In order to work well, many computer vision algorithms require that their parameters be adjusted according to the image noise level, making it an important quantity to estimate. We show how to estimate an upper bound on the noise level from a single image based on a piecewise smooth image prior model and measured CCD camera response functions. We also learn the space of noise level functions how noise level changes with respect to brightness and use Bayesian MAP inference to infer the noise level function from a single image. We illustrate the utility of this noise estimation for two algorithms: edge detection and featurepreserving smoothing through bilateral filtering. For a variety of different noise levels, we obtain good results for both these algorithms with no user-specified inputs.