In this paper we propose a simple Bayesian block wavelet shrinkage method for estimating an unknown function in the presence of Gaussian noise. A data–driven procedure which can adaptively choose the block size and the shrinkage level at each resolution level is provided. The asymptotic property of the proposed method, BBN (Bayesian BlockNorm shrinkage), is investigated in the Besov sequence sp...

Wavelet shrinkage is an image denoising technique based on the concept of thresholding the wavelet coefficients. The key challenge of wavelet shrinkage is to find an appropriate threshold value, which is typically controlled by the signal variance. To tackle this challenge, a new image shrinkage approach, called AntShrink, is proposed in this paper. The proposed approach exploits the intra-scal...

We propose a new class of generalized thresholding operators that combine thresholding with shrinkage, and study generalized thresholding of the sample covariance matrix in high dimensions. Generalized thresholding of the covariance matrix has good theoretical properties and carries almost no computational burden. We obtain an explicit convergence rate in the operator norm that shows the tradeo...

This article derives the probability density function (pdf) of the sum of a normal random variable and a (sphered) Student’s-t distribution on odd degrees of freedom greater than or equal to three. Apart from its intrinsic interest applications of this result include Bayesian wavelet shrinkage, Bayesian posterior density derivations, calculations in the theoretical analysis of projection indice...

Entropy-based image thresholding are used widely in image processing. Conventional methods are efficient in the case of bilevel thresholding. But they are very computationally time consuming when extended to multilevel thresholding since they exhaustively search the optimal thresholds to optimize the objective functions. In this paper, we propose a conditional probability entropy (CPE) based on...

Bayesian shrinkage analysis is the state-of-the-art method for whole genome analysis of quantitative traits. It can estimate the genetic effects for the entire genome using a dense marker map. The technique is now called genome selection. A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size...

⎯A novel and efficient speckle noise reduction algorithm based on Bayesian contourlet shrinkage using contourlet transform is proposed. First, we show the sub-band decompositions of SAR images using contourlet transforms, which provides sparse representation at both spatial and directional resolutions. Then, a Bayesian contourlet shrinkage factor is applied to the decomposed data to estimate th...

The paper proposed a new scheme for parallel implementation of compressive sensing based SAR imaging on GPU with Iterative Shrinkage/Thresholding algorithm. To get a faster recovery speed, we modified the existed IST algorithm structure, and realized the fast implementation on GPU. The experiment result shows that parallel computing capabilities of GPU have a significant speedup in comparison w...