The Influence of Noise on 2D Gaussian Profile Parameters Estimation

The precise estimation of the Gaussian profile parameters plays an important role in many scientific fields. In astronomical images, the 2D Gaussian profiles are good approximations of stellar objects, which are point sources spread in the image plane due to various degradations in the imaging process. The accurate estimation of the 2D Gaussian parameters enables stellar object identification and outlier detection. However, various noise types present in astronomical images complicate the estimation process. Image noise can have an additive or multiplicative nature. The primary cause of additive noise is the so-called readout noise, which has a Gaussian distribution and is temperature-dependent. The second noise type is the multiplicative Poisson noise caused by the quantum nature of the light with the standard deviation proportional to the square root of the pixel intensity. Additionally, there are uniformly distributed quantization noise caused by the conversion of the continuous signal to discrete levels and heavy-tailed salt and pepper noise caused by the bad pixels. All these noise types represent the challenge in the precise estimation of Gaussian parameters. Since the iteratively reweighted least squares method (IRWLS) with Huber weights calculated from statistical analysis of estimation errors showed a good performance as a robust estimator in other applications, it is used in this paper for the 2D Gaussian profile parameters estimation from noisy data. The goal of this paper is to analyze the robustness of the IRWLS method to different noise types.