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In this paper, we consider the generalized Bayes estimator of mean vector parameter for multivariate normal distribution with Unknown mean vector and covariance matrix under reflected normal loss function. We also prove admissibility and minimaxity of the generalized Bayes estimator. We obtain stein’s unbiased risk estimator (SURE) threshold based on generalized Bayes estimator and we find the wavelet shrinkage generalized bayes SURE estimator. At the end, we check the performance of this estimator and we provide two real examples. [ABSTRACT FROM AUTHOR]

In this paper, a new noisy remote sensing image segmentation algorithm combined with wavelet shrinkage and graph cuts model is proposed. The entire process of noisy remote sensing image segmentation is composed of two steps. Firstly, the wavelet transform is used to extract information about sharp variations in the remote sensing images and the shrinkage function is applied to adapt the image features, and image noise is eliminated by utilizing the feature adaptive threshold method. Secondly, graph cuts based on active contour (GCBAC) model is applied to segment the de-noised image. Additionally, a new energy function which disregards the regularising parameter is proposed in the GCBAC model in order to avoid the edge and region balance problems, and the GCBAC model is used to extract the desired segmentation object by constructing a specified graph. Simulation results indicate that the proposed algorithm can effectively improve the quality of image segmentation and demonstrates improved robustness to noise. [ABSTRACT FROM AUTHOR]

The NeighShrink and ModiNeighShrink areefficient image denoising algorithms that are based on universal threshold and discrete wavelet transform. The improved image denoising method based on wavelet thresholding (IIDMWT) method gives better results than the NeighShrink and ModiNeighShrink by using the modified universal threshold. These methods kill too many wavelet coefficients; some of them may contain useful image information. Thus, we may not get good quality of image using these methods. In this paper, we extend the idea of Cai and Silverman for developing a new image denoising method and determine the coefficients of neighboring window for every subband. The experimental results show that in most of the cases, our proposed method performs better than the NeighShrink, ModiNeighShrink, and IIDMWT in terms of peak signal- to-noise ratio and structural similarity index measure. [ABSTRACT FROM AUTHOR]

We propose a new algorithm for denoising of multivariate function values given at scattered points in $${\mathbb{R}^{d}}$$ . The method is based on the one-dimensional wavelet transform that is applied along suitably chosen path vectors at each transform level. The idea can be seen as a generalization of the relaxed easy path wavelet transform by Plonka (Multiscale Model Simul 7:1474-1496, ) to the case of multivariate scattered data. The choice of the path vectors is crucial for the success of the algorithm. We propose two adaptive path constructions that take the distribution of the scattered points as well as the corresponding function values into account. Further, we present some theoretical results on the wavelet transform along path vectors in order to indicate that the wavelet shrinkage along path vectors can really remove noise. The numerical results show the efficiency of the proposed denoising method. [ABSTRACT FROM AUTHOR]

Many shrinkage functions have been introduced and applied for the wavelet shrinkage denoising of computed tomography (CT) images. However, these functions have problems in continuity of functions and cause “shrinkage artifacts”. Therefore, we designed a new and smooth shrinkage function using noise distribution. The proposed shrinkage function was designed under the following four conditions: (1) use of noise distribution, (2) shrunk coefficients having all ranges of amplitude, (3) function continuity, and (4) property of a function that is controllable by two parameters. The designed function was applied to phantom and chest CT images and denoising performance was compared with other functions. In the proposed method, edge and pixel values were maintained when compared with previous functions, the occurrence of shrinkage artifacts was smaller, and high- quality denoised images were obtained. The proposed shrinkage function is effective for low-dose noisy CT images when using accurately selected parameters. [ABSTRACT FROM AUTHOR]

We study the connections between discrete one-dimensional schemes for nonlinear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of a (stabilised) explicit discretisation of nonlinear diffusion can be expressed in terms of wavelet shrinkage on a single spatial level. This equivalence allows a fruitful exchange of ideas between the two fields. In this paper we derive new wavelet shrinkage functions from existing diffusivity functions, and identify some previously used shrinkage functions as corresponding to well known diffusivities. We demonstrate experimentally that some of the diffusion-inspired shrinkage functions are among the best for translation-invariant multiscale wavelet denoising. Moreover, by transferring stability notions from diffusion filtering to wavelet shrinkage, we derive conditions on the shrinkage function that ensure that shift invariant single-level Haar wavelet shrinkage is maximum–minimum stable, monotonicity preserving, and variation diminishing. [ABSTRACT FROM AUTHOR]

The Wavelet-Domain Projection Pursuit Learning Network (WDPPLN) is proposed for restoring degraded image. The new network combines the advantages of both projection pursuit and wavelet shrinkage. Restoring image is very difficult when little is known about a priori knowledge for multisource degraded factors. WDPPLN successfully resolves this problem by separately processing wavelet coefficients and scale coefficients. Parameters in WDPPLN, which are used to simulate degraded factors, are estimated via WDPPLN training, using scale coefficients. Also, WDPPLN uses soft-threshold of wavelet shrinkage technique to suppress noise in three high frequency subbands. The new method is compared with the traditional methods and the Projection Pursuit Learning Network (PPLN) method. Experimental results demonstrate that it is an effective method for unsupervised restoring degraded image. [ABSTRACT FROM AUTHOR]

A new wavelet-based nonparametric estimator is introduced in an effort toapproximate variance functions. The new estimator possesses some superiorqualities that are illustrated through its actual performance in somesimulations. [ABSTRACT FROM AUTHOR]