We develop a sequential wavelet domain and temporal filtering scheme, with jointly optimized parameters, which results in high-quality video denoising over a large range of noise levels. In this scheme, spatial filtering is performed by a spatially adaptive Bayesian wavelet shrinkage in a redundant wavelet representation. In the next filtering stage, a motion detector controls selective, recurs...

In this paper our aim is to provide tools for easily calculating the maxisets of several procedures. Then we apply these results to perform a comparison between several Bayesian estimators in a non parametric setting. We obtain that many Bayesian rules can be described through a general behavior such as being shrinkage rules, limited, and/or elitist rules. This has consequences on their maxiset...

This paper introduces a framework for nonlinear, multiscale decompositions of Poisson data with piecewise smooth intensity curves. The key concept is conditioning on the sum of the observations that are involved in the computation of a given coefficient. Within this framework, most classical wavelet thresholding schemes for data with additive, homoscedastic noise apply. Any family of wavelet tr...

We discuss a Bayesian discovery procedure for multiple comparison problems. We show that under a coherent decision theoretic framework, a loss function combining true positive and false positive counts leads to a decision rule based on a threshold of the posterior probability of the alternative. Under a semi-parametric model for the data, we show that the Bayes rule can be approximated by the o...

Wavelet shrinkage denoising methods are widely used for estimation of biological signals from noisy environment. The popular Hard and Soft thresholding filters are commonly used in these methods. In this paper shrinkage method based on a New Thresholding filter for denoising of biological signals is proposed. The efficacy of this filter is evaluated by applying this filter for denoising of ECG ...

Interpolating the missing traces of regularly or irregularly sampled seismic record is an exceedingly important issue in the geophysical community. Many modern acquisition and reconstruction methods are designed to exploit the transform domain sparsity of the few randomly recorded but informative seismic data using thresholding techniques. In this paper, to regularize randomly sampled seismic d...

Methods based on thresholding of wavelet coefficients have been found to be popular in the estimation of biological signals from noisy environment. Hard and soft filters are most commonly used in these methods. In this paper a novel thresholding filter for wavelet shrinkage estimation of biological signals is proposed. The proposed novel filter is applied using Visu Shrink rule and top rule to ...

We consider the class of Iterative Shrinkage-Thresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) which preserves the computational simplicity of ISTA...

This paper proposes an Adaptive Image Denoising Method based on Thresholding that follows the similar approach as in the NeighShrink method. This method shrinks the noisy wavelet coefficients using an adaptive threshold. The NeighShrink and its versions namely, IAWDMBNC and IIDMWT always produce unfavourable smoothing of edges and details of the noisy image because these methods kill more noisy...

Penalized regression methods, such as L1 regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimension...