  Multiplicative noise models are often used instead of additive noise models
in cases in which the noise variance depends on the state. Furthermore, when
Poisson distributions with relatively small counts are approximated with normal
distributions, multiplicative noise approximations are straightforward to
implement. There are a number of limitations in existing approaches to
marginalize over multiplicative errors, such as positivity of the
multiplicative noise term. The focus in this paper is in large dimensional
(inverse) problems for which sampling type approaches have too high
computational complexity. In this paper, we propose an alternative approach to
carry out approximative marginalization over the multiplicative error by
embedding the statistics in an additive error term. The approach is essentially
a Bayesian one in that the statistics of the additive error is induced by the
statistics of the other unknowns. As an example, we consider a deconvolution
problem on random fields with different statistics of the multiplicative noise.
Furthermore, the approach allows for correlated multiplicative noise. We show
that the proposed approach provides feasible error estimates in the sense that
the posterior models support the actual image.
