A frequency-domain formulation of the Fréchet derivative to exploit the inherent parallelism of the distorted Born iterative method

Improving the effectiveness of the distorted Born iterative method with a parallel, multi-frequency approach

“…The resulting reduction in computation time makes the method better-suited for a multi-frequency approach. This approach is discussed more thoroughly in [6].…”

Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm

“…In analogy with the frequency hopping employed to solve multiple-frequency imaging problems, 8,9,15,20,30,38,39 the round-robin technique attempts to avoid local minima associated with the solution of a single, restricted inverse problem ͑e.g., involving a single imaging frequency and a limited set of transmit angles͒ by using a previously obtained solution as a starting guess for a subsequent inversion. If local minima associated with distinct transmit angles do not coincide, a solution stagnating in a local minimum for one transmit angle may move away from the local minimum and toward the global minimum when the transmit angle is shifted.…”

“…͑13͒. As detailed for two-dimensional problems, 30 the distorted Born iterative method distributed in this fashion scales almost ideally up to T processors when there are T unique transmit angles in an inverse scattering experiment. However, the algorithm does not scale above T processors.…”

“…A more thorough derivation of this matrix-free formulation of the Fréchet derivative and adjoint Fréchet derivative operators is presented in Ref. 30.…”

“…A formulation of the DBIM has been previously developed 30 to invert the Fréchet derivative operator in the differential scattering Eq. ͑8͒ without the need to construct an explicit matrix equation or to compute Green's functions for inhomogeneous background media.…”