Synthetic aperture radar (SAR) is a tomographic sensor that measures 2D slices of the 3D spatial Fourier transform of the scene. In many operational scenarios, the measured set of 2D slices does not fill the 3D space in the Fourier domain, resulting in significant artifacts in the reconstructed imagery. Traditionally, simple priors, such as sparsity in the image domain, are used to regularize the inverse problem. In this paper, we review our recent work that achieves state-of-the-art results in 3D SAR imaging employing neural structures to model the surface scattering that dominates SAR returns. These neural structures encode the surface of the objects in the form of a signed distance function learned from the sparse scattering data. Since estimating a smooth surface from a sparse and noisy point cloud is an ill-posed problem, we regularize the surface estimation by sampling points from the implicit surface representation during the training step. We demonstrate the model's ability to represent target scattering using measured and simulated data from single vehicles and a larger scene with a large number of vehicles. We conclude with future research directions calling for methods to learn complex-valued neural representations to enable synthesizing new collections from the volumetric neural implicit representation.
Synthetic aperture radar (SAR) is a tomographic sensor that measures 2D slices out of the 3D Spatial Fourier transform of the scene. Traditional 3D reconstruction techniques involve aggregating and indexing phase history data in the spatial Fourier domain and applying an inverse 3D Fourier Transform to the data as shown in references [1,2]. Obtaining high-resolution imagery requires the data collected to be densely distributed in both azimuth and elevation angle, which is often not satisfied in operational scenarios. For instance, the sampling in the elevation dimension is sparse and non-uniform in the GOTCHA dataset [3,4]. To cope with the sparsely sampled data in elevation, regularized inversion methods [5] that combine a non-uniform fast Fourier transform method to model the forward operator with regularization priors for the scene that promote a structured solution such as sparsity [6], limited persistence in the viewing angle domain [7][8][9], vertical structures [10]. These regularization-based approaches promote dominant scattering mechanisms [11,12] and produce sparse point clouds in the spatial domain.
In addition, scattering from multiple internal reflections can appear as scattering centers away from the physical surface of the object. Moreover, nonuniform sampling in elevation introduces ambiguities in the height direction, leading to aliased copies of the object. In this paper, we review our recent work that achieves state-of-the-art results in 3D SAR imaging employing neural structures to model the surface scattering that dominates SAR returns. These neural structures encode the surface of the objects in the form of a signed distance function learned from the sparse scattering data. Since estimating a smooth surface from a sparse and noisy point cloud is an ill-posed problem, we regularize the surface estimation by sampling points from the implicit surface representation during the training step. We demonstrate the model’s ability to represent target scattering using measured and simulated data from single vehicles and larger scenes containing hundreds of objects. We conclude with future research directions calling for methods to learn complex-valued neural representations to synthesize tomographic projections from previously unseen viewpoints/apertures.
A common approach for 3D imaging is to formulate the inversion of the Fourier operator as an inverse problem imposing regularization to enforce sparsity in the spatial domain and promote correlation of scattering coefficients in the neighboring sub-apertures [13]. Reference [1] solves the recovery problem over individual sub-apertures and non-coherently integrates the result to obtain a wide-angle 3D representation of the object. The backscattered response of the object is also modeled as a superposition of the backscattered response of 3D canonical scattering mechanisms such as dihedral, trihedral, plate, cylinder, and tophat [14]. The scattering behavior of these canonical reflectors has been derived as a function of the size of the scattering mechanism using the predictions from the Geometric theory of diffraction [15]. References [7,10,16] jointly model the sparsity in scattering center locations and the persistence of scattering coefficients in the azimuth domain. Alternatively, the imaging problem has been posed as an interferometric imaging problem using measurements obtained from multiple baselines [4] and [17]. The 3D non-uniform Fourier transform is approximated by a set of 2D non-uniform Fourier transforms for each baseline for range and crossrange estimation and a 1D non-uniform Fourier transform for height estimation. The effect of the persistence of the target on the ambiguities in the point-spread function is presented in Reference [18]. The uncertainty in the localization of scattering centers is dictated by the persistence, which leads to ambiguities in the target localizations along the vertical direction projected along the viewing angle of elevation.
Meanwhile, in computer vision, implicit neural representations, like Neural Radiance Fields (NeRF) and its derivatives [19,20], have become popular volume rendering methods, boasting strong performance even when dealing with highly intricate objects. This volume rendering approach uses focal-plane camera geometry to sample multiple points along rays and perform composition of the colors of the sampled points to link the 3D model to 2D views. The traditional discrete representations of objects, scene geometry, and appearance using meshes and voxel grids scale poorly with the scene’s size. Recent developments utilize continuous functions parameterized by deep neural structures. These coordinatebased Deep-nets are trained to map the low-dimensional spatial coordinates to output a representation of shape or density for each spatial location. Coordinatebased Deep-Nets have been used to represent images [21], volume density [20], occupancy [22], and signed distance [23]. The signe
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