DEM Enhancement For LASAR Based On Variational Model

By synthesizing the linear motion of the platform and the linear array,a virtual 2D array is obtained by Linear array synthetic aperture radar(LASAR),which leads to a real 3D resolving ability by combining with the pulse compression technique.And with the ability of downward-looking,it can overcome shadow problem which troubled traditional 2D SAR a lot.This thesis discusses the digital elevation model(DEM)estimation problem for the LASAR.LASAR's application scenarios are always sparse,and there are many imaging methods of LASAR based on compressed sensing(CS).However,all of these methods choose to convert echo signal into vectors before further processing,which may break the one-to-one mapping between the horizontal grid nodes and the elevations completely.This paper proposed a method based on 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.The main work is as follows:1.This chapter introduces the imaging theory and signal model of LASAR,the properties of ambiguity function and the relationship between the ambiguity function of LASAR and the resolution.Then two traditional imaging algorithms(3D RD algorithm and 3D BP algorithm)are introduced and compared with each other.2.LASAR 3D image reconstruction based on sparsity and how to apply compressed sensing into LASAR imaging are analyzed.Several sparse reconstruction algorithm are introduced,which mainly introduced the OMP algorithm based on greedy strategy and CoSaMP algorithm,as well as the LASSO algorithm based on convex optimization.The simulation experiment of CoSaMP algorithm and LASSO algorithm for DEM reconstruction problem are performed in the end of this chapter.3.The deficiency of LASAR imaging based on sparse reconstruction is discussed first and DEM modeling estimation problem is convert into a variational problem.Introduced the concept of the variational method and functional.And in the process of research,we found that the optimization problem in this paper is a nonlinear variation related with ambiguity function and the Mean Square Error criterion(MSE)has no effect for most of the height offsets so that it is hard to solve the problem by euler Lagrange equation and proposed a new method.Under the condition that observation is row full rank matrix,with the ambiguity function limit and sliding window structure,the global optimal path can be got by solving a series of local optimization problem.And local optimization problems can be seen as a sparse reconstruction and solved through an optimized OMP algorithm(in this paper called Var-OMP).4.By a series of numerical experiments,we show that the MSE exists instability so that it was modified.And the performance of Var-OMP is influenced by both the resolution enhancement factor(L)and the signal-noise-ratio(SNR).The larger 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.