of the two-dimensional wavenumber domain signal based on the mapping relationship defined by the two-dimensional resampling factor. The expression for this resampling is as follows: ； ； in, This represents the range wavenumber vector after two-dimensional resampling. This represents the azimuth wavenumber vector after two-dimensional resampling. This represents the wavenumber domain signal after two-dimensional resampling.

10. The airborne large-slant-look SAR imaging method according to claim 9, characterized in that, The two-dimensional inverse transform of the resampled signal described in step 4 is obtained by the following formula: ； in, This represents a two-dimensional signal where the distance dimension is in the spatial domain and the orientation dimension is in the spatial domain. The sinc function .

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