3D SLICED TOMOGRAPHIC INVERSE SCATTERING EXPERIMENTAL RESULTS

Localized Sliced Inverse Regression

We developed localized sliced inverse regression for supervised dimension reduction. It has the advantages of preventing degeneracy, increasing estimation accuracy, and automatic subclass discovery in classification problems. A semisupervised version is proposed for the use of unlabeled data. The utility is illustrated on simulated as well as real data sets.

Student Sliced Inverse Regression

Sliced Inverse Regression (SIR) has been extensively used to reduce the dimension of the predictor space before performing regression. SIR is originally a model free method but it has been shown to actually correspond to the maximum likelihood of an inverse regression model with Gaussian errors. This intrinsic Gaussianity of standard SIR may explain its high sensitivity to outliers as observed ...

A comparison of the Colton–Kirsch inverse scattering methods with linearized tomographic inverse scattering

We present a numerical comparison of the so-called ‘linear sampling’ inverse scattering methods developed by Colton and Kirsch, published in this journal, and linearized tomographic inverse scattering algorithms based on either holographic filtered backpropagation principles or a plain matrix inversion scheme. Although we restrict ourselves to two-dimensional obstacle scattering, we investigate...

Some Results on Inverse Scattering

A review of some of the author’s results in the area of inverse scattering is given. The following topics are discussed: 1) Property C and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3) Inverse scattering with ”incomplete“ data, 4) Inverse scattering for inhomogeneous Schrödinger equation, 5) Krein’s inverse scattering method, 6) Invertibility of...

A Bayesian approach for nonlinear inverse scattering tomographic imaging