Linear Motion Blur Parameter Estimation in Noisy Images Using Fuzzy Sets and Power Spectrum
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Research Article Linear Motion Blur Parameter Estimation in Noisy Images Using Fuzzy Sets and Power Spectrum Mohsen Ebrahimi Moghaddam and Mansour Jamzad Department of Computer Engineering, Sharif University of Technology, 11365-8639 Tehran, Iran Received 17 July 2005; Revised 11 March 2006; Accepted 15 March 2006 Recommended by Rafael Molina Motion blur is one of the most common causes of image degradation. Restoration of such images is highly dependent on accurate estimation of motion blur parameters. To estimate these parameters, many algorithms have been proposed. These algorithms are different in their performance, time complexity, precision, and robustness in noisy environments. In this paper, we present a novel algorithm to estimate direction and length of motion blur, using Radon transform and fuzzy set concepts. The most important advantage of this algorithm is its robustness and precision in noisy images. This method was tested on a wide range of different types of standard images that were degraded with different directions (between 0◦ and 180◦ ) and motion lengths (between 10 and 50 pixels). The results showed that the method works highly satisfactory for SNR > 22 dB and supports lower SNR compared with other algorithms. Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
1.
INTRODUCTION
The aim of image restoration is to reconstruct or estimate an uncorrupted image by using the degraded version of the same image. One of the most common degradation functions is linear motion blur with additive noise. Equation (1) shows the relationship between the observed image g(x, y) and its uncorrupted version f (x, y) [1]: g(x, y) = f (x, y) ∗ h(x, y) + n(x, y).
(1)
In this equation, h is the blurring function (or point spread function (PSF)), that is, convolved in the original image and n is the additive noise function. According to (1), in order to determine the uncorrupted image, we need to find the blurring function (h) (i.e., blur identification) which is an ill-posed problem. Finding motion blur parameters in none additive noise environments was addressed in [2–4], where these researchers tried to extend their algorithms to noisy images as well. The authors in [4, 5] have divided the image into several windows to reduce noise effects and to extend their methods to support noisy images. Linear motion blur identification in noisy images was also addressed using bispectrum in [3, 6]. This method is not precise enough because theoretically, to remove the noise by using this method, many windows are required, which in practice is impossible. The authors in [3, 6] did not specify
the lowest SNR that their method can support. A different method was presented for noisy images in [2] where authors used AR (auto regressive) model to present images and have proved the lowest allowed SNR that their method can support. In [7], we presented a method based on mathematical modeling to estimate parameters in noisy images at low SNRs. In many other research areas, fuzzy concepts have been used to improve th
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