A TSVD Analysis of Microwave Inverse Scattering for Breast Imaging

A variety of methods have been applied to the inverse scattering problem for breast imaging at microwave frequencies. While many techniques have been leveraged toward a microwave imaging solution, they are all fundamentally dependent on the quality of the scattering data. Evaluating and optimizing the information contained in the data are, therefore, instrumental in understanding and achieving optimal performance from any particular imaging method. In this paper, a method of analysis is employed for the evaluation of the information contained in simulated scattering data from a known dielectric profile. The method estimates optimal imaging performance by mapping the data through the inverse of the scattering system. The inverse is computed by truncated singular-value decomposition of a system of scattering equations. The equations are made linear by use of the exact total fields in the imaging volume, which are available in the computational domain. The analysis is applied to anatomically realistic numerical breast phantoms. The utility of the method is demonstrated for a given imaging system through the analysis of various considerations in system design and problem formulation. The method offers an avenue for decoupling the problem of data selection from the problem of image formation from that data.