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In this book, we introduce a new method of blurring and deblurring digital images using new filters that generated from Average filter using HB Markov basis. We call these filters HB-filters. These new filters cause a motion blur and remove it from the images. Also, we study the action of the Dihedral group on HB-filters to find another HB-filters that give another different types of blur by using the action of the largest subgroup of Dihedral group. We apply our method on gray and RGB (Lena, Baboon and Pepper) images with using the two formats (jpg. format) and (png. format). Finally, the enhanced images by HB-filters and other methods are compared like Average, Gaussian and Motion, by using two standard distortion measures; peak signal to noise ratio (PSNR) and Root mean square error (RMSE). The results and analyses showed that the HB-filters are better in PSNR and RMSE.
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