A multi-frequency tomographic SAR three-dimensional imaging method

Abstract

The present invention belongs to the field of synthetic aperture radar technology, and in particular relates to a multi-frequency tomographic SAR (Synthetic Aperture Radar) three-dimensional imaging method. The specific process is as follows: first, multiple observations are performed at different spatial locations using a SAR payload to acquire SAR images at different operating frequencies; second, the acquired SAR images are registered so that image pixels on the same coordinate grid correspond to the same scattering unit on the ground; third, interferometry is performed on the SAR images with the same operating frequency to obtain an expected interference signal, and amplitude normalization is performed based on the expected interference signal to construct an interferogram stack for multi-frequency tomographic processing; finally, elevation estimation is performed based on the interferogram stack to complete the three-dimensional imaging.

Description

Technical Field

[0001] The present invention belongs to the technical field of synthetic aperture radar (SAR), and in particular relates to a multi-frequency tomography SAR three-dimensional imaging method. Background Art

[0002] Tomographic synthetic aperture radar can overcome the inherent overlap problem of SAR imaging and achieve three-dimensional imaging. Therefore, it is an effective 3D mapping method and provides a valuable solution for urban management and disaster detection.

[0003] Ideally, tomographic SAR requires radar platforms to fly along densely distributed parallel trajectories at varying altitudes to acquire a sufficient number of baselines. For observations of a dozen or so flybys, airborne platforms often require days or even weeks, while spaceborne platforms often require months or even years. This low observation efficiency limits the application of tomographic SAR in three-dimensional mapping.

[0004] Therefore, a time-efficient tomographic SAR three-dimensional imaging method is needed. Summary of the Invention

[0005] In view of this, the present invention proposes a multi-frequency tomographic SAR three-dimensional imaging method, which combines multiple working frequencies and multiple baselines to complete tomographic processing. It can complete three-dimensional imaging with a limited number of observations, greatly improving the observation efficiency.

[0006] The technical solutions for implementing the present invention are as follows:

[0007] A multi-frequency tomographic SAR three-dimensional imaging method, the specific process is as follows:

[0008] First, the SAR payload is used to perform multiple observations at different locations in space to obtain SAR images at different operating frequencies.

[0009] Secondly, the acquired SAR images are registered so that the image pixels in the same coordinate grid correspond to the same scattering unit on the ground;

[0010] Thirdly, interferometric processing is performed on SAR images with the same operating frequency to obtain an expected interference signal, amplitude normalization processing is performed based on the expected interference signal, and an interferogram stack for multi-frequency tomography processing is constructed;

[0011] Finally, elevation estimation is performed based on the interferogram stack to complete three-dimensional imaging.

[0012] Furthermore, the interferometric processing of SAR images with the same operating frequency described in the present invention is specifically as follows: assuming that M observations are performed at different positions in space using a SAR payload, and each observation of the SAR payload acquires L SAR images with different operating frequencies;

[0013] The interferometric processing comprises: performing deskewing on the SAR image to remove the phase term caused by the reference slant range, then using the SAR image obtained by the Kth observation as the master image, performing complex conjugate multiplication on the slave images with the same operating frequency and the master image to obtain an (M-1)L-amplitude interferogram.

[0014] Furthermore, the expectation of the interference signals of the m-th and K-th images of the present invention is:

[0015]

[0016] Among them, p(s,f l ) is the spatial power spectrum in the NSR direction, Δs is the height range in the NSR direction, is the spatial frequency corresponding to the baseline of the mth and Kth images, and s is the NSR height.

[0017] Furthermore, the present invention is based on the expectation of performing amplitude normalization processing on the interference signal, removing its amplitude information and retaining its phase information. The normalization processing process is:

[0018] The spatial power spectrum p(s,f) of the NSR direction is expressed as:

[0019] p(s,f)=A(f)p0(s)

[0020] Where A(f) is the amplitude of the spatial power spectrum, and p0(s) is the normalized spatial power spectrum;

[0021] The interference signal is expected to be expressed as:

[0022]

[0023] Among them, A(f l ) is the interference signal The amplitude value of

[0024]

[0025] Perform amplitude normalization on the interference signal, that is, remove its amplitude information and retain only the phase information;

[0026]

[0027] The normalized interference pattern stack is obtained, which is expressed as:

[0028]

[0029] The normalized interference pattern stack is then discretely represented as:

[0030] η0=Ψp0+ε

[0031] in, is the (M-1)L-dimensional observation vector;

[0032] Ψ=[ψ(s1),ψ(s2),...,ψ(s N )] is a (M-1)L×N dimensional mapping matrix;

[0033] is p0(s i ) corresponding mapping vector;

[0034] p0=[p0(s1),p0(s2),...,p0(s N )] T is the N-dimensional space power spectrum vector; ε is the noise vector.

[0035] Furthermore, the present invention uses spectrum estimation or compressed sensing methods to perform spectrum estimation processing in the height dimension based on the interference pattern stack after amplitude normalization to obtain elevation information.

[0036] Furthermore, the present invention utilizes a SAR payload to perform multiple observations at different locations in space to obtain SAR images of different operating frequencies, specifically:

[0037] The flight platform is equipped with multiple SAR payloads with different operating frequencies. During observation, each SAR payload works independently and simultaneously to obtain SAR images with different operating frequencies.

[0038] Furthermore, the present invention utilizes a SAR payload to perform multiple observations at different locations in space to obtain SAR images of different operating frequencies, specifically:

[0039] The SAR payload transmits and receives a set of chirp signals with step-changing operating frequencies in a stepped frequency manner. The received echoes with different operating frequencies are regarded as echoes from different channels. The signals of each channel are independently imaged to obtain SAR images with different operating frequencies.

[0040] Furthermore, the present invention utilizes a SAR payload to perform multiple observations at different locations in space to obtain SAR images of different operating frequencies, specifically:

[0041] The received echo is spectrum-segmented along the range direction, and the sub-band data of each spectrum after segmentation is imaged separately to obtain SAR images of different working frequencies.

[0042] Beneficial effects:

[0043] This invention uses SAR images at multiple operating frequencies for multi-frequency tomography processing, enabling 3D imaging with a limited number of observations by increasing the frequency freedom. While achieving imaging quality comparable to traditional tomographic SAR, this invention significantly improves observation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0045] Figure 1 Schematic diagram of the multi-frequency tomographic SAR observation configuration;

[0046] Figure 2 This is a multi-frequency tomographic SAR processing flow chart;

[0047] Figure 3 Track distribution of (a) multi-frequency tomography SAR and (b) traditional multi-baseline tomography SAR; equivalent sampling of (c) multi-frequency tomography SAR and (d) traditional multi-baseline tomography SAR in spatial frequency;

[0048] Figure 4 The set of elevation estimation profiles obtained by (a) multi-frequency tomography SAR and (c) traditional multi-baseline tomography SAR; the elevation estimation profiles of the 41st group of point targets obtained by (b) multi-frequency tomography SAR and (d) traditional multi-baseline tomography SAR. DETAILED DESCRIPTION

[0049] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0050] It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments may be combined with each other; and, based on the embodiments in this disclosure, all other embodiments obtained by persons of ordinary skill in the art without creative work are within the scope of protection of this disclosure.

[0051] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0052] like Figure 1-2 As shown, the embodiment of the present application provides a multi-frequency tomographic SAR three-dimensional imaging method, the specific process is as follows:

[0053] First, multiple observations are made at different locations in space using a SAR payload to acquire SAR images of different operating frequencies. Second, the acquired SAR images are registered so that image pixels on the same coordinate grid correspond to the same scattering unit on the ground. Third, SAR images with the same operating frequency are interferometrically processed to obtain the expected interference signal. Based on this expected interference signal, amplitude normalization is performed to construct an interferogram stack for multi-frequency tomography processing. Finally, elevation estimation is performed based on the interferogram stack to complete three-dimensional imaging.

[0054] like Figure 2 As shown, the above process is described in detail below:

[0055] Step 1: Multi-frequency SAR image acquisition

[0056] Acquisition: SAR payloads are used to perform M observations at different locations in space. In each observation, the SAR payload can acquire L SAR images with different operating frequencies. The main methods for acquiring multi-frequency SAR images include:

[0057] (1) The flight platform is equipped with multiple SAR payloads with different operating frequencies. During observation, each SAR payload works independently and simultaneously to obtain SAR images with different operating frequencies.

[0058] (2) The SAR payload transmits and receives a set of chirp signals with step-changing operating frequencies in a stepped frequency manner. The received echoes with different operating frequencies are regarded as echoes from different channels. The signals of each channel are imaged independently to obtain SAR images with different operating frequencies.

[0059] (3) The received echo is spectrum-segmented along the range direction, and the sub-band data of each spectrum after segmentation is imaged separately to obtain SAR images of different working frequencies.

[0060] The present invention has no requirements on the method of acquiring multi-frequency data, and is therefore not limited to the above three acquisition methods.

[0061] Step 2: Image Registration

[0062] Due to differences in viewing angles, the coordinates of the same target in different SAR images may shift, and the images themselves may be distorted. To ensure that identical coordinates in different SAR images correspond to the same ground object, registration is necessary. Numerous mature algorithms are available for SAR image registration, so we will not elaborate on them here.

[0063] Step 3: Interference processing

[0064] After image registration, the Kth SAR image is used as the master image. The slave images with the same operating frequency are complex-conjugate multiplied with the master image to produce (M-1)L interferograms. All interferograms are then de-skewing to remove the phase term caused by the reference slant range, allowing for subsequent focusing in the altitude direction.

[0065] Consider performing multi-frequency tomography processing based on interferograms. That is, instead of directly using multiple SAR images with different operating frequencies, multiple interferograms with different operating frequencies are used for tomography processing. This processing has the following advantages:

[0066] (1) Interference processing can eliminate the differences in scattering characteristics caused by different operating frequencies.

[0067] (2) Interference processing does not destroy phase information, which is important information for elevation reconstruction.

[0068] In the mth observation, the operating frequency is f l The complex value of a single pixel in the SAR image can be expressed as

[0069]

[0070] Where Δs is the height range of NSR (normal-slant-range). γ(s,f l ) is the operating frequency f l The scattering coefficient under . is the NSR height s, operating frequency f l The corresponding spatial frequency is expressed as

[0071]

[0072] Among them, f l is the operating frequency, b m represents the position of the SAR payload, and r represents the slant range.

[0073] Here we will specifically explain the difference between operating frequency and spatial frequency. Operating frequency is the center frequency of the radar transmission signal, and its unit is Hz. The "multi-frequency tomography" mentioned above refers to the radar having multiple operating frequencies. Spatial frequency refers to the frequency term of the complex exponential in the Fourier transform represented by formula (1), and its unit is m. -1 Since it is the Fourier transform of the spatial scattering function of the NSR upward, this frequency is called the spatial frequency.

[0074] The Kth image is selected as the main image, and other SAR images with the same operating frequency are subjected to interference processing.

[0075]

[0076] Assuming the scattering coefficient γ(s,f l ) obeys Gaussian distribution and is white, then its power spectrum density is stationary, then we have

[0077] E{γ(s,f l )γ * (s',f l )}=p(s,f l )δ(s-s') (4)

[0078] Among them, p(s,f l ) is the operating frequency f l The spatial power spectrum function under .

[0079] At this time, the expectation of the interference signal can be expressed as

[0080]

[0081] Define the baseline of the mth and kth images as b m,K =b m -b K , and its corresponding spatial frequency is

[0082]

[0083] The expectation of the interference signal, that is, the autocorrelation function of the original signal, can be expressed as

[0084]

[0085] in, It can be considered as the sampling of the autocorrelation function of the original signal at different spatial frequencies. Due to the spatial stationarity of the signal, It has nothing to do with the absolute spatial position, but is related to the spatial position difference (baseline), and it is related to the spatial power spectrum p(s,f l) is still the relationship of Fourier transform.

[0086] Step 4: Amplitude Normalization

[0087] p(s,f) is the spatial power spectrum in the NSR direction. It is not only a function of the NSR direction but also related to the operating frequency. According to Equation (4), the interferometric processing eliminates the phase information of the target scattering function and only retains the amplitude information. In other words, changes in the operating frequency only affect the amplitude of p(s,f), so p(s,f) can be expressed as:

[0088] p(s,f)=A(f)p0(s) (8)

[0089] Where A(f) is the amplitude of the spatial power spectrum, which is related to the operating frequency. p0(s) is the normalized spatial power spectrum, which is independent of the operating frequency and depends only on the scatterer distribution in the NSR direction. Substituting (8) into (7) yields:

[0090]

[0091] For simplicity, we assume that the vertical direction is ideally focused and the target is an ideal point scatterer. In this case, p0(s) is a Dirac function, p0(s) = δ(s). Substituting into (9), we can obtain A(f l ) is the interference signal The amplitude value of .

[0092]

[0093] For SAR images with the same operating frequency and different baselines, it is assumed that within the critical baseline, the target maintains coherence and its scattering coefficient remains unchanged. In other words, at the same operating frequency, the amplitude of the interference signal is the same for different baselines. Therefore, the interference signal is also amplitude normalized, removing the amplitude information and retaining only the phase information.

[0094]

[0095] At this time, formula (9) can be expressed as

[0096]

[0097] By normalizing the interferogram, the problem of varying scattering characteristics due to different operating frequencies is resolved. Although this process results in p0(s) being unable to represent the target's scattering information, it still provides information about the target's elevation. Furthermore, Equation (12) remains a spectrum estimation problem. Therefore, multi-frequency tomography can be implemented based on Equation (12).

[0098] Discretize (12) and consider the noise, then (12) can be expressed in matrix form. Solve (13) to complete the target elevation estimation.

[0099] η0=Ψp0+ε (13)

[0100] in, is the (M-1)L-dimensional observation vector. Ψ=[ψ(s1),ψ(s2),...,ψ(s N )] is a (M-1)L×N dimensional mapping matrix.

[0101] is p0(s i ) corresponding mapping vector. p0=[p0(s1),p0(s2),...,p0(s N )] T is the N-dimensional space power spectrum vector. ε is the noise vector.

[0102] Step 5: Elevation estimation

[0103] Equation (13) shows that the elevation estimation problem for tomographic SAR is essentially a spectral estimation problem. Therefore, spectral estimation or compressed sensing methods can be used to perform height-dimensional spectral estimation based on the amplitude-normalized interferogram stack. Algorithms for solving this problem, such as ISTA and BPDN, are already well-established and will not be elaborated on here.

[0104] Implementation Examples

[0105] The effect of the present invention is further illustrated below through a point target simulation test.

[0106] Simulation conditions: The simulation was conducted based on point targets, with a total of 81 groups of point targets. Each group contained two overlapping scatterers, one of which had a fixed elevation of 0m and the other whose elevation varied linearly from -40m to +40m.

[0107] Multi-frequency tomography SAR and traditional multi-baseline tomography SAR were simulated to verify the effectiveness of the proposed method. Multi-frequency tomography SAR made 5 observations, and the track distribution is as follows: Figure 3 As shown in (a), four baselines are formed. Each observation is performed at seven operating frequencies (280, 320, 360, 400, 440, 480, 520 MHz). The equivalent sampling in spatial frequency is as follows: Figure 3 (c) shows a Rayleigh resolution of 1.25 m. A total of 19 observations were made using conventional multi-baseline tomographic SAR, with the track distribution shown in Figure 2. Figure 3 As shown in (b), 18 baselines are formed. Each observation is performed at the same operating frequency (400MHz). The equivalent sampling in spatial frequency is as follows: Figure 3 As shown in (d), a Rayleigh resolution of 1.63 m is achieved. Both methods use the TSVD algorithm as the elevation estimation algorithm.

[0108] Figure 4 (a) and (c) show the sets of all elevation profiles obtained using the two methods. Each column represents the elevation profile of a set of point targets. The horizontal axis is the true height of the moving scatterer in the two scatterers, and the vertical axis is the estimated elevation value. Each elevation profile is normalized based on its maximum peak value. Figure 4 (b) and (d) show the elevation estimation results for the 41st point target (height 0 m) using the six methods. As can be seen from the figures, the proposed multi-frequency tomographic SAR, with a limited number of observations, can achieve similar estimation results as traditional multi-baseline tomographic SAR, which requires a larger number of observations.

[0109] The two methods were quantitatively evaluated for resolution, integrated sidelobe ratio, elevation estimation accuracy, and number of observations. The results are shown in Table 1. The proposed multi-frequency tomographic SAR, using only five observations, achieves performance similar to that of conventional multi-baseline tomographic SAR, which requires a much larger number of observations (19). Therefore, the proposed method significantly improves observation efficiency while maintaining image quality.

[0110] Table 1 Evaluation results of simulation experiments

[0111]

[0112] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may of course make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

[0113] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A multi-frequency tomographic SAR three-dimensional imaging method, characterized in that: The specific process is: First, the SAR payload is used to perform multiple observations at different locations in space to obtain SAR images at different operating frequencies. Secondly, the acquired SAR images are registered so that the image pixels in the same coordinate grid correspond to the same scattering unit on the ground; Thirdly, interferometric processing is performed on SAR images with the same operating frequency to obtain an expected interference signal, amplitude normalization processing is performed based on the expected interference signal, and an interferogram stack for multi-frequency tomography processing is constructed; Finally, elevation estimation is performed based on the interferogram stack to complete the three-dimensional imaging; Assume that the expectation of the interference signal of the mth and Kth images is: Among them, p(s,f l ) is the spatial power spectrum in the NSR direction, Δs is the height range in the NSR direction, is the spatial frequency corresponding to the baseline of the mth and Kth images, s is the NSR height, f l is the operating frequency; The amplitude normalization processing is performed based on the expectation of the interference signal, and the amplitude information is removed while the phase information is retained. The normalization processing process is: The spatial power spectrum p(s,f l ) is expressed as: p(s,f l )=A(f l )p0(s) Among them, A(f l ) is the amplitude of the spatial power spectrum, p0(s) is the normalized spatial power spectrum; The interference signal is expected to be expressed as: Among them, A(f l ) is the interference signal The amplitude value of Perform amplitude normalization on the interference signal, that is, remove its amplitude information and retain only the phase information; The normalized interference pattern stack is obtained, which is expressed as: The normalized interference pattern stack is then discretely represented as: η0=Ψp0+ε in, is the (M-1)L-dimensional observation vector; Ψ=[ψ(s1),ψ(s2),...,ψ(s N )] is a (M-1)L×N dimensional mapping matrix; is p0(s i ) corresponding mapping vector; p0=[p0(s1),p0(s2),...,p0(s N )] T is the N-dimensional space power spectrum vector; ε is the noise vector.

2. The multi-frequency tomographic SAR three-dimensional imaging method according to claim 1, characterized in that: The interferometric processing of SAR images with the same operating frequency is specifically as follows: assuming that M observations are performed at different positions in space using a SAR payload, and each observation of the SAR payload acquires L SAR images with different operating frequencies; The interferometric processing comprises: performing deskewing on the SAR image to remove the phase term caused by the reference slant range, then using the SAR image obtained by the Kth observation as the master image, performing complex conjugate multiplication on the slave images with the same operating frequency and the master image to obtain an (M-1)L-amplitude interferogram.

3. The multi-frequency tomographic SAR three-dimensional imaging method according to claim 1, characterized in that: Based on the amplitude-normalized interference pattern stack, spectral estimation or compressed sensing method is used to perform spectral estimation processing in the height dimension to obtain elevation information.

4. The multi-frequency tomographic SAR three-dimensional imaging method according to claim 1, characterized in that: The SAR payload is used to perform multiple observations at different locations in space to obtain SAR images at different operating frequencies, specifically: The flight platform is equipped with multiple SAR payloads with different operating frequencies. During observation, each SAR payload works independently and simultaneously to obtain SAR images with different operating frequencies.

5. The multi-frequency tomographic SAR three-dimensional imaging method according to claim 1, characterized in that: The SAR payload is used to perform multiple observations at different locations in space to obtain SAR images at different operating frequencies, specifically: The SAR payload transmits and receives a set of chirp signals with step-changing operating frequencies in a stepped frequency manner. The received echoes with different operating frequencies are regarded as echoes from different channels. The signals of each channel are independently imaged to obtain SAR images with different operating frequencies.

6. The multi-frequency tomographic SAR three-dimensional imaging method according to claim 1, characterized in that: The SAR payload is used to perform multiple observations at different locations in space to obtain SAR images at different operating frequencies, specifically: The received echo is spectrum-segmented along the range direction, and the sub-band data of each spectrum after segmentation is imaged separately to obtain SAR images of different working frequencies.

Images