# Modulus Stretch-Based Circular SAR Imaging with Contour Thinning
## 1 Introduction  
Synthetic Aperture Radar (SAR) is a type of Radar capable of performing high-resolution microwave imaging on target areas under all-weather and all-day conditions. The research on SAR includes imaging, target detection, time-frequency analysis and other aspects, among which imaging is one of the more studied fields [1; 2; 3; 4]. The development of SAR always aims at improving image resolution. Wide-angle SAR (WSAR) refers to SAR which spans a wide range of azimuth during data acquisition to obtain higher azimuth resolution and more azimuth scattering information. Circular SAR (CSAR) is a special case of wide-angle SAR. CSAR moves 360\({}^{\circ}\) in a circle with the radar platform centering on the observation scene, and the beam always shines on the same ground scene to achieve all-round observation. The imaging mode of circular SAR was first proposed by [PERSON] in 1996. [PERSON] also presented the time-domain model of CSAR echo signal and CSAR imaging algorithm based on wavefront reconstruction [5]. Subsequently, many researchers have studied the imaging theory of circular SAR. The Air Force Research Laboratory (AFRL) and other organizations have conducted several experimental tests of WSAR and CSAR and released several test datasets and challenge problems about WSAR and CSAR [6; 7; 8; 9; 10; 11; 12; 13]. [PERSON] et al. presented an approximation method using linear spottight SAR to simulate CSAR [14; 15]. [PERSON], [PERSON] and [PERSON] et al. have done a series of research on the three-dimensional imaging, imaging accuracy and imaging algorithm of CSAR [16; 17; 18; 19; 20]. [PERSON] et al. used an Experimental airborne SAR (E-SAR) system to conduct L-band experiments with circular SAR systems and adopted a fast factorized backprojection algorithm for imaging [21]. [PERSON] et al. presented a modified Omega-K algorithm to focus accurately. The accuracy can be controlled by keeping enough terms in the two series expansions so that a well-focused image can be achievedwith a proper range approximation [22; 23]. [PERSON] et al. investigated the availability of an expediting backprojection algorithm for CSAR imaging. Without time-consuming 2D interpolation, it is capable of decreasing the loss of spectrum, while significantly improving the computational efficiency compared with direct backprojection [24]. [PERSON] et al. proposed a distributed compressed sensing algorithm for circular SAR imaging, which improves the resolution and reduces the side-lobe effect in the full-aperture 3D image, and meanwhile reduces the computation [25]. In recent years, the research on Circular SAR imaging mainly focuses on Deep Learning, Compression Sensing, 3D imaging and other aspects [26; 27; 28; 29; 30; 31; 32; 33; 34]. Many excellent research results and algorithm theories have emerged. Starting from the traditional backprojection imaging algorithm, this paper re-examines the imaging algorithm in order to improve the recognizability of the target. The idea of combining imaging and target detection has been studied a lot in the field of infrared target detection [35; 36; 37; 38]. This paper presents an imaging method which is more beneficial to target recognition. The traditional backprojection imaging algorithm has high imaging accuracy and simple implementation, which has been widely used in the radar imaging field. However, in a real scene, a target may have a clear contour through visible light imaging that will become blurred in SAR imaging. The target may have a continuous reflection surface, and there will be a continuous strong signal response in the reflected echo detected by radar. In the imaging process, the original obvious contour will be connected and cannot be distinguished, which is not conducive to classification and recognition. This paper proposes a contour thinning imaging algorithm by modulus stretch. Based on the principle of backprojection imaging, the modulus stretch transform function is introduced to reduce the low modulus area of the intermediate image.