Finite Impulse Response Filter with Square-Exponential Frequency Response

Abstract

This article is devoted to resolving problems with synthesis of FIR-filter restoring distortions such as defocusing. We propose a new parametrical class of finite impulse response filters (FIR-filters) based on a model of the one-dimensional radially-symmetric frequency response. In the proposed synthesis method, the one-dimensional frequency response was composed of square and exponential functions. The two-dimensional filter’s impulse response (SE-filter) was constructed by sampling one-dimensional impulse responses for all directions. For filter parameters estimation, the iterative scheme was used. We considered two approaches to estimating the filter parameters: with training images and in the absence of training images. The important advantages of the proposed synthesis method are the possibility of high quality restoration with a minimum of prior information and the low amount of computing resources required. Given examples illustrates the possibility of the high-quality distortion correction. The proposed method provides higher quality restorations than optimal Wiener filter (from Open CV) due to a lack of distortion on the border of images.