Modeling and estimation of signal-dependent and correlated noise

Abstract

The additive white Gaussian noise (AWGN) model is ubiquitous in signal processing. This model is often justified by central-limit theorem (CLT) arguments. However, whereas the CLT may support a Gaussian distribution for the random errors, it does not provide any justification for the assumed additivity and whiteness. As a matter of fact, data acquired in real applications can seldom be described with good approximation by the AWGN model, especially because errors are typically correlated and not additive. Failure to model accurately the noise leads to inaccurate analysis, ineffective filtering, and distortion or even failure in the estimation. This chapter provides an introduction to both signal-dependent and correlated noise and to the relevant models and basic methods for the analysis and estimation of these types of noise. Generic one-parameter families of distributions are used as the essential mathematical setting for the observed signals. The distribution families covered as leading examples include Poisson, mixed Poisson–Gaussian, various forms of signal-dependent Gaussian noise (including multiplicative families and approximations of the Poisson family), as well as doubly censored heteroskedastic Gaussian distributions. We also consider various forms of noise correlation, encompassing pixel and readout cross-talk, fixed-pattern noise, column/row noise, etc., as well as related issues like photo-response and gain nonuniformity. The introduced models and methods are applicable to several important imaging scenarios and technologies, such as raw data from digital camera sensors, various types of radiation imaging relevant to security and to biomedical imaging.