NSF Award
9560150
*** 9560150 Jannson This Phase I Small Business Innovation Research project will provide an innovative method that can be used to solve multi-dimensional (4-D) inverse scattering problems (ISPs) in diffusion tomography, without artifacts. Physical Optics Corporation (POC) will develop a new inverse technique with rigorously established global convergence, called the Globally Optimized Inverse Method (GOIM). The GOIM is based on the globally convex cost function (and Carleman's estimates). This will provide for the first time, the solution of time-dependent inverse problems in 3-D space for strongly-scattering media. A backscattering inverse problem for Ground Penetrating Radar (GPR) is used as a quantitative example, and potential application scenario for Phase II. In Phase I, POC will develop a time-effective inverse numerical technique based on layer-stripping procedure, applicable to real-life opto-medical, Radar, NDE and seismic scenarios. Its features will be evaluated in the context of electromagnetic wave source type, specific technical parameters of a sensing device (including the grid structure of the boundary value set), and the computer power required (for either Work Stations, PCs, or parallel computers). The GOIM can be applied to novel diffusion tomography (DT) devices that can effectively (i.e., with a minimal number of grid points) evaluate, for the first time, either backscattered GPR waves, or diffuse photons in turbid media; thus, providing an entirely new category of advanced DT devices applicable to nuclear waste monitoring, seismic activity monitoring, aging aircraft NDE monitoring, and early breast cancer diagnostics. ***
