Efficient Recursive Multichannel Blind Image Restoration
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Research Article Efficient Recursive Multichannel Blind Image Restoration Li Chen, Kim-Hui Yap, and Yu He Division of Information Engineering, School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 Received 3 May 2006; Revised 25 August 2006; Accepted 26 August 2006 Recommended by Mark Liao This paper presents a novel multichannel recursive filtering (MRF) technique to address blind image restoration. The primary motivation for developing the MRF algorithm to solve multichannel restoration is due to its fast convergence in joint blur identification and image restoration. The estimated image is recursively updated from its previous estimates using a regularization framework. The multichannel blurs are identified iteratively using conjugate gradient optimization. The proposed algorithm incorporates a forgetting factor to discard the old unreliable estimates, hence achieving better convergence performance. A key feature of the method is its computational simplicity and efficiency. This allows the method to be adopted readily in real-life applications. Experimental results show that it is effective in performing blind multichannel blind restoration. Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
Image restoration deals with the estimation of the original images from the observed blurred, degraded images using the partial information about the imaging system. It is an illposed problem as the uniqueness and stability of the solution are not guaranteed [1]. In many applications such as remote sensing and microscopy imaging, multiple degraded images of a single scene become available while the blurring function or point spread function (PSF) of each channel remains unknown. Therefore, the recovery of the original scene from its multiple observations is required and this problem is, commonly, referred to as multichannel blind image restoration [2]. Various researchers have investigated the problem of multichannel image restoration over the years. With the assumption that the multichannel PSFs are weakly coprime, and in the absence of noise, the desired image and PSFs can be transformed into the null space of a special matrix constructed from the degraded images [3–6]. Centered on this idea, several techniques have been proposed which include greatest common divisor (GCD) [3], subspace-based [4, 5], and eigenstructure-based approaches [6]. The GCD method is based on the notion that the desired image can be regarded as the polynomial GCD among the degraded images in the z-domain. Subspace-based methods work by first estimating the blurring function using a procedure of min-eigenvector, followed by conventional image restoration using the identi-
fied PSFs. In similar concept, eigenstructure-based algorithm transforms the null space problem into a constrained optimization framework and performs direct deconvolver estimation. The aforementioned null space-based methods, however, suffer from noise amplification, which often lea
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