Image reconstruction using singular-value decomposition of scattering operators

Abstract

Efficient inverse scattering algorithms for nonradial lossy objects are presented using singular-value decomposition to form reduced rank representations of the scattering operator. These algorithms extend eigenfunction methods that are not applicable to nonradial lossy scattering objects because the scattering operators for these objects are not normal. A method of local reconstruction by segregation of scattering contributions from different local regions is also presented. Scattering from each region is isolated by forming a reduced rank representation of the scattering operator that has domain and range spaces comprised of far-field patterns with retransmitted fields that focus on the local region. Accurate methods for the estimation of the boundary, average sound speed, and average attenuation slope of the scattering object are also given. These methods yield initial approximations of scattering objects that reduce the number of distorted Born iterations needed for high quality reconstruction. Calculated scattering from two lossy elliptical objects is used to evaluate the performance of the proposed methods. In both cases, the reconstruction procedures result in high-quality quantitative images of tissue parameters with sub-wavelength resolution.