DEM Estimation for LASAR Based on Variational Model

Abstract

This paper discusses the digital elevation model (DEM) estimation problem for the linear array synthetic aperture radar based on the variational model. Compared with the sparse recovery model, the one-to-one mapping between the horizontal grid nodes and the elevations is preserved explicitly, which is important for the topographic surveying and mapping mission. During the research, we find that since the mean square error criterion is insensitive to the amount of the elevation offsets, the numerical method by solving the Euler-Lagrange equation is unreliable and the global optimization method is necessary to solve the variational problem. With the ambiguity function localization and the sliding-window architecture, the global optimal path can be obtained by solving a series of local optimization problems provided that the observation matrix is row full rank. Furthermore, the local optimization problem can be relaxed as a sparse recovery problem and can be solved by a modified orthogonal matching pursuit (OMP) method (named as Var-OMP), whose computational cost is acceptable for the actual data processing. By a series of numerical experiments, we show that the performance of Var-OMP is influenced by both the resolution enhancement factor (L) and the signal-to-noise ratio (SNR). The larger the SNR is, the better the performance is; the smaller L is, the more stable and faster the Var-OMP algorithm is. Compared with the sparse recovery methods, the variational model and the Var-OMP algorithm are more suitable for the DEM estimation application in the face of all kinds of terrains.