The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decompositions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural extension of the Wiener solution, and that exploits these higher-order statistics. The resulting nonlinear estimator performs a ``coring'' operation. We provide a simple model for the subband statistics, and use it to develop a semi-blind noise-removal algorithm based on a steerable wavelet pyramid. Related: