Inverse Filters and Image Enhancement - from DFT to DST

Abstract

Image restoration and enhancement are ones of fundamental problems in image processing. Many research activities, therefore, have been continuously carried out during almost three decades [1, 2, 3]. Inverse filtering, Wiener filtering with or without constrains, and Kalman filtering-smoothing techniques have been applied to the image restoration problem in the cases of either known or unknown blurring functions. Many methods in image restoration and enhancement rely upon the Fourier transformation and its discrete version; DFT (discrete Fourier transformation).

In this paper, we emphasize the usefulness of the DST (discrete Sine transformation) instead of DFT in case of image restoration and enhancement for many cases such as inverse filtering, Wiener filtering and blind deconvolution [4]. Especially, we concentrate here to design 2D (two dimensional) inverse filters for blurred images without observation noises. The main purpose of the present study is to provide the images to the presbyopic as well as the myopia persons based on inverse filtering.