Traditional median smoother for 2D images is insensitive to impulse noise but generates flat areas as unwanted artifacts. The proposed approach to overcome this issue is based on the minimization of the regularized form of total variation functional. At first the continuous functional is defined for n-dimensional signal in an integral form with regularization term. The continuous functional is converted to the discrete form using equidistant spatial sampling in point grid of pixels, voxels or other elements. This approach is suitable for traditional signal and image processing. The total variance is then converted to the sum of absolute intensity differences as a minimization criterion. The functional convexity guarantees the existence of global minimum and absence of local extremes. Resulting non-linear filter iteratively calculates local medians using red-black method of Successive Over/Under Relaxation (SOR) scheme. The optimal value of the relaxation parameter is also subject to our study. The sensitivity to regularization parameter enables to design high-pass and nonlinear band-pass filters as the difference between the image and low-pass smoother or as the difference between two different low-pass smoothers, respectively. Various median based approaches are compared in the paper.
KEYWORDS: Stochastic processes, Signal to noise ratio, Atmospheric turbulence, Atmospheric modeling, Fourier transforms, Monte Carlo methods, Optical transfer functions, Turbulence, Filtering (signal processing), Image processing
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.
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