In this paper, we study the fundamental performance limits of image denoising where the aim is to recover the original image from its noisy observation. Our study is based on a general class of estimators whose bias can be modeled to be affine. A bound on the performance in terms of mean squared error (MSE) of the recovered image is derived in a Bayesian framework. In this work, we assume that the original image is available, from which we learn the image statistics. Performances of some current state-of-the-art methods are compared to our MSE bounds for some commonly used experimental images. These show that some gain in denoising performance is yet to be achieved.