A method for improving two-dimensional resolution of GEO SAR based on spatial spectrum synthesis

Abstract

The application discloses a method for improving two-dimensional resolution of GEO SAR based on space spectrum synthesis, constructs a space spectrum shape of the GEO SAR and an expression of a space spectrum offset of an image under different viewing angles in a vector form, replaces space spectrum domain movement with image domain de-skewing, and realizes improvement of two-dimensional resolution of the GEO SAR through space spectrum synthesis.

Description

Technical Field

[0001] The present invention belongs to the technical field of synthetic aperture radar, and in particular relates to a method for improving the two-dimensional resolution of GEO SAR based on spatial spectrum synthesis. Background Art

[0002] Geosynchronous Synthetic Aperture Radar (GEOSAR) is a spaceborne SAR system operating in a geosynchronous orbit at an altitude of 36,000 km. Compared to traditional low-Earth orbit SAR, it offers advantages such as a shorter revisit period (several hours to a day) and a larger beam coverage area (with an imaging swath exceeding 1,000 km). In recent years, research trends in spaceborne SAR have focused on large constellation configurations, high resolution, and multi-dimensional monitoring. High resolution is a core performance characteristic of spaceborne SAR systems.

[0003] However, the existing GEO SAR concept is mainly aimed at imaging and measuring large-scale scenes, and has the problem of poor resolution (greater than 10m), which cannot meet the high-precision observation requirements of urban areas. The short revisit period and large beam coverage of GEO SAR enable it to improve resolution by synthesizing the spatial spectrum of SAR images acquired from different viewing angles. However, existing algorithms based on spatial spectrum synthesis are all based on airborne, LEO SAR (Low Earth Orbit SAR) or dual / multi-base platforms, and are suitable for radars operating in the front-side looking mode, but not for GEOSAR platforms that usually operate in the squint mode. Due to the squint working mode of GEO SAR and the two-dimensional spatial baseline formed by the repeated tracks, the spatial spectrum shape and relative offset of its image are different from those of the front-side looking LEO SAR. This is not mentioned in the various existing SAR resolution improvement algorithms based on spatial spectrum synthesis. Summary of the Invention

[0004] To address the above issues, the present invention provides a method for improving the two-dimensional resolution of GEO SAR images based on spatial spectrum synthesis. By interpolating, deskewing, spatial spectrum splicing, and windowing two GEO SAR images, a larger spatial spectrum bandwidth is obtained, thereby improving the two-dimensional resolution of GEO SAR images. A method for improving the two-dimensional resolution of GEO SAR images based on spatial spectrum synthesis is characterized by comprising the following steps:

[0005] Step 1: Obtain two registered SAR images of the same area;

[0006] Step 2, interpolating the two images obtained in step 1;

[0007] Step 3: De-skew each interpolated image, and then perform a two-dimensional Fourier transform on the de-skewed SAR image to obtain the image's spatial spectrum;

[0008] Step 4: Splice the spatial spectra of the two images and synthesize them using a window function in the overlapping area of ​​the spatial spectra. The specific steps are as follows:

[0009] Step 4-1: Calculate the sight direction at the center of the synthetic aperture corresponding to the center of the two images Then calculate the projection of the sight direction on the ground respectively Then calculate the spatial spectrum offset of the two images λ is the radar wavelength;

[0010] Step 4-2, calculate the boundary of the spatial spectrum overlapping area:

[0011] The overlapping part of the image space spectrum is a parallelogram, and the two adjacent sides are

[0012]

[0013]

[0014] in, is the projection of the GEOSAR effective velocity direction on the ground, B is the signal bandwidth, R is the slant range, is the sight direction at the moment of the aperture center; is the effective speed of GEO SAR, express and The angle of and are the equal Doppler direction and the equal distance direction, is the ground normal vector, then the four vertices are:

[0015]

[0016]

[0017] Step 4-3, constructing a spatial spectrum splicing window function;

[0018] Let any point in the space spectrum be P, and calculate the vector and a unit vector perpendicular to BD pointing to point A Then construct the window function:

[0019]

[0020] win2=1-win1

[0021] The spatial spectra of the two images are multiplied by the window functions win1 and win2 respectively, and then weighted added to obtain the spliced ​​spatial spectrum;

[0022] Step 5, add a Hamming window to the spliced ​​spatial spectrum;

[0023] Step 6: Perform inverse Fourier transform on the windowed spatial spectrum to obtain a GEO SAR image with improved two-dimensional resolution.

[0024] Preferably, in step 3, the de-skewing operation is as follows: first, a de-skewing phase corresponding to each pixel in the image is calculated, and then the phase corresponding to the slant range is removed from the SAR image to complete the de-skewing operation.

[0025] Preferably, in step 5, the specific method of adding a Hamming window to the spliced ​​spatial spectrum is:

[0026] First, calculate the boundary of the smallest parallelogram containing the spliced ​​spatial spectrum, and record any two adjacent sides as The four vertices are:

[0027]

[0028]

[0029] Then, the Hamming window constructed along the length of both sides of this parallelogram is:

[0030]

[0031]

[0032] The beneficial effects of the present invention are:

[0033] The present invention constructs the GEO SAR spatial spectrum shape and the spatial spectrum offset expression of images at different viewing angles in vector form, replaces the spatial spectrum domain shift with image domain deskewing, and realizes the two-dimensional resolution improvement of GEO SAR through spatial spectrum synthesis. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 To realize the algorithm flow of GEO SAR two-dimensional resolution improvement based on spatial spectrum synthesis;

[0035] Figure 2 Schematic diagram of data acquisition for GEO SAR;

[0036] Figure 3 This is the principle diagram of GEO SAR spatial spectrum synthesis;

[0037] Figure 4is the original GEO SAR main image obtained by simulation;

[0038] Figure 5 is the synthesized GEO SAR spatial spectrum obtained by simulation;

[0039] Figure 6 is the windowed GEO SAR spatial spectrum obtained by simulation;

[0040] Figure 7(a) and Figure 7(b) are the GEO SAR images before and after the two-dimensional resolution improvement obtained by simulation;

[0041] Figure 8(a) and Figure 8(b) are the cross-sections along the x-axis and y-axis of the GEO SAR image before and after the two-dimensional resolution improvement obtained by simulation, respectively. DETAILED DESCRIPTION

[0042] The present invention will be described in detail below with reference to the accompanying drawings.

[0043] The flow chart of the present invention is as follows Figure 1 Improving the two-dimensional resolution of GEO SAR based on spatial spectrum synthesis requires two SAR images, which can be obtained by illuminating the same area multiple times by the same GEO satellite, as shown in Figure 2. Figure 2 The specific steps are as follows:

[0044] Step 1: Obtain two SAR images of the same area after registration, denoted as I n , n=1,2; obtain the position and velocity of the SAR at the center of the orbital aperture corresponding to the two images, which are recorded as and Get the coordinates of the pixel at the center of the SAR image (corresponding to the center of the scene), recorded as

[0045] Step 2: Interpolate each image. Since the original sampling interval and resolution of the image are usually roughly the same, they cannot meet the requirements of the improved image resolution. Perform a two-dimensional Fourier transform on the image, and then perform zero padding on the spatial spectrum in the two-dimensional spatial spectrum domain to complete the interpolation processing in the image domain. The interpolated SAR image is denoted as I interp_n , n=1,2.

[0046] Step 3: De-skew each interpolated image. De-skew is to compensate all pixels in the image for the theoretical imaging phase of the ground plane corresponding to the pixel. First, calculate the de-skew phase corresponding to each pixel in the image. in Indicates the tracks corresponding to the two images to the image pixels The slant range is λ, and the radar wavelength is λ. Then, the phase corresponding to the slant range is removed from the SAR image, and the SAR image after slant removal is recorded as Finally, a two-dimensional Fourier transform is performed on the de-skewing SAR image to obtain the spatial spectrum of the image.

[0047] Here, image domain de-skewing is used instead of spatial spectrum domain shifting. The specific principle is as follows.

[0048] Consider the ground at For a point target at , after SAR imaging, the point spread function (PSF) of the target is:

[0049]

[0050]

[0051] Where c is the speed of light, A(·) is the envelope of the PSF, Represents the scattering coefficient and phase of the target. is the complex scattering coefficient of the target. is the position of any point on the ground, are the aperture center moment (ACM) position and velocity of the satellite, respectively.

[0052] is the line of sight direction at the aperture center moment. B is the signal bandwidth, T is the synthetic aperture time, R is the slant distance, and λ is the wavelength. Therefore is the projection matrix of the normal vector.

[0053] Assume the center of the scene is but:

[0054]

[0055] in, represents the distance between the target and the center of the scene, Indicates the direction of sight Projection on the ground.

[0056] Combining (1) and (2), we can get:

[0057]

[0058] Next, we analyze the process of de-skewing. Assume that there is only one point target in the scene, and the imaging result contains the main lobe and multiple side lobes. Assume that the center of the main lobe is located at The entire imaging area can be expressed as The size of is usually several side lobes, which is greater than 1. Then the phase of the point target after imaging is:

[0059]

[0060] Where φ0 is the scattering phase of the target, is the position of the satellite at the center of the synthetic aperture.

[0061] Deskewing is to remove the phase corresponding to the slant range in the SAR image. The slant range used for deskewing each pixel is determined by the location of each pixel. Similar to (2), the phase obtained after deskewing is:

[0062]

[0063] Comparing (4) and (5), the phase of the image before de-skewing is spatially invariant. However, after de-skewing, the phase of the image changes linearly along the ground range direction. According to the properties of the Fourier transform, when the point target PSF is transformed into the two-dimensional frequency domain, an offset along the ground range direction will occur.

[0064] According to (3) and (5), the residual phase after de-skewing is equivalent to the phase corresponding to the spatial spectrum shift. Therefore, we use the image domain de-skewing operation to replace the spatial spectrum domain spectrum shifting process.

[0065] Step 4: Splice the spatial spectra of the two images and synthesize them using a window function in the overlapping area of ​​the spatial spectra. The specific steps are as follows.

[0066] Step 4-1: Calculate the sight direction at the center of the synthetic aperture corresponding to the center of the two images The projections of the sight lines on the ground are Then calculate the spatial spectrum offset of the two images using The specific principles are as follows.

[0067] Assuming that there are multiple scattering points on the ground, The imaging result at can be expressed as:

[0068]

[0069] in Represents the convolution operation.

[0070] The two-dimensional spatial spectrum of the image is (6) The result of the two-dimensional Fourier transform on the two-dimensional plane where the image is located. According to the properties of the Fourier transform, the image space spectrum can be expressed as:

[0071]

[0072] in represents a two-dimensional beam domain.

[0073] According to the properties of Fourier transform, In the wavenumber domain it can be expressed as:

[0074]

[0075] Taking the complex scattering coefficient σ as a reference, the offset of the image spatial spectrum is Assume that the projections of the sight lines of the two images on the ground are Then the spectral shift between the two images is:

[0076]

[0077] Step 4-2, calculate the boundary of the spatial spectrum overlapping area. The overlapping part of the image spatial spectrum is a parallelogram, and the two adjacent sides are The calculation method is

[0078] in is the projection of the GEO SAR effective velocity direction on the ground, express and The angle of and Are equal Doppler direction and equal distance direction respectively, then the four vertices are The specific principles are as follows.

[0079] In formula (7), is the spatial spectrum of the PSF envelope, which can be expressed as:

[0080]

[0081] Where C is a constant that has nothing to do with the shape of the spatial spectrum, and They are the equal Doppler direction and the equal distance direction respectively:

[0082]

[0083]

[0084] in, is the effective speed of GEO SAR, is the ground normal vector, Indicates the direction of sight Projection on the ground, P g The projection matrix representing the projection onto the target's plane.

[0085] From (10), we can see that the shape of the spatial spectrum is a parallelogram composed of rectangular window functions, and two adjacent sides can be expressed as:

[0086]

[0087] in, express and The angle of Indicates effective speed Projection on the ground. For GEO SAR, and They are usually not orthogonal, so the shape of the spatial spectrum is a general parallelogram.

[0088] Considering that the overlapping area of ​​the spatial spectrum is a parallelogram, the splicing window function should be a two-dimensional window function that gradually changes along the diagonal, such as Figure 3 The center of the overlapping area is The four vertices A, B, C, and D of a parallelogram can be expressed as:

[0089]

[0090] in, are two adjacent sides of the parallelogram, that is:

[0091]

[0092] Step 4-3, construct the spatial spectrum splicing window function. Let any point in the spatial spectrum be P, and calculate the vector and a unit vector perpendicular to BD pointing to point A Then construct the window function:

[0093]

[0094] The spatial spectra of the two images are multiplied by the window functions win1 and win2 respectively, and then weighted added to obtain the spliced ​​spatial spectrum.

[0095] Step 5: Add a Hamming window to the spliced ​​spatial spectrum. First, calculate the boundary of the smallest parallelogram containing the spliced ​​spatial spectrum, and record the two adjacent sides as The calculation method is The four vertices are:

[0096]

[0097] Then, within this parallelogram, a Hamming window is constructed along the length of both sides using the following method:

[0098]

[0099]

[0100] Where p represents the variable of the Hamming window.

[0101] Step 6: Perform inverse Fourier transform on the windowed spatial spectrum to obtain a GEO SAR image with improved two-dimensional resolution.

[0102] Next, an implementation example is given with specific parameters.

[0103] In this example, we consider GEO SAR imaging of a point target. The satellite orbit elements and platform parameters used in the simulation are shown in Table 1. The SAR image has a ground resolution of 8.86 m and an azimuth resolution of 8.86 m.

[0104] Table 1

[0105]

[0106] First, follow step 1 to obtain information such as satellite speed and coordinates, scene coordinates, etc.; then obtain images (here we use the SAR BP imaging algorithm, the first day image is as follows Figure 4 Since the BP imaging algorithm is used, the images do not need to be registered.

[0107] Execute step 2 to perform interpolation on the two images.

[0108] Execute step 3 to perform a deskew operation on the two images and perform a two-dimensional Fourier transform on the images.

[0109] Execute step 4 to stitch the spatial spectra of each image. Figure 5 The synthesized GEO SAR spatial spectrum is shown.

[0110] Execute step 5 to add a Hamming window to the spliced ​​spatial spectrum. Figure 6 The windowed GEO SAR spatial spectrum is shown.

[0111] Execute step 6 to perform inverse Fourier transform on the windowed spatial spectrum.

[0112] Figure 7 shows the GEO SAR imagery before and after two-dimensional resolution enhancement after windowing. It can be seen that point targets in the spatial spectrum synthesized image have narrower main lobes than the original GEO SAR imagery. The resolution unit area is increased from 58.67 m² to 33.78 m².

[0113] Figure 8 shows a 2D cross-section of a GEO SAR image before and after the 2D resolution enhancement. The 3dB mainlobe width along the x-axis increases from 9.07m to 7.20m, and the 3dB mainlobe width along the y-axis increases from 9.07m to 6.13m, verifying the effectiveness of this method.

Claims

1. A method for improving the two-dimensional resolution of GEO SAR based on spatial spectrum synthesis, characterized in that: The steps include: Step 1: Obtain two registered SAR images of the same area; Step 2, interpolating the two images obtained in step 1; Step 3: De-skew each interpolated image, and then perform a two-dimensional Fourier transform on the de-skewed SAR image to obtain the image's spatial spectrum; Step 4: Splice the spatial spectra of the two images and synthesize them using a window function in the overlapping area of ​​the spatial spectra. The specific steps are as follows: Step 4-1: Calculate the sight direction at the center of the synthetic aperture corresponding to the center of the two images Then calculate the projection of the sight direction on the ground respectively Then calculate the spatial spectrum offset of the two images λ is the radar wavelength; Step 4-2, calculate the boundary of the spatial spectrum overlapping area: The overlapping part of the image space spectrum is a parallelogram, and the two adjacent sides are in, is the projection of the GEO SAR effective velocity direction on the ground, B is the signal bandwidth, R is the slant range, is the sight direction at the moment of the aperture center; is the effective speed of GEOSAR, express and The angle of and are the equal Doppler direction and the equal distance direction, is the ground normal vector, then the four vertices are: Step 4-3, constructing a spatial spectrum splicing window function; Let any point in the space spectrum be P, and calculate the vector and a unit vector perpendicular to BD pointing to point A Then construct the window function: win2=1-win1 The spatial spectra of the two images are multiplied by the window functions win1 and win2 respectively, and then weighted added to obtain the spliced ​​spatial spectrum; Step 5, add a Hamming window to the spliced ​​spatial spectrum; Step 6: Perform inverse Fourier transform on the windowed spatial spectrum to obtain a GEO SAR image with improved two-dimensional resolution.

2. The method for improving GEO SAR two-dimensional resolution based on spatial spectrum synthesis according to claim 1, characterized in that: In step 3, the de-skewing operation is as follows: first, the de-skewing phase corresponding to each pixel in the image is calculated, and then the phase corresponding to the slant range is removed from the SAR image to complete the de-skewing operation.

3. The method for improving GEO SAR two-dimensional resolution based on spatial spectrum synthesis according to claim 1, characterized in that: In step 5, the specific method of adding a Hamming window to the spliced ​​spatial spectrum is: First, calculate the boundary of the smallest parallelogram containing the spliced ​​spatial spectrum, and record any two adjacent sides as The four vertices are: Then, the Hamming window constructed along the length of both sides of this parallelogram is:

Images