Wavelet-based demosaicing techniques have the advantage of being computationally relatively fast, while having a reconstruction performance that is similar to state-of-the-art techniques. Because the demosaicing rules are linear, it is fairly simple to integrate denoising into the demosaicing. In this paper, we present a method that performs joint denoising and demosaicing, using a Gaussian Scale Mixture (GSM) prior model, thereby modeling the local edge direction as a hidden variable. The results indicate that this technique offers a better reconstruction performance (in PSNR sense and visually) than sequential demosaicing and denoising. On a recent GPU, our algorithm takes 3.5 s for reconstructing a 12 megapixel RAW digital camera image.