Graphical models are powerful tools for processing images. However, the large dimensionality of even local image data poses a difficulty: representing the range of possible graphical model node variables with discrete states leads to an overwhelmingly large number of states for the model, often making both exact and approximate inference computationally intractable. We propose a representation that allows a small number of discrete states to represent the large number of possible image values at each pixel or local image patch. Each node in the graph represents the best regression function, chosen from a set of candidate functions, for estimating the unobserved image pixels from the observed samples. This permits a small number of discrete states to summarize the range of possible image values at each point in the image. Belief propagation is then used to find the best regressor to use at each point. To demonstrate the usefulness of this technique, we apply it to two problems: super-resolution and color demosaicing. In both cases, we find our method compares well against other techniques for these problems.