Stochastic and analytic modeling of atmospheric turbulence in image processing

Abstract

Modeling of atmospheric turbulence through Kolmogorov theorem belongs to traditional applications of 2D Fourier Transform (2D FT). It is based on Point Spread Function (PSF) in the spatial domain and its frequency domain image known as Optical Transfer Function (OTF). The latter is available in the explicit form. It enables to create an artificial fog effect in traditional image processing using 2D Discrete Fourier Transform (2D DFT). Exact knowledge of the Optical Transfer Function allows performing the image deblurring as deconvolution through Wiener method. The difference between the reference image and the deconvolution outcome can be quantified using SNR in traditional and rank modification. However, the real star image is a result of a stochastic process which is driven by 2D alpha-stable distribution. There is an efficient method how to generate a pseudorandom sample from the alpha-stable distribution. The distribution then enables to simulate the photon distribution following the theoretical PSF, i.e. convergence according to distribution is guaranteed. The comparison of both models and optimal parameter setting of Wiener deconvolution are studied for various exposure times and CCD camera noise levels. Obtained results can be generalized and applied to turbulent noise suppression.