Poissonruis

Poissonruis, known in English as Poisson noise, is a type of random variation that arises when the number of detected events, such as photons, is governed by counting statistics. It is common in imaging sensors where photons arrive randomly over a finite exposure. The detected signal at a pixel is a Poisson random variable with mean proportional to the true light intensity; the observed value X_i has expectation equal to the underlying intensity lambda_i and variance equal to lambda_i. This makes Poisson noise inherently signal-dependent: brighter regions exhibit more variance, while darker regions can have low signal but relatively high relative noise.

Poisson noise reflects the quantum nature of light and the discrete nature of detector electrons. It is especially relevant in photon-limited situations such as astronomical imaging, fluorescence microscopy, and low-light photography, as well as certain medical imaging modalities like positron emission tomography (PET) and single-photon emission computed tomography (SPECT). At high photon counts the Poisson distribution approaches a Gaussian distribution with variance approximately equal to the mean, which explains why Gaussian approximations are often used in analysis.

Handling Poisson noise often involves variance-stabilizing transforms, such as the Anscombe transform, to convert the data into a form with more uniform variance suitable for standard denoising methods. Other approaches model the Poisson likelihood directly, as in Richardson–Lucy deconvolution, Poisson-adapted nonlocal means, or BM3D variants. Properly accounting for Poisson noise improves the quantitative interpretation of photon-limited images and the reliability of subsequent analyses.