Multiscale Denoising of Photographic Images

Signal acquisition is a noisy business. In photographic images, there is noise within the light intensity signal (e.g., photon noise), and additional noise can arise within the sensor (e.g., thermal noise in a CMOS chip), as well as in subsequent processing (e.g., quantization). 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. In this chapter, we’ll describe the basics of image denoising, with an emphasis on signal properties. For noise modeling, we’ll restrict ourselves to the case in which images are corrupted by additive, white, Gaussian noise that is, we’ll assume each pixel is contaminated by adding a sample drawn independently from a Gaussian probability distribution of fixed variance. A variety of other noise models and corruption processes are considered in Chapter 7. Throughout, we’ll use the well known mean squared error (MSE) measure as an objective function. We develop a sequence of three image denoising methods, motivating each one by observing a particular property of photographic images that emerges when they are decomposed into subbands at different spatial scales. We’ll examine each of these properties quantitatively by examining statistics across a training set of photographic images and noise samples. And for each property, we’ll use this quantitative characterization to develop two example denoising functions: a binary threshold function that retains or discards each multi-scale coefficient depending on whether it is more likely to be dominated by noise or signal, and a continuous-valued function that multiplies each coefficient by an optimized scalar value. Although these methods are quite simple, they capture many of the concepts that are used in state-of-the-art denoising systems. Toward the end of the chapter, we briefly describe several alternative approaches.