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 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 misleading analysis, ineffective filtering, and distortion or even failure in the estimation.
This course provides an introduction to both signal-dependent and correlated noise and to the relevant models and methods for the analysis and practical processing of signals corrupted by these types of noise. Special emphasis is placed on effective techniques for noise suppression. We also discuss the role of these noise models and filters as a versatile regularization prior for solving inverse imaging problems under the plug-and-play framework.
The distribution families covered as leading examples include Poisson, Rayleigh, Rice, multiplicative families, as well as doubly censored distributions. We consider various form of noise correlation, encompassing pixel and read-out cross-talk, fixed-pattern noise, column noise, etc., as well as related issues like photo-response and gain non-uniformities, and processing-induced noise correlation. Consequently, the introduced models and techniques 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, ultrasound and seismic sensing, magnetic resonance imaging, synthetic aperture radar imaging, photon-limited imaging of faint astronomical sources, microbolometer arrays for long-wavelength infrared imaging in thermography, etc. During the laboratory and exercise sessions we will review basic statistical estimators and learn how to analyze and characterize noise, how to transform it, and how to reproduce it in simulations and for data augmentation.