Noise in imaging: focus on correlation and nonlinearity

Understanding and characterizing noise is a foundational part of the design and analysis of an imaging system, and it is also essential for the development of the corresponding image processing modules. In this talk we consider broad classes of heteroskedastic image observations and specifically focus on the noise correlation, the noise anisotropy, and on the nonlinear effects that can arise when dealing with capture at low signal-to-noise ratio or when maximizing the coverage of a narrow dynamic range. We demonstrate possibly unexpected and perhaps counter-intuitive phenomena which, unless suitably modeled and accounted for, can significantly disrupt the noise analysis and other operations in an image processing pipeline.

The talk is divided into two parts.

Part I: I will introduce concrete examples and the relevant mathematical models of noise found in various imaging and image processing systems used in biomedical, defense, security, as well as consumer applications, including x-ray tomography, infrared thermography, confocal fluorescence microscopy, and on-demand video streaming.

Part II: I will discuss the spectral distortion that takes place when nonlinear transformations are applied to correlated noise. In particular, I will consider the case of clipping (e.g., saturation, over-exposure, under-exposure) and the application of variance-stabilizing transformations.