In this work, we present a new approach to image denoising derived from the general framework of wavelets with composite dilations. This framework extends the traditional wavelet approach by allowing for waveforms to be defined not only at various scales and locations but also according to various orthogonal transformations such as shearing transformations. The shearlet representation is, perhaps, the most widely known example of wavelets with composite dilations. However, many other representations are obtained within this framework, where directionality properties are controlled by different types of orthogonal matrices, such as the newly defined hyperbolets. In this paper, we show how to take advantage of different wavelets with composite dilations to sparsely represent important features such as edges and texture independently, and apply these techniques to derive improved algorithms for image denoising.