بهینه سازی کلونی مورچه برای الحاق تصویر مبتنی بر موج با استفاده از مدل سه مولفه مخلوط نمایی

Wavelet-based image interpolation typically treats the input image as the low frequency subbands of an unknown wavelet-transformed high-resolution image, and then produces the unknown high-resolution image by estimating the wavelet coefficients of the high frequency subbands. For that, a new approach is proposed in this paper, the contribution of which are twofold. First, unlike that the conventional Gaussian mixture (GM) model only exploits the magnitude information of the wavelet coefficients, a three-component exponential mixture (TCEM) model is proposed in this paper to investigate both the magnitude information and the sign information of the wavelet coefficients. The proposed TCEM model consists of a Gaussian component, a positive exponential component and a negative exponential component. Second, to address the parameter estimation challenge of the proposed TCEM model, the ant colony optimization (ACO) technique is exploited in this paper to classify the wavelet coefficients into one of three components of the proposed TCEM model for estimating their parameters. Experiments are conducted to demonstrate that the proposed approach outperform a number of approaches developed in the literature.

Wavelet-based techniques have been widely used for performing image interpolation. A common assumption of the wavelet-based image interpolation approaches is that the input image is treated as the low frequency subbands of an unknown wavelet-transformed high-resolution image. Then the unknown high-resolution image can be reconstructed by estimating the wavelet coefficients of the high frequency subbands, followed by applying the inverse wavelet transform (Chang et al., 1995 and Temizel and Vlachos, 2006). The challenge of conducting wavelet-based interpolation is to estimate the unknown wavelet coefficients of the high frequency subbands. The major widely-used approach is to exploit the inter-scale correlations between the high frequency wavelet coefficients and the low frequency subbsands using statistical models, particularly the Gaussian mixture (GM) model ( Crouse et al., 1998, Kim et al., 2006, Kinebuchi et al., 2001, Woo et al., 2004 and Zhao et al., 2003). However, this GM model neglects the correlations among the sign information of the wavelet coefficients, since the Gaussian distribution is symmetrical around the zero (Temizel, 2007). Inaccurate estimation of the sign of wavelet coefficients could result in implausible artifacts in the reconstructed image. To justify this, a simulation is conducted using the Lena image. A one-level wavelet decomposition (using the well-known Daubechies-97 wavelets) is applied on the test image (shown in Fig. 1(a)), then the signs of all high frequency wavelet coefficients are changed, finally an inverse wavelet transform is applied to produce an image (shown in Fig. 1(b)). Comparing Fig. 1(a) and Fig. 1(b), one can see that the sign information of the wavelet coefficients has a critical role to control the quality of the reconstructed image.To tackle the above challenge, a three-component exponential mixture (TCEM) model is proposed in this paper by formulating the probability distribution of individual wavelet coefficient using three components: (i) a Gaussian component, (ii) a positive exponential component, and (iii) a negative exponential component. Due to the fact that the exponential distribution is not symmetrical around the zero, the proposed model is able to exploit both the magnitude information and the sign information of the wavelet coefficients. Then, the proposed TCEM model is exploited to develop an image interpolation algorithm, by exploiting the inter-scale correlation between the low frequency wavelet coefficients and the high frequency wavelet coefficients. There is a key fundamental issue that needs to be addressed for the proposed TCEM model; that is how to estimate the parameters of the proposed TCEM model. To tackle this issue, the ant colony optimization technique is used in this paper. The ACO technique is exploited to classify the wavelet coefficients into one of three components of the proposed TCEM model, then estimate the parameters of each component. ACO is a nature-inspired optimization algorithm (Dorigo & Thomas, 2004) motivated by the natural collective foraging behavior of real-world ant colonies. Despite the fact that ACO has been widely applied to tackle numerous optimization problems (Dorigo, Gambardella, Middendorf, & Stutzle, 2002), its applications in image processing are quite a few ( Hegarat-Mascle et al., 2007, Malisia and Tizhoosh, 2006, Ouadfel and Batouche, 2003 and Tian et al., 2008b). The rest of this paper is organized as follows. The proposed image interpolation approach is presented in Section 2 where a brief introduction to the conventional GM model and the proposed TCEM model is first provided, followed by estimating the parameters of the proposed TCEM model using the ACO technique. Extensive experimental results are presented in Section 3. Finally, Section 4 concludes this paper

A three-component exponential mixture model has been successfully proposed in this paper to develop a wavelet-based image interpolation approach. Due to the fact that the exponential distribution is not symmetrical around the zero, the proposed model is able to exploit both the magnitude information and the sign information of the wavelet coefficients. Consequently, the proposed approach can effectively exploit the correlation among the low-pass filtered wavelet coefficients and the high-pass filtered wavelet coefficients to yield superior interpolated image result, as verified in our extensive experimental results. Furthermore, the ACO technique has been exploited to perform parameter estimation of the proposed approach. There are several directions that could be considered for future research. First, the proposed approach is independently applied for each high-pass filtered subband of the noisy image. It could be further improved by considering the inter-scale correlation among the wavelet coefficients (Sendur & Selesnick, 2002) to perform classifying. Second, the parallel ACO algorithm (Randall & Lewis, 2002) can be exploited to further reduce the computational load of the proposed image classification algorithm; consequently, shorten the execution time of the proposed approach.