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Neural networks functions are supposed to be able to encode the desiredsolution of an inverse problem very efficiently. In this paper, we consider theproblem of solving linear inverse problems with neural network coders. First weestablish some correspondences of this formulation with existing concepts inregularization theory, in particular with state space regularization, operatordecomposition and iterative regularization methods. A Gauss-Newton's method issuitable for solving encoded linear inverse problems, which is supported by alocal convergence result. The convergence studies, however, are not complete,and are based on a conjecture on linear independence of activation functionsand its derivatives.

Newton's methods for solving linear inverse problems with neural network coders