PhD Thesis Defense - Archive
Image Reconstruction Based on Estimated Scattering Object Characteristics
Prof. Robert C. Waag
Monday, April 19, 2010
Image reconstruction based on inverse scattering requires a priori knowledge of the scattering objects, iteration, or both. This thesis investigates ways to estimate object characteristics so that a model object may be formed that is suitable for initiating iterative reconstruction. A radial implementation of an inverse scattering method that uses eigenfunctions of the far-field scattering operator is also extended to nonradial reconstruction. The thesis has three main parts. In the first part, two methods are developed to estimate the boundary and sound speed of a two-dimensional penetrable object. One method is for circular objects centered in the coordinate system of the scattering observation. This method uses an orthogonal function expansion for the scattering and yields the object radius and sound speed. The other method uses cross correlation to obtain time differences that determine a family of parabolas whose envelope is the boundary of the object. The method also yields the average sound speed in the object. A curve-fitting and a phase-based methods are described to estimate and correct the offset of an un-centered radial or elliptical object. A method based on the extinction theorem is described to estimate absorption in the object. The methods are applied to calculated scattering from an offset circular object and to measured scattering from an offset noncircular object. The results show that the methods perform well when the assumptions of the methods are reasonably satisfied. Furthermore, application of the methods to measured scattering from a tissue-mimicking phantom results in accurate recovery of the sound speed, the absorption coefficient, and the boundary of the scattering object. For comparison, the linear sampling method is also employed to estimate the shape of a circular model object, and an elliptical object. In the second part, an inverse scattering program that was designed for use with radially symmetric scattering measurements is extended to be applicable to nonradial measurements. The algorithm for this extension is based on expansion of the scattering potential as a linear combination of products of retransmitted digenfields for the far-field scattering operator. The scattering data used to test the extension was calculated by a two-dimensional finite-difference time-domain (FDTD) method that uses time steps in the spatial-frequency domain (i.e.,a kspace method). The extended algorithm applied to scattering measurements from a homogeneous elliptical scattering object. In the last part, a three-dimensional boundary determination method using point source transmissions is investigated. The method is first applied to twodimensional scattering object to verify its accuracy. Then, the method is used to find the bounding surface of a three-dimensional object in an initial model for applications such as three-dimensional imaging of the breast.