Image estimation from scattered field data

Abstract

The purpose of this paper is to reappraise the linearizing methods frequently used to solve inverse scattering problems. We describe inversion algorithms based on the Born and the Rytov approximations and the nature of the distortions obtained in the reconstructions when using them. We present extensions of these methods, namely, the distorted-wave Born and the distorted-wave Rytov approximations, which incorporate prior knowledge about part of the scattering structure. A method for inverting scattered field data using these distorted-wave approximations is described, which retains the computational simplicity of the Born and the Rytov techniques. Some examples of their use with simulated and real data are given. A further extension of our distorted-wave formalism, which leads to improvements of the reconstructed image, is suggested. This entails a spectral estimation procedure also based on the incorporation of prior knowledge about the scatterer. This spectral estimation procedure can be useful for interpolation of scattered field data as well as resolution enhancement.

Experimental Synthetic Aperture Radar With Dynamic Metasurfaces

“…To properly process the backscattered signal, a model to relate the measurements with the radiated fields and the reflectivity of the scene needs to be developed. Various approaches have been pursued in the literature for this purpose, ranging from simple Born and Rayleigh approximations [45], [46] to non-linear models accounting for the materials properties of objects in the scene [47], [48]. The choice of imaging model is usually determined by the intended application.…”

“…The added computational demands are particularly substantial in SAR environments, where the large number of synthetic aperture positions, frequency points, and tuning states, leads to an extremely large measurement set [51]. A large factor in the simplicity of this model is derived from the use of the Born approximation, which linearizes the inverse problem [46]. While this model may break down in scenes with multiply-scattering features, the approach typically returns satisfactory qualitative images.…”

Efficient Reconstruction of Dielectric Objects Based on Integral Equation Approach With Gauss–Newton Minimization

“…Solving inverse scattering problems is more challenging than solving forward (or direct) scattering problems because the involved governing equations are nonlinear and the solutions are inherently nonunique. Usually, the inverse problems are solved iteratively through the linearization of governing equations and the widely-used methods could be the Born iterative method (BIM) [7], distorted Born iterative method (DBIM) [8], and contrast source inversion method (CSIM) [9], [10], although other methods also exist [11], [12].…”

Inversion of strongly scattering data: imaging and structure synthesis

“…Since this is a function of the complex permittivity, e([), of that volume, the problem is inherently nonlinear and severely ill-posed. In some simple situations, the first Born approximation or the first Rytov approximation, one can linearize the inversion problem, making a solution possible at least in principle [1]. In cases for which this cannot be done, the inversion or backpropagation step can be executed using a Fourier transform, assuming a 2D problem and far field data of the form F(x, x) J=ffV(u,v)exp(-ik(ux,+v x))dudv where k is the wavenumber.…”

“…In cases for which this cannot be done, the inversion or backpropagation step can be executed using a Fourier transform, assuming a 2D problem and far field data of the form F(x, x) J=ffV(u,v)exp(-ik(ux,+v x))dudv where k is the wavenumber. This provides information about the so-called secondary source or contrast source which is formally related to the product of the fluctuation of the permittivity distribution about the mean and the total field, 1, inside the scattering volume, F(x1 x) = ff V(u, v)F(u, v)exp(-ik(ux,+vx))dudv (1) where FT = j/A0 and V =V., the incident field.…”