Image deblurring process based on separable restoration methods
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Image deblurring process based on separable restoration methods P. Stanimirovi´c · I. Stojanovi´c · S. Chountasis · D. Pappas
Received: 22 May 2013 / Revised: 25 June 2013 / Accepted: 4 July 2013 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2013
Abstract This paper proposes a method for reconstruction of blurred images damaged by a separable motion blur. The method can be used after the application of currently developed image restoration algorithms. Our approach is based on the usage of least squares solutions of certain matrix equations which define the separable motion blur. The method uses appropriately selected matrices besides the Moore–Penrose inverse. The method is tested by reconstructing a set of images after the removal of blur caused by uniform and separable motion. The quality of the restoration is observable by a human eye. The measurements such as the Improvement in Signal to Noise Ratio and the Peak in Signal to Noise Ratio have been increased significantly in comparison with the classical image restoration methods as well as the image restoration proposals based on the usage of the Moore–Penrose inverse.
Communicated by Jinyun Yuan. The first author gratefully acknowledges support from the Research Project 174013 of the Serbian Ministry of Science. P. Stanimirovi´c (B) Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia e-mail: [email protected] I. Stojanovi´c Faculty of Computer Science, Goce Delˇcev University, Goce Delˇcev 89, 2000 Štip, Macedonia e-mail: [email protected] S. Chountasis Independent Power Transmission Operator, 22 Asklipiou Str, 145 68 Krioneri, Athens, Greece e-mail: [email protected] D. Pappas Department of Statistics, Athens University of Economics and Business, 76 Patission Str, 10434 Athens, Greece e-mail: [email protected]
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Keywords Least squares solution · Matrix equation · Image restoration · Moore–Penrose inverse · Spatial–spectral image reconstruction Mathematics Subject Classification
Primary 65F20; Secondary 15A09 · 68U10 · 94A08
1 Introduction In practice, the recorded image inevitably represents a degraded version of the original scene because of the imperfections in the imaging and capturing process. Images such as medical images, satellite images, astronomical images or poor-quality family portraits can be slightly blurred. A wide range of different degradations need to be taken into account, covering for instance, noise, blur, illumination and color imperfections, and geometrical degradations. The elimination of these imperfections is crucial in various tasks of image processing and image analysis. Image restoration methods are used in such problems for reconstructing the original image from a degraded model. The problem of image restoration is studied and shown in many articles (Banham and Katsaggelos 1997; Bovik 2009; Esedoglu and Osher 2004; Gonzalez and Woods 2007; Hansen et al. 2006; Kundur and Hatzinakos 1996; Park et al. 2003). Applications of least
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