A neural network algorithm to pattern recognition in inverse problems

Considerable attention is currently being devoted to new possibilities of artificial neural networks (ANN) using in view of their increasing importance for solving the problem of automated reconstruction of the inner structure of an object. Accompanying algorithms that effectively quantify uncertainties, deal with ill-posedness, and fully take the nonlinear model into account are needed. A new ANN-based regularization model is generated and applied to the task of reconstruction of an inhomogeneous object. Pattern recognition may be viewed as an ill-posed inverse problem to which the method of regularization can be applied. In this study, applications of methods from the theory of inverse problems to pattern recognition are studied. A new learning algorithm derived from a well-known regularization model is generated and applied to the task of reconstruction of an inhomogeneous object as pattern recognition. Particularly, it is demonstrated that pattern recognition can be reformulated in terms of inverse problems defined by a Riesz-type kernel. This reformulation can be employed to design a learning algorithm based on a numerical solution of a system of linear equations. Finally, numerical experiments have been carried out with synthetic experimental data considering noise level up to 5%. Reasonable good recoveries have been achieved with this methodology, and the results of simulations of this are compatible with the existing methods. This method can be used in practice of pattern recognition technology and its development and deployment for applications in industry.