Blind Image Deblurring Driven by Nonlinear Processing in the Edge Domain
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Blind Image Deblurring Driven by Nonlinear Processing in the Edge Domain Stefania Colonnese Dipartimento Infocom, Universit`a degli Studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italy Email: [email protected]
Patrizio Campisi Dipartimento Elettronica Applicata, Universit`a degli Studi “Roma Tre,” Via Della Vasca Navale 84, 00146 Roma, Italy Email: [email protected]
Gianpiero Panci Dipartimento Infocom, Universit`a degli Studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italy Email: [email protected]
Gaetano Scarano Dipartimento Infocom, Universit`a degli Studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italy Email: [email protected] Received 2 September 2003; Revised 20 February 2004 This work addresses the problem of blind image deblurring, that is, of recovering an original image observed through one or more unknown linear channels and corrupted by additive noise. We resort to an iterative algorithm, belonging to the class of Bussgang algorithms, based on alternating a linear and a nonlinear image estimation stage. In detail, we investigate the design of a novel nonlinear processing acting on the Radon transform of the image edges. This choice is motivated by the fact that the Radon transform of the image edges well describes the structural image features and the effect of blur, thus simplifying the nonlinearity design. The effect of the nonlinear processing is to thin the blurred image edges and to drive the overall blind restoration algorithm to a sharp, focused image. The performance of the algorithm is assessed by experimental results pertaining to restoration of blurred natural images. Keywords and phrases: blind image restoration, Bussgang deconvolution, nonlinear processing, Radon transform.
1.
INTRODUCTION
Image deblurring has been widely studied in literature because of its theoretical as well as practical importance in fields such as astronomical imaging [1], remote sensing [2], medical imaging [3], to cite only a few. Its goal consists in recovering the original image from a single or multiple blurred observations. In some application cases, the blur is assumed known, and well-known deconvolution methods, such as Wiener filtering, recursive Kalman filtering, and constrained iterative deconvolution methods, are fruitfully employed for restoration. However, in many practical situations, the blur is partially known [4] or unknown, because an exact knowledge of the mechanism of the image degradation process is not avail-
able. Therefore, the blurring action needs to be characterized on the basis of the available blurred data, and blind image restoration techniques have to be devised for restoration. These techniques aim at the retrieval of the image of interest observed through a nonideal channel whose characteristics are unknown or partially known in the restoration phase. Many blind restoration algorithms have been proposed in the past, and an extended survey can be found in [5, 6]. In some applications, the observation system is able
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