A modified gradient method for two-dimensional problems in tomography
Journal of Computational and Applied Mathematics - Special issue on inverse problems in scattering theory
Numerical Recipes in FORTRAN: The Art of Scientific Computing
Numerical Recipes in FORTRAN: The Art of Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Total variation as a multiplicative constraint for solving inverse problems
IEEE Transactions on Image Processing
Journal of Computational Physics
Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework
Journal of Computational Physics
Three-dimensional visco-acoustic modeling using a renormalized integral equation iterative solver
Journal of Computational Physics
Enhanced multilevel linear sampling methods for inverse scattering problems
Journal of Computational Physics
Hi-index | 31.47 |
An iterative approach to full vector three-dimensional inverse scattering problems, where the unknown objects can have conductivity, permittivity and permeability different from the known background medium, is discussed. Since this problem involves a large number of unknowns, it has to be solved effectively and efficiently so that the results can be obtained in timely manner. The forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium. Our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations, and hence it is also of significant importance in the optimization process of the inverse problem. The inverse scattering problem is attacked using the Multiplicative Regularized Contrast Source Inversion method as known in the literature. The complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type. Furthermore, this inverse method has been armed with a weighted L2-norm regularizer which has been included as a multiplicative constraint. Some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms.