Sparse Constraint Based Inverse Scattering Algorithm For Complex Objects Reconstruction

Study on inverse problem for a long time, there is an inverse problem in many areas, the problem also exists in inverse electromagnetic scattering. Electromagnetic inverse scattering technique is one of the most important means of obtaining scattering body electrical performance parameters and geometry. Because of its non-contact detection and non-destructive characteristics, now widely used in locating radar, military reconnaissance, microwave remote sensing, bio-medical diagnostic imaging and other fields. Electromagnetic inverse scattering technique is the use of an external object to be measured field data and electromagnetic scattering model, to reconstruction target's geometry, location, boundaries and electrical performance parameters in the spatial distribution.The paper main content is about the electromagnetic inverse scattering algorithm research. In the second chapter, we obtain two nonlinear equations by establish and analysis the basic model of electromagnetic inverse scattering problem. This paper mainly introduces the process of the source inversion method, the subspace optimization algorithm, and introduces the similarities and differences between the two methods. Through theoretical analysis and numerical results compared contrast source inversion method and subspace optimization algorithms.Secondly the study of nonlinear electromagnetic inverse scattering imaging methods, the lack of prior information will result in the cost of computing and the reconstructed spatial dimensions are too high. Generally speaking, the computational cost of the non-linear inverse scattering algorithms are much higher than the linear inverse scattering algorithms which can inverse the scattering body's number and area location. We propose a mixed nonlinear inverse scattering method, which combined with a linear and a nonlinear inverse scattering methods. The reconstruction results of a linear method are used as the prior information to provide the number and the location of the targets for the nonlinear method, which reduce the amount of computation and the dimension of refactoring space. Experimental results certificate the effectiveness of the mixed method.In this paper, we will propose a nonlinear inverse scattering imaging method which based on sparse constraint. Scattering field equations of the method is second-order Born approximation equation, nonlinear side of the equation is solved by the inexact Newton method. The differential equation obtained by the Newton scheme is an ill conditioned equation, thus sparse regularization method is needed to solve the ill posed nature. Construct an objective function composed of the data error term and the penalty term. Minimize the objective function and sparse the solution by truncation and threshold Landweber iterative method. The reconstruction result of this method is not only accurate but also very clear. Finally, this paper will give the results of the imaging algorithm and compared with other algorithms to demonstrate the effectiveness of the method.