Maximum entropy solution to ill-posed inverse problems with approximately known operator

We consider the linear inverse problem of reconstructing an unknown finite measure it from a noisy observation of a generalized moment of mu defined as the integral of a continuous and bounded operator Phi with respect to mu. Motivated by various applications, we focus on the case where the operator Phi is unknown; instead, only an approximation Phi to it is available. An approximate maximum entropy solution to the inverse problem is introduced in the form of a minimizer of a convex functional subject to a sequence of convex constraints. Under several assumptions on the convex functional, the convergence of the approximate solution is established. (C) 2008 Elsevier Inc. All rights reserved.