Differentiable Gaussian Splatting Models of Limited Persistence Scattering in SAR Backscatter Measurements

Traditional synthetic aperture radar (SAR) imaging techniques effectively produce high-resolution two-dimensional (2D) images, but often fail to accurately represent the underlying 3D structure due to overlay and shadowing effects inherent in projecting 3D scenes onto 2D imaging planes. 3D SAR imaging methods attempt to address these shortcomings using multipass SAR data, but sub-Nyquist rate sampling in the elevation domain requires regularized inversion techniques employing a prior model for the 3D scene. This paper introduces a novel modeling strategy for multi-pass SAR backscatter measurements of a 3D scene that can be employed in regularized inversion. Inspired by recently developed Gaussian splatting techniques in computer vision, the proposed method models scattering centers with anisotropic properties in azimuth and elevation using differentiable Gaussian basis functions. Specifically, our model represents scattering centers with their 3D locations and models their persistence using 2D Gaussians with positive definite covariance matrices. The model is differentiable in all its parameters and, therefore, can be trained efficiently using gradient descent techniques. Experimental evaluations on the GOTCHA dataset demonstrate that the proposed model accurately captures the anisotropic scattering behavior and effectively reconstructs the 3D structure from undersampled elevation data, surpassing the limitations of conventional sparsity regularized inversion methods.