Constructing a quadratic-exponential FIR-filter with an extended frequency response midrange

This article is concerned with synthesizing filter with finite impulse response (FIR-filters) employed to correct radially symmetric distortions such as defocusing. We propose a new parametric class of finite impulse response filters (FIR-filters) based on a model of the one-dimensional radially symmetric frequency response. In the proposed method, the one-dimensional frequency response is composed of quadratic and exponential functions. The two-dimensional impulse response of the filter is constructed by sampling one-dimensional impulse responses for all directions. The development consists in introducing an extended mid-frequency region of the frequency response, thus increasing the contribution of the frequencies to image correction. Examples are given in order to illustrate the possibility of the high-quality distortion correction. In particular, it is shown that the proposed method provides the restoration quality higher than that obtained when using an optimal Wiener filter (taken from OpenCV).