Non-Gaussian model-based fusion of noisy images in the wavelet domain

Loza, Artur; Bull, David; Canagarajah, N.; Achim, Alin

doi:10.1016/j.cviu.2009.09.002

Cited by 66 publications

(46 citation statements)

References 17 publications

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“…Previous work revealed that there are strong dependencies between the coefficients, their parent (adjacent coarser scale locations), and their sibling coefficients across different orientations [39,37]. In this study, we consider the problem of modeling the statistical dependencies between coefficients and corresponding parent coefficients.…”

Section: Bivariate Modelmentioning

confidence: 99%

“…Gaussian and Cauchy processes are special cases of stable processes with α = 2 and α = 1, respectively. The probability distribution for the Cauchy density with location parameter δ = 0 is given by: Although the SαS density function behaves approximately like a Gaussian density function near the origin, the stable densities have algebraic tails (heavy tails) while the Gaussian density function has exponential tails which decay at a faster rate [37,38]. One consequence of heavy tails is that only moments of order less than α exit for the non-Gaussian alpha-stable family members, i.e., E|x| m = C(m, α)γ m α for −1 < m < α, where m is the moment order and…”

Section: Symmetric Alpha-stable Model 221 Univariate Modelmentioning

confidence: 99%

“…Wan et al [38] have graphically showed that histogram of wavelet coefficients has heavy tails and sharply peaked modes at zero (non-Gaussian heavy tailed behavior), which deviate significantly from the Gaussian distribution. In addition, Loza et al [37] showed that wavelet subband coefficients can be better modeled by the generalized Gaussian distribution (GGD) or symmetric alpha-stable (SαS) distributions compared to the Gaussian model. Although statistical modeling (GGD and SαS models) in wavelet domain has been widely adopted in the computer vision and recently in the medical image processing field [45,46,47], this method has not been fully explored in the computerized histology analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The DT-CWT offered a compact representation while providing the desirable properties of approximate shift invariance, improved directional selectivity (6 directional subbands per scale), and complex valued coefficients, which are useful for magnitude/phase analysis within the transform domain. The DT-CWT has been widely applied to image modeling [34], denoising [35], enhancement [36], fusion [37,38], and segmentation [39]. [42].…”

Section: Introductionmentioning

confidence: 99%

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Automated mitosis detection in histopathology based on non-gaussian modeling of complex wavelet coefficients

et al. 2017

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractTo diagnose breast cancer, the number of mitotic cells present in histology sections is an important indicator for examining and grading biopsy specimen. This study aims at improving the accuracy of automated mitosis detection by characterizing mitotic cells in wavelet based multi-resolution representations via a non-Gaussian modeling method. The potential mitosis candidates were decomposed into multi-scale forms by an undecimated dual-tree complex wavelet transform. Two non-Gaussian models (the generalized Gaussian distribution (GGD) and the symmetric alpha-stable (SαS) distributions) were used to accurately model the heavy-tailed behavior of wavelet marginal distributions. The method was evaluated on two independent data cohorts, including the benchmark dataset (MITOS), via a support vector machine classifier.

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Section: Bivariate Modelmentioning

confidence: 99%

Section: Symmetric Alpha-stable Model 221 Univariate Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Automated mitosis detection in histopathology based on non-gaussian modeling of complex wavelet coefficients

et al. 2017

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“…In 2005, Achim and Kuruoǧlu utilized a bivariate maximum a posteriori estimator (BMAP) to propose a new statistical model in the complex wavelet domain for removing Cauchy noise [1]. In [34], Loza et al proposed a statistical approach based on non-Gaussian distributions in the wavelet domain for tackling the image fusion problem. Their method achieved a significant improvement in fusion quality and noise reduction.…”

Section: Introductionmentioning

confidence: 99%

Cauchy Noise Removal by Nonconvex ADMM with Convergence Guarantees

et al. 2017

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Image restoration is one of the essential tasks in image processing. In order to restore images from blurs and noise while also preserving their edges, one often applies total variation (TV) minimization. Cauchy noise, which frequently appears in engineering applications, is a kind of impulsive and non-Gaussian noise. Removing Cauchy noise can be achieved by solving a nonconvex TV minimization problem, which is difficult due to its nonconvexity and nonsmoothness. In this paper, we adapt recent results in the literature and develop a specific alternating direction method of multiplier to solve this problem. Theoretically, we establish the convergence of our method to a stationary point. Experimental results demonstrate that the proposed method is competitive with other methods in visual and quantitative measures. In particular, our method achieves higher PSNRs for 0.5 dB on average.

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Fusion of noisy images based on joint distribution model in dual‐tree complex wavelet domain

Sun

Zhu

Luo

et al. 2018

Int J Imaging Syst Tech

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Source images are frequently corrupted by noise before fusion, which will lead to the quality decline of fused image and the inconvenience for subsequent observation. However, at present, most of the traditional medical image fusion scheme cannot be implemented in noisy environment. Besides, the existing fusion methods scarcely make full use of the dependencies between source images. In this research, a novel fusion algorithm based on the statistical properties of wavelet coefficients is proposed, which incorporates fusion and denoising simultaneously. In the proposed algorithm, the new saliency and matching measures are defined by two distributions: the marginal statistical distribution of single wavelet coefficient fit by the generalized Gaussian Distribution and joint distribution of dual source wavelet coefficients modeled by the anisotropic bivariate Laplacian model. Additionally, the bivariate shrinkage is introduced to develop a noise robust fusion method, and a moment-based parameter estimation applied in the fusion scheme is also exploited in denoising method, which allows to achieve the consistency of fusion and denoising. The experiments demonstrate that the proposed algorithm performs very well on both noisy and noise-free images from multimodal medical datasets (computerized tomography, magnetic resonance imaging, magnetic resonance angiography, etc.), outperforming the conventional methods in terms of both fusion quality and noise reduction. K E Y W O R D Sbi-shrinkage, image fusion, KL-divergence, mutual information, statistical distribution 1 | INTRODUCTION Imagology plays an important role in medical science, owing to the application for the visualization of anatomy structure, function, and metabolism information. 1 Actually, singular modality medical images exhibit limitations due to the imaging mechanism. Computerized tomography (CT) images can provide bone tissue information with high resolutions, but they cannot show the soft tissue. Although magnetic resonance imaging (MRI) images are good at showing the anatomical information of soft tissue, they cannot provide metabolism information, while T2 weighted MRI (MRI-T2) and magnetic resonance angiography (MRA) images could achieve good vision of pathological tissue. 2 In practical clinical applications, the multi-modal medical image fusion technology, which combines the complementary information from multi-modal images, is helpful to facilitate a better observation of anatomical and metabolism information. 3 This technology provides an easy but very efficient access for diagnosis and assessment of disease. 4 Image fusion based on multiscale transform has become a more common approach for pixel-level image fusion and abundant research results have been achieved. For waveletbased fusion methods, wavelet transforms are performed first on each source image to obtain different sub-bands which contain decomposition information of varying

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Non-Gaussian model-based fusion of noisy images in the wavelet domain

Cited by 66 publications

References 17 publications

Automated mitosis detection in histopathology based on non-gaussian modeling of complex wavelet coefficients

Automated mitosis detection in histopathology based on non-gaussian modeling of complex wavelet coefficients

Cauchy Noise Removal by Nonconvex ADMM with Convergence Guarantees

Fusion of noisy images based on joint distribution model in dual‐tree complex wavelet domain

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