Støjmodel

Støjmodel is a probabilistic framework used to describe and quantify the random fluctuations that contaminate measurements or signals. In practice, observed data are often considered as the sum of a true signal and noise, written as y = s + n, or as a product y = s · n in cases of multiplicative noise. A støjmodel specifies the statistical properties of the noise term n, including its distribution, variance, and correlation structure. Many models assume stationarity and independence to simplify analysis, though non-stationary and dependent noise also occur in real applications.

Common noise models include additive Gaussian white noise, which assumes a normal distribution with constant variance and no autocorrelation; Poisson noise, typical for photon-counting measurements; and impulsive or heavy-tailed noise, which features sporadic large deviations. Colored noise has autocorrelation and may be modeled by autoregressive processes. In imaging, specialized models such as Rician or Rayleigh noise may be used to reflect physical imaging processes. Multiplicative noise arises in speckle and certain radar or sonar applications.

Støjmodeller underpin estimation, filtering, and inference. Likelihood-based methods rely on the chosen noise distribution, while Kalman filters use specified process and observation noise. Robust estimation and denoising techniques are developed to cope with departures from idealized models. Model validation and diagnostic checks are important to avoid biased results from misspecification.

Common applications span signal processing, communications, medical imaging, astronomy, and econometrics, wherever measurements are degraded by random fluctuations.