Utilizarea filtrului Wiener pentru restabilirea imaginilor distorsionate prin focus blur și motion blur

Abstract

Wiener theory, formulated by Norbert Wiener in 1940, forms the foundation of data-dependent linear least square error filters. Wiener filters play a central role in a wide range of applications such as linear prediction, echo cancellation, signal restoration, channel equalization and system identification. The coefficients of a Wiener filter are calculated to minimize the average squared distance between the filter output and a desired signal. In its basic form, the Wiener theory assumes that the signals are stationary processes. However, if the filter coefficients are periodically recalculated for every block of N signal samples then the filter adapts itself to the average characteristics of the signals within the blocks and becomes block-adaptive. A block-adaptive (or segment adaptive) filter can be used for signals such as speech and image that may be considered almost stationary over a relatively small block of samples. In this paper, we study Wiener filter theory, and consider alternative methods of formulation of the Wiener filter problem. We consider the application of Wiener filters in restoration of image for focus blure and motion blur and also additive noise reduction. A case study of the frequency response of a Wiener filter, for additive noise reduction, provides useful insight into the operation of the filter. We also deal with some implementation issues of Wiener filters.