1. Introduction
Synthetic aperture radar (SAR), which can provide remote sensing images during the day and night regardless of weather conditions, plays an important role in Earth and planetary observation [
1,
2,
3]. In recent years, high resolution SAR imaging attracts growing interest due to its wide applications especially in military reconnaissance and disaster monitoring [
4,
5,
6,
7,
8,
9,
10]. Several spaceborne SAR systems have the ability of submeter imaging. For example, the COSMO-SkyMed SAR can achieve a high azimuth resolution better than 0.9 m [
6], while TerraSAR-X can achieve 0.16 m azimuth resolution [
7]. In addition, the Gaofen-3 (GF-3) satellite, a C-band multi-polarization SAR of China launched in 2016, can achieve 0.4 m azimuth resolution [
5,
10]. The realization of high resolution SAR imaging not only puts forward new requirements to the hardware of SAR system but also poses new challenges to the imaging algorithm.
In the high resolution spotlight mode, the satellite steers its antenna beam to continuously illuminate the same area of interest. As a result, the raw signal azimuth bandwidth is larger than pulse repetition frequency (PRF) [
11], which increases the difficulty of imaging processing compared with the stripmap mode. A standard approach employed when processing the SAR data is based on the start-stop approximation, with the assumption that the radar transmits and receives the signal at the same position [
12]. Although it has been widely used in SAR echo model, it is no longer applicable in high resolution spotlight case [
7]. Therefore, the non-start-stop model should be used in imaging processing [
13]. Additionally, due to the long trajectory, the error introduced by curved orbit should also be corrected [
6]. Topography dependence and atmospheric effects should be considered [
7,
14], which further increases the complexity of imaging processing.
In order to solve the problems mentioned above, numerous algorithms have been proposed for high resolution SAR imaging. The full-aperture algorithm and subaperture algorithm are two typical frequency domain algorithms. The two-step processing approach [
11], integrated with the efficiency of SPECAN algorithms and the precision of stripmap focusing techniques, is a typical full aperture approach and has been further studied in [
15]. The subaperture algorithm first divides the raw data into subapertures in the azimuth time domain and the high-resolution is obtained by synthesizing the coarse resolution images of each subaperture [
7,
16]. The subaperture algorithm solves the curved orbit problem by motion compensation. However, there are residual errors due to the variance of echo signal property along range and azimuth directions. Besides, there are some inconveniences for frequency domain algorithms to adapt to the topography variance in the ground. The time domain algorithm is available for different SAR configurations and the imaging result on the ground can be obtained directly by time domain algorithm [
14,
17,
18]. The backprojection algorithm (BPA), a typical time domain algorithm, has been widely used in SAR imaging [
19,
20]. The disadvantage of BPA is its high computational burden. There are two strategies for improving the efficiency of BPA. One strategy is using parallel computing tool, for example, GPU. In recent years, the development of GPU has made significant progress. The parallel BPA based on the GPU has been attracting more and more attention and there is great progress in the acceleration of the BPA [
19,
20,
21]. Another strategy is developing the fast algorithms. Numerous fast algorithms of BPA have been developed in the last few decades [
22,
23,
24,
25,
26,
27,
28,
29]. The fast factorized BP (FFBP) algorithm, which splits long synthetic aperture into short subapertures to generate coarse resolution images and then fuses coarse resolution images to form the final image via interpolation, is an effective algorithm to reduce the computational burden [
23,
30]. However, the massive interpolations limit the efficiency and introduce errors that result in artifacts in the final image. The accelerating fast BP (AFBP) algorithm is proposed for the high-resolution SAR imaging [
29]. The AFBP algorithm only contains two stages: subimage formation in unified polar coordinate and subimage fusion in the 2-D wavenumber domain, which can improve efficiency compared with FFBP algorithm [
29]. The Cartesian factorized BP (CFBP) algorithm is proposed in [
25,
31] and has been further studied in [
26,
32,
33]. Two spectrum compressing filters are applied in CFBP algorithm, which can decrease the cross-range Nyquist sampling rate (NSR) enormously, therefore reducing the computational burden. In addition, during image combination, interpolation can be easily achieved by zero-padding in the azimuth frequency domain, leading to a substantial improvement on both the accuracy and the efficiency [
33].
In this paper, a modified CFBP algorithm is proposed for high resolution spotlight SAR imaging. Since the traditional echo model is derived based on start-stop approximation, there will be intolerable error in high resolution case, which will cause defocusing of the target. In order to solve this problem, an accurate correct echo model is firstly derived. The non-start-stop model and curved orbit are all taken into consideration in the correct model. Then, based on the correct echo mode, an azimuth-time-varying range frequency modulation (FM) rate is used for range compression. The position of the target after range compression is also derived. In addition, the azimuth phase in the correct echo model is also changed compared with the traditional echo mode. A discussion for residual phase error after range compression is given, which shows that the error is small and has little effect on the focusing of the target.
The correct echo model and CFBP algorithm are combined, which can integrate the non-start-stop model and curved orbit, further improving the imaging processing efficiency. The algorithm can be divided into seven steps: aperture division and subimage formation, first compression filter step, second compression filter step, azimuth sampling, second compression filter recovery step, first compression filter recovery step, coherent accumulation of subimage and recursion. After recursion step, the final image with full resolution can be obtained. The detailed processing flow of the proposed algorithm is introduced in detail in the paper. In addition, the simulation experiment with 0.07 m azimuth resolution and 0.21 m ground range resolution is performed to show the performance of the proposed algorithm. GF-3 data with 8.58 s synthetic aperture time are also performed to verify the effectiveness of the proposed algorithm. The azimuth-time-varying FM rates of targets in the center and edge of the scene are calculated for comparison. The focusing quality of targets is also evaluated.
The rest of this paper is organized as follows. The echo model of SAR is introduced in
Section 2. The comparison of correct echo model and traditional echo model is discussed. The modified CFBP algorithm is also described in detail and the processing flow of the proposed algorithm is presented. In
Section 3, the validity of the proposed method is confirmed by simulation experiment and GF-3 data experiment. In
Section 4, a discussion is given to show the performance and advantages of the proposed algorithm.
Section 5 concludes this paper.
5. Conclusions
The high resolution spotlight mode of SAR plays an increasingly important role in remote sensing. In this paper, a modified CFBP algorithm integrating with non-start-stop model is proposed for very high resolution spotlight mode of SAR data processing. In the high resolution case, the start-stop model will introduce errors, which will cause the target to be defocused in the image. In addition, under the condition of long synthetic aperture time, the error introduced by curved orbit should also be considered, further increasing the difficulty of imaging processing.
In this paper, an accurate correct echo model is used to depict the SAR signal with high accuracy. The non-start-stop model and curved orbit are all considered in the correct echo model. Then, The correct echo model and CFBP algorithm are combined to improve the accuracy and efficiency of imaging processing. Based on the echo model, at first, an azimuth-time-varying range FM rate of the center target is used for range compression. The residual error of the proposed algorithm is also discussed in detail. Then, the range history and compensation phase are derived for imaging processing. The modified CFBP algorithm is divided into seven steps. After all the steps are complete, the final image with full resolution is obtained. In the end, the simulation experiment and GF-3 data experiment demonstrate the feasibility of the proposed algorithm. What is more, the high resolution mode is sensitive to the topographic change. Therefore, combing the imaging algorithm and topographic change is a new challenge. In the future, further research will be carried out on this problem.