A regularization method for nonlinear inverse problems by using a Volterra model

In this paper, a nonlinear inverse problem is proposed. The main idea is to apply the well known Tikhonov regularization to a Volterra model. The Volterra model allows to represent a large variety of nonlinearities, but for inverse problem, a nonlinear optimization procedure must be used and an important computational burden is required. A particular computational implementation is proposed to reduce the computational burden and to simplify the use. Here the Volterra model consists in an approximation of each Volterra kernel by a multidimensional orthonormal basis expansion.