АВТОМАТИЧНЕ ВИДАЛЕННЯ ГАУСОВОГО ШУМУ НА ЦИФРОВИХ ЗОБРАЖЕННЯХ ЗА ДОПОМОГОЮ КВАЗІОПТИМАЛЬНОГО ФІЛЬТРА ГАУСА

Abstract

A mathematical model, method and software are developed for the automatic removal of Gaussian noise in digital images by quasioptimal Gaussian filter. The calculation of Gaussian noise level is performed by a method which based on image filtering and iterative selection of region of interest. As the noise level its standard deviation is used. The useful signal in the image is described by the sum of sinusoids. In the first model the brightness of the useful signal is described by one sinusoid, and in the second model by two mutually perpendicular sinusoids. The used models allow us to take into account distortions of useful signal that arise when filtering images to remove noise. The periods and amplitudes of the sinusoid of the useful signal are calculated based on the radial distribution for the power spectrum of the initial image. The orientation of the brightness of the initial image is expressed in terms of the eccentricity, which is calculated on the basis of the central discrete moments of its power spectrum, transformed in accordance with Parseval's theorem. The parameters of the quasioptimal Gaussian filter are calculated on the basis of the four above-described parameters of the initial image: noise level, eccentricity of the image, period and amplitude of sinusoid of the useful signal. The quasioptimal value of the standard deviation of the Gaussian filter kernel is obtained as the value, at which the standard deviation of brightness of the filtered image from the brightness of useful signal is minimized. When calculating the quasioptimal kernel of the Gaussian filter, simultaneous reduction of the noise level and distortion of the useful signal that occur as a result of low-frequency filtering of the initial image are taken into account. The accuracy of the developed filtering method was verified by removing of Gaussian noise on a set of 100 test images. To estimate the accuracy of the filtering of test images, the root mean square error between the brightness of the filtered and the initial images was used, as well as the peak signal-to-noise ratio for the filtered images. An analysis of the peak signal-to-noise ratio for test filtered images showed that the developed method for removing Gaussian noise is quasioptimal. Software implementation of the developed method of automatic removal of Gaussian noise in digital images is performed in the MATLAB system.