We develop a statistical model for images that explicitly captures variations in local orientation and contrast. Patches of wavelet coefficients are described as samples of a fixed Gaussian process that are rotated and scaled according to a set of hidden variables representing the local image contrast and orientation. An optimal Bayesian least squares estimator is developed by conditioning upon and integrating over the hidden orientation and scale variables. The resulting denoising procedure gives results that are visually superior to those obtained with a Gaussian scale mixture model that does not explicitly incorporate local image orientation.