Priorconditioned CGLS-Based Quasi-MAP Estimate, Statistical Stopping Rule, and Ranking of Priors
We consider linear discrete ill-posed problems within the Bayesian framework, assuming a Gaussian additive noise model and a Gaussian prior whose covariance matrices may be known modulo multiplicative scaling factors. In that context, we propose a new pointwise estimator for the posterior density, the prior conditioned CGLS-based quasi-MAP (qMAP) as a computationally attractive approximation of the classical maximum a posteriori (MAP) estimate, in particular when the e?ective rank of the matrix A is much smaller than the dimension of the unknown.