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Biases in the estimation of 3D noise in thermal imagers

The three dimensional noise model (3D noise) is a widely used model for characterizing noise in thermal imaging system. In this model, a sequence of images of a uniform background are acquired, and organized in a three dimensional matrix. This matrix is then decomposed into eight orthogonal noise components that can be assessed individually to yield an understanding about the magnitude and source of noise in a given system. Here we show that the estimators used to assess 3D noise are biased statistical estimators, which can lead to systematic errors when measuring system noise using this model. We provide mathematical proof of the estimator bias and demonstrate the effect with Monte-Carlo simulations.