Efficient Recursive Multichannel Blind Image Restoration

EURASIP Journal on Advances in Signal Processing, Nov 2006

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.

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Efficient Recursive Multichannel Blind Image Restoration

EURASIP Journal on Advances in Signal Processing Hindawi Publishing Corporation Efficient Recursive Multichannel Blind Image Restoration Li Chen 0 Kim-Hui Yap 0 Yu He 0 0 Division of Information Engineering, School of Electrical and Electronic Engineering, Nanyang Technological University , 50 Nanyang Avenue , Singapore 639798 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. 1. 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 identified 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 lead to poor solutions in the noisy environments. There are some successful works on the development of multichannel restoration, which exploit the features of single-channel restoration algorithms [7–15]. These techniques develop a cost function within the framework of constrained least squares minimization [7, 8]. The minimization step involves two processes of blur identification and image restoration centered on the principle of projection onto convex sets (POCS). The alternating minimization (AM) strategy is first proposed in [9], and later extended to double Tikhonov regularization in [10, 11]. Double regularization (DR) [12] and the Gauss-Markov random fields [13] have also been applied in blind image restoration. Total variation (TV) has been incorporated into the DR to achieve edge preservation and noise suppression. A promising attempt has been made by utilizing the blur null space as the regularization term in the framework of TV [14]. Recently, the extension of the Bussgang blind equalization algorithm to iterative multichannel deconvolution has been proposed in [15]. The basic idea is focused on Wiener filtering of the observed degraded images, and updating the filters using a nonlinear Bayesian estimation of the estimated image. Generally speaking, these iterative methods are extensions of single-channel blind image restorations approaches. Therefore, if an extra degraded image becomes available at a later stage, the iterative schemes will require a complete rerun, rather than a recursive process to update the estimate. This is, clearly, inflexible and computationally inefficient. In view of this, we develop a new efficient algorithm called multichannel recursive filtering (MRF) to solve blind multichannel image restoration. To the best of our knowledge, no previous work on recursive filtering has been developed to address blind multichannel image restoration. The estimated image is recursively updated from the previous estimate using a regularization framework. All the operat (...truncated)


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Li Chen, Kim-Hui Yap, Yu He. Efficient Recursive Multichannel Blind Image Restoration, EURASIP Journal on Advances in Signal Processing, 2006, pp. 019675, Volume 2007, Issue 1, DOI: 10.1155/2007/19675