Multiscale Denoising of Photographic Images

Image noise can be quite noticeable, as in images captured by inexpensive cameras built into cellular telephones, or imperceptible, as in images captured by professional digital cameras. Stated simply, the goal of image denoising is to recover the true signal (or its best approximation) from these noisy acquired observations. All such methods rely on understanding and exploiting the differences between the properties of signal and noise. Formally, solutions to the denoising problem rely on three fundamental components: a signal model, a noise model, and finally a measure of signal fidelity (commonly known as the objective function) that is to be minimized. A simple strategy for denoising an image is to separate it into smooth and nonsmooth parts, or equivalently, low-frequency and high-frequency components. This decomposition can then be applied recursively to the lowpass component to generate a multiscale representation. The lower frequency subbands are smoother, and thus can be subsampled to allow a more efficient representation, generally known as a multiscale pyramid. The resulting collection of frequency subbands contains the exact same information as the input image, but as one shall see, it has been separated in such a way that it is more easily distinguished from noise.