# FDBP-InSAR: An Efficient Algorithm for InSAR Imaging via Frequency Domain Back Projection
## 1 Introduction  
Synthetic aperture radar (SAR) [1; 2; 3; 4; 5; 6] is a breakthrough in the field of modern remote-sensing science. It replaces the wave-front spatial sampling set obtained by the real array antenna with the echo time sampling sequence received by the synthetic array element at different spatial locations. In recent decades, SAR has demonstrated significant applications in terrain mapping, natural resource exploration, and target tracking field due to its strong transmission, all-weather, and all-day features. Interferometric synthetic aperture radar (InSAR) [7; 8; 9; 10; 11] is developed on the basis of SAR technology to higher imaging dimensions. Combining the phase information and geometric relationship of two or more pairs of SAR images relative to the same scene, InSAR can acquire a high-resolution Digital Elevation Model (DEM) and an orthophoto map of a large area. Hence, InSAR has become an effective and important remote-sensing technology for a large rolling terrain, and it is of great significance to terrain mapping, natural disaster monitoring, and resource investigation. High-precision measurement and sensing is not only one of the inevitable trend in the future development of InSAR technology butalso an urgent need in the current InSAR applications. In recent years, more and more high-precision space-borne InSAR satellite systems that are developed for terrain observation, such as ALOS2 PaISAR satellite [12], Cosmo-Skymed system [13], TerraSAR/TanDEM-X binary system [14], and RCM satellite constellation [15], have been successfully launched and operated. These satellites make a great contribution to the management and exploration of the geological environment and other issues on a global scale by InSAR technology. Serval types of algorithms based on conventional SAR image formation have been developed in the past few decades. Generally, these algorithms can be divided into two categories: one is the frequency-domain-based algorithm, e.g., range-Doppler algorithm (RDA) [16; 17; 18; 19], chirp scaling algorithm (CSA) [20], wavenumber-domain algorithm (WKA) [21; 22; 23; 24; 25]. Another is the time-domain-based algorithm, such as the matched filter algorithm (MFA) and the back-projection algorithm (BPA) [26; 27; 28; 29]. Classical frequency-domain algorithms are limited in their precision due to processor approximations, e.g., the platform is moving uniformly in a straight line or the reference focusing function is the same in all areas of the underlying scene. In practice, these assumptions are not always true, such as the reference focusing function will cause defocusing and phase errors of the area which are far from the reference scene center. Hence, to improve the focusing quality of InSAR, error compensation is necessary for these frequency-domain-based algorithms. Usually, the compensation process in these algorithms is complex and difficult to accurately. Moreover, the traditional frequency-domain-based methods are range-plane projection-based imaging, which may result in the interferometric phase wrapping and the target geometry distortion serious if the terrain is abrupt. In addition, due to the influences of airflow, obstacles, and other factors, the movement trajectory of the radar platform usually is complex and deviates greatly from the ideal trajectory in practice. It increases the difficulty of frequency-domain focusing, resulting in a decrease in imaging accuracy and phase extraction accuracy. Different from the frequency-domain-based algorithms, time-domain back-projection algorithm (TDBPA) is more suitable for SAR high-resolution imaging in the case of the complex trajectory of the platform, because it can provide precise focusing and phase information of a large scene by point-to-point coherent integration without any assumption constrained.