We describe a set of techniques for mapping one image to another based on the statistics of a training set. We
apply these techniques to the problems of image denoising and superresolution, but they should also be useful
for many vision problems where training data are available. Given a local feature vector computed from an
input image patch, we learn to estimate a subband coefficient of the output image conditioned on the patch.
This entails approximating a multidimensional function, which we make tractable by nested binning and linear
regression within bins. This method performs as well as nearest neighbor techniques, but is much faster. After
attaining this local (patch based) estimate, we force the marginal subband histograms to match a set of target
histograms, in the style of Heeger and Bergen.1 The target histograms are themselves estimated from the
training data. With the combined techniques, denoising performance is similar to state of the art techniques
in terms of PSNR, and is slightly superior in subjective quality. In the case of superresolution, our techniques
produce higher subjective quality than the competing methods, allowing us to attain large increases in apparent
resolution. Thus, for these two tasks, our method is very fast and very effective.