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Removal of blur in images based on least squares solutions
Author(s) -
Stanimirović Predrag S.,
Chountasis Spiros,
Pappas Dimitrios,
Stojanović Igor
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2751
Subject(s) - image restoration , mathematics , matrix (chemical analysis) , image (mathematics) , noise (video) , pixel , computer vision , algorithm , artificial intelligence , image processing , computer science , materials science , composite material
We propose an image restoration method. The method generalizes 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, wherein an arbitrary matrix of appropriate dimensions is included besides the Moore–Penrose inverse. In addition, the method is a useful tool for improving results obtained by other image restoration methods. Toward that direction, we investigate the case where the arbitrary matrix is replaced by the matrix obtained by the Haar basis reconstructed image. The method has been tested by reconstructing an image after the removal of blur caused by the uniform linear motion and 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 method are illustrated by the values of the improvement in signal‐to‐noise ratio and in the values of peak signal‐to‐noise ratio. Copyright © 2013 John Wiley & Sons, Ltd.