## A level-set approach for inverse problems involving obstacles |

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_ uext Advanced Computing Research Aiping Liao algorithm choose Coleman and Wei Computing Research Institute Cornell University cutout is reconstructed deconvolution descent direction desired unknown diffraction data diffraction screen reconstruction displayed in Figure ds(x evolution method Figure 2a Fourier transform function of number Gauss-Newton update given a level-set Global Optimization Graph Hamilton-Jacobi equation initial value problem inner product inverse obstacle problem INVERSE PROBLEMS INVOLVING INVOLVING OBSTACLES FADIL Jacobian Least Squares level-set approach level-set description level-set function linear Matlab Minimization multiply connected node points nonlinear Note that 6u number of iterations obstacle inverse problems OBSTACLES FADIL SANTOSA optimization approach optimization method original cutout partial differential equation pixel plane wave problems involving obstacles real and imaginary representing the unknown residual screen reconstruction problem severely illposed problems step length subregions Theory Center Trust Region uint ujnt unknown characteristic function wave field wavenumber Wei Yuan x£dDk Yuying zero-level set