Cauchy Machine for Blind Inversion in Linear Space-variant Imaging

We revisited Cauchy Machine for solving blind space-variant imaging problem on the pixel by pixel basis. Under-determinacy of the pixel by pixel blind-matrix inversion was accomplished non-statistically by a physicsconstraint of open information systems in a dynamic balance by minimizing the thermodynamics free energy H=U-T0S where U is estimation error energy, T0 is temperature and S is the entropy. Solution was found through algorithm that computes the unknown source vector and unknown mixing matrix using Cauchy Machine to find the global minimum of H for each pixel. We demonstrated the algorithm capability to perfectly recover images from the noise free linear mixture of images. Capability of the Cauchy Machine to find the global minimum of the ‘golf hole’ type of landscape has been demonstrated in higher dimensions with a less computation complexity than an exhaustive search algorithm.