Last modified: 2014-02-21
Abstract
In this work we examine the problem of image restoration methods. The methods that will be presented generalize image restoration algorithms that are based on the
Moore–Penrose solution of certain matrix equations that define the linear motion blur. Our approach is based on the usage of least squares solutions of these matrix equations, where an arbitrary matrix of appropriate dimensions is included besides the Moore–Penrose inverse. The arbitrary matrix is replaced by the results given by some of known image restoration methods, such as moment based methods (the Haar basis and Fourier basis). In addition, the method is a useful tool for improving results obtained by other image restoration methods. The methods have been tested by reconstructing an image after the removal of blur caused by uniform linear motion or by separable motion blur, filtering the noise that is corrupted with the image pixels. The quality of the restoration is observable by a human eye. Benefits of using the presented methods are illustrated by the values of the improvement in signal-to-noise ratio (ISNR) and in the values of peak signal-to-noise ratio (PSNR).