Efficient computational methods for wavelet domain signal restoration problems

We present an efficient, wavelet domain algorithm for computing the error variances associated with a wide class of linear inverse problems posed in a maximum a posteriori (MAP) estimation framework. Our method is based on the permutation and subsequent partitioning of the Fisher information matrix into a 2×2 block structure with the lower-right block well approximated as diagonal and significantly larger than the upper-left block. We prove that under appropriate conditions, this diagonal approximation does, in fact, allow for the accurate recovery of the error variances, and we introduce a greedy-type method based on the optimization of a diagonal dominance criterion for determining the “best” partition. We demonstrate the speed of this technique and its accuracy for a set of inverse problems corresponding to a variety of blurring kernels, problem sizes, and noise conditions