Передискретизація зображень з застосуванням узагальнених рядів Уіттекера-Котельникова-Шеннона

Abstract

The operation scaling leads to search for information about the pixels that are not on the original image. The conventional approach to digital signal processing is based on sampling theorem, which solves the problem of interpolation samples only of function on an infinite time interval. But the assumption made in sampling theorem, and complexity of calculations to restore function numerical series does not allow to get rid of the disadvantages associated with unlimited range of real stochastic signals.Generalized series of Whittaker-Kotelnikov-Shannon, based on the atomic functions. They satisfy all the requirements of the sampling theorem and they have better convergence in the case of discontinuous and local time signals. The computation uses end product and there is an exact decomposition.The image zoom adds the new information into original image and so it contains new information. It is necessary to identify how the entropy of new image matches the original. The similar elements as such as lines and squares are always in image. That reduces them to fractals. Then we can calculate the fractal dimension of the original and the source image and apply the metric PSNR.This approach was tested for the interpolation of the field vectors in the problem of motion estimation between frames video sequence and showed better results compared to known algorithms interpolation