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Nonlinear Filtration on the Base of the Power Transform


V.A. Tolstunov, P.V. Stepanets

It is found algorithm digital nonlinear smoothing filter with slithering window for a case of degree transformation of values of an input signal. The problem of synthesis of the filter is considered as a statistical problem of an estimation of the unknown determined parameter. It is shown that on the basis of the general received parities it is possible to construct family of smoothing filters among which is well-known, for example, exponential, median. The received algorithm of the filter is investigated analytically. In particular, for a filter output the probability density, a mathematical expectation and dispersion are found. It is shown that at the expense of increase in parameter of nonlinearity of the filter it is possible to improve smoothing characteristics. The algorithm of the filter is generalized for a filtration of images. Filtration with degree transformation is simulated digitally when Gaussian and pulse noises were additively imposed on the monochrome image. Comparison of the received results of modeling with corresponding results of the median filter, the Wiener's filter, the Gaussian filter of low frequencies and the filter «Dust and scratches» from program Adobe® Photoshop® is given. According to results of modeling in a case of Gaussian noise all compared algorithms show identical results, except filter «Dust and scratches». And, if it is required to save image fine details, using the small aperture, the last filter becomes more preferable. In case of pulse noise the best results are given by median filter and the filter with degree transformation. At weak intensity of pulse noise filtration’s errors are similar for them, and with growth occurrence probability of pulse noise filter with degree transformation have better smoothing quality. According to results of the modeling, the offered filter pulse noise almost completely removes with noisy images unless noisy areas are grouped so that their area exceeds the area of the filter’s aperture.

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