image noise

Image noise is the random, unwanted fluctuation in pixel values that corrupts the true scene, the grainy speckle you see in a dim photo, or the stray bright and dark dots in an old scan. It arises from the physics of capturing and transmitting light: photons arrive at random, sensor electronics add thermal jitter, and analog-to-digital conversion introduces rounding. Crucially, different physical sources produce statistically different noise, and choosing the right denoiser depends entirely on getting the noise model right.

The three canonical models are these. Gaussian noise is additive and signal-independent: each pixel gets a random offset drawn from a normal distribution, observed = true + n with n having mean 0 and variance sigma-squared; it models thermal and read noise and is what most filters assume. Poisson noise (shot noise) is signal-dependent and arises because light is quantized into photons that arrive randomly, its variance equals its mean, so bright regions are noisier in absolute terms but cleaner relative to signal; it dominates low-light photography. Salt-and-pepper noise (impulse noise) sets scattered pixels to pure black or pure white, modelling dead or hot sensor pixels and bit errors in transmission.

Beyond these, real cameras add quantization noise (from limited bit depth), fixed-pattern noise (per-pixel sensitivity differences), and read/dark-current noise; real sensor noise is typically a Poisson-Gaussian mixture. Noise level is quantified by signal-to-noise ratio (SNR) or, for comparing a noisy image to a clean reference, peak signal-to-noise ratio (PSNR). Because Poisson noise has a variance that changes with brightness, a variance-stabilizing transform such as the Anscombe transform is often applied to make it behave like constant-variance Gaussian noise so that standard tools apply.