We consider the problem of image denoising wherein the statistical characterization of the noise corruption mechanism is known. We make no assumptions on the nature or statistics of the underlying noise-free signal. A denoiser is proposed which, although ignorant of the statistical properties of the noise-free image, does essentially as well as a scheme with full knowledge of the statistics. The solution is presented as a sequence of schemes that progressively consider larger neighborhoods (contexts) around a pixel being denoised, to achieve optimum performance under a user-defined distortion measure.