SAR Imaging Distortions Induced by Topography: A Compact Analytical Formulation for Radiometric Calibration

Abstract

Modeling of synthetic aperture radar (SAR) imaging distortions induced by topography is addressed and a novel radiometric calibration method is proposed in this paper. An analytical formulation of the problem is primarily provided in purely geometrical terms, by adopting the theoretical notions of the differential geometry of surfaces. The novel and conceptually simple formulation relies on a cylindrical coordinate system, whose longitudinal axis corresponds to the sensor flight direction. A 3D representation of the terrain shape is then incorporated into the SAR imaging model by resorting to a suitable parametrization of the observed ground surface. Within this analytical framework, the area-stretching function quantitatively expresses in geometrical terms the inherent local radiometric distortions. This paper establishes its analytical expression in terms of the magnitude of the gradient of the look-angle function uniquely defined in the image domain, thus resulting in being mathematically concise and amenable to a straightforward implementation. The practical relevance of the formulation is also illustrated from a computational perspective, by elucidating its effective discrete implementation. In particular, an inverse cylindrical mapping approach is adopted, thus avoiding the drawback of pixel area fragmentation and integration required in forward-mapping-based approaches. The effectiveness of the proposed SAR radiometric calibration method is experimentally demonstrated by using COSMO-SkyMed SAR data acquired over a mountainous area in Italy.

SAR Radiometric Calibration Based on Differential Geometry: From Theory to Experimentation on SAOCOM Imagery

“…By contrast, scene-dependent radiometric distortions arise from the inherent 2D imaging process of a 3D irregular ground shape, and they are inherently local in nature [2][3][4][5][6][7][8][9][10][11]. Accordingly, the 2D imaging process of an irregular relief intrinsically implies unavoidable radiometric distortions.…”

“…Regarding topography-induced SAR radiometric distortions, some calibration approaches are available in the literature [2][3][4][5][6][7][8][9][10]. More recently, an effective method for radiometric calibration derived in the rigorous framework of differential geometry of the surfaces has been developed, and it exhibits important advantages [10,17].…”

“…Regarding topography-induced SAR radiometric distortions, some calibration approaches are available in the literature [2][3][4][5][6][7][8][9][10]. More recently, an effective method for radiometric calibration derived in the rigorous framework of differential geometry of the surfaces has been developed, and it exhibits important advantages [10,17]. In particular, as discussed in [10] the method essentially requires image-domain processing based on the evaluation of a scalar function, with important implications in terms of the computational burden.…”

“…More recently, an effective method for radiometric calibration derived in the rigorous framework of differential geometry of the surfaces has been developed, and it exhibits important advantages [10,17]. In particular, as discussed in [10] the method essentially requires image-domain processing based on the evaluation of a scalar function, with important implications in terms of the computational burden. However, to the best of our knowledge, the compensation of local SAR radiometric distortions induced by topography for SAOCOM images hitherto has not been investigated.…”

“…Therefore, in this paper, the focus is on the modeling, computation, and compensation of topography-induced radiometric distortions affecting SAR imaging, with special emphasis on the use of SAOCOM data. In particular, this investigation relies on the analytical formulation of the recently developed method proposed in [10], and it is aimed at extending its physical interpretation and applicability. Therefore, the novelty of the present work is twofold, pertaining to both the strengthening of the theoretical understanding of the calibration framework originally proposed in [10] and the implementation and analysis of its application to SAOCOM data.…”