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1 April 2003 Blind inversion in nonlinear space-variant imaging using Cauchy machine
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A Cauchy Machine has been applied to solve nonlinear space-variant blind imaging problem with positivity constraints on the pixel-by-pixel basis. Nonlinearity parameters, de-mixing matrix and source vector are found at the minimum of the thermodynamics free energy H=U-T0S, where U is estimation error energy, T0 is temperature and S is the entropy. Free energy represents dynamic balance of an open information system with constraints defined by data vector. Solution was found through Lagrange Constraint Neural Network algorithm for computing the unknown source vector, exhaustive search to find unknown nonlinearity parameters and Cauchy Machine for seeking de-mixing matrix at the global minimum of H for each pixel. We demonstrate the algorithm capability to recover images from the synthetic noise free nonlinear mixture of two images. Capability of the Cauchy Machine to find the global minimum of the golf hole type of landscape has hitherto never been demonstrated in higher dimensions with a much less computation complexity than an exhaustive search algorithm.
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Ivica Kopriva and Harold H. Szu "Blind inversion in nonlinear space-variant imaging using Cauchy machine", Proc. SPIE 5102, Independent Component Analyses, Wavelets, and Neural Networks, (1 April 2003);

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