Solutions to the denoising problem rely on three fundamental components: a signal model, a noise model, and a measure of signal fidelity. In this chapter, we present an intuitive introduction to multiscale image denoising with an emphasis on the signal properties. Using pairs of noise-free and noisy versions of a database of natural images, we illustrate how empirically-observed properties of noise and image structure can be formalized statistically and used to design and optimize denoising methods. Using this data-driven approach, we present a sequence of three different techniques for image denoising, each based on an increasingly refined signal model. We highlight the similarities between each of these approaches and other popular mulitiscale denoising methods.