Iterative Truncated SVD for Inverse Scattering Problems
Prof. Hongkai Zhao, Duke University
Abstract: We propose an iterative truncated SVD (iTSVD) algorithm for Newton's method to solve inverse scattering problems. The key idea is to estimate the effective rank of the corresponding linearized operator (or the Jacobian matrix after discretization), which defines the dimension of the signal/information space of the associated forward operator. Once the effective rank is estimated, TSVD reconstruction in the signal space can be computed efficiently based on fast random SVD (RSVD). A key point is that random SVD only needs the application of the matrix to a set of random vectors whose cardinality is comparable to the effective rank. Moreover, these matrix vector multiplications have a matrix free formulation which only requires solving the same forward problem with different forcing terms.
Our analysis and numerical experiments show that iTSVD can markedly improve computational efficiency by reducing the number of iterations, and enhance stability by effective rank estimate. Moreover, the effective rank estimate is naturally model- and data-based. Extensive experiments, including far- or near-field, limited aperture, and random measurement data without or with noise, are presented.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
