Discrete Gel'fand-Levitan and Marchenko matrix equations and layer stripping algorithms for the discrete two-dimensional Schrödinger equation inverse scattering problem with a nonlocal potential
JavaScript is disabled for your browser. Some features of this site may not work without it.
Discrete Gel'fand-Levitan and Marchenko matrix equations and layer stripping algorithms for the discrete two-dimensional Schrödinger equation inverse scattering problem with a nonlocal potential
Yagle, Andrew E.
Yagle, Andrew E.
1998-06-01
Citation:Yagle, Andrew E (1998). "Discrete Gel'fand-Levitan and Marchenko matrix equations and layer stripping algorithms for the discrete two-dimensional Schrödinger equation inverse scattering problem with a nonlocal potential ." Inverse Problems. 14(3): 763-778. <http://hdl.handle.net/2027.42/49103>
Abstract: We develop discrete counterparts to the Gel'fand-Levitan and Marchenko integral equations for the two-dimensional (2D) discrete inverse scattering problem in polar coordinates with a nonlocal potential. We also develop fast layer stripping algorithms that solve these systems of equations exactly. The significance of these results is: (1) they are the first numerical implementation of Newton's multidimensional inverse scattering theory; (2) they show that the result will almost always be a nonlocal potential, unless the data are `miraculous'; (3) they show that layer stripping algorithms implement fast `split' signal processing fast algorithms; (4) they link 2D discrete inverse scattering with 2D discrete random field linear least-squares estimation; and (5) they formulate and solve 2D discrete Schrödinger equation inverse scattering problems in polar coordinates.