A Lorentzian Stochastic Estimation for a Robust Iterative Multiframe Super-Resolution Reconstruction with Lorentzian-Tik
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Research Article A Lorentzian Stochastic Estimation for a Robust Iterative Multiframe Super-Resolution Reconstruction with Lorentzian-Tikhonov Regularization V. Patanavijit and S. Jitapunkul Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand Received 31 August 2006; Revised 12 March 2007; Accepted 16 April 2007 Recommended by Richard R. Schultz Recently, there has been a great deal of work developing super-resolution reconstruction (SRR) algorithms. While many such algorithms have been proposed, the almost SRR estimations are based on L1 or L2 statistical norm estimation, therefore these SRR algorithms are usually very sensitive to their assumed noise model that limits their utility. The real noise models that corrupt the measure sequence are unknown; consequently, SRR algorithm using L1 or L2 norm may degrade the image sequence rather than enhance it. Therefore, the robust norm applicable to several noise and data models is desired in SRR algorithms. This paper first comprehensively reviews the SRR algorithms in this last decade and addresses their shortcomings, and latter proposes a novel robust SRR algorithm that can be applied on several noise models. The proposed SRR algorithm is based on the stochastic regularization technique of Bayesian MAP estimation by minimizing a cost function. For removing outliers in the data, the Lorentzian error norm is used for measuring the difference between the projected estimate of the high-resolution image and each low-resolution image. Moreover, Tikhonov regularization and Lorentzian-Tikhonov regularization are used to remove artifacts from the final answer and improve the rate of convergence. The experimental results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods based on L1 and L2 norms for several noise models such as noiseless, additive white Gaussian noise (AWGN), poisson noise, salt and pepper noise, and speckle noise. Copyright © 2007 V. Patanavijit and S. Jitapunkul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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GENERAL INTRODUCTION
Traditionally, theoretical and practical limitations constrain the achievable resolution of any devices. super-resolution reconstruction (SRR) algorithms investigate the relative motion information between multiple low-resolution (LR) images (or a video sequence) and increase the spatial resolution by fusing them into a single frame. In doing so, SRR also removes the effect of possible blurring and noise in the LR images [1–8]. Recent work relates this problem to restoration theory [4, 9]. As such, the problem is shown to be an inverse problem, where an unknown image is to be reconstructed, based on measurements related to it through linear operators and additive noise. This linear relation is composed of geometric warp, blur, and decimation operations.
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