  In this paper we extend a recent idea of formulating and regularizing inverse
problems as minimization problems, so without using a forward operator, thus
avoiding explicit evaluation of a parameter-to-state map. We do so by
rephrasing three application examples in this minimization form, namely (a)
electrical impedance tomography with the complete electrode model (b)
identification of a nonlinear magnetic permeability from magnetic flux
measurements (c) localization of sound sources from microphone array
measurements. To establish convergence of the proposed regularization approach
for these problems, we first of all extend the existing theory. In particular,
we take advantage of the fact that observations are finite dimensional here, so
that inversion of the noisy data can to some extent be done separately, using a
right inverse of the observation operator. This new approach is actually
applicable to a wide range of real world problems.
