Related papers: Bayesian wavelet de-noising with the caravan prior

In this paper we propose a new adaptive wavelet denoising methodology using complex wavelets. The method is based on a fully Bayesian hierarchical model in the complex wavelet domain that uses a bivariate mixture prior on the wavelet…

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…

We introduce a new method of Bayesian wavelet shrinkage for reconstructing a signal when we observe a noisy version. Rather than making the common assumption that the wavelet coefficients of the signal are independent, we allow for the…

In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution…

A successful class of image denoising methods is based on Bayesian approaches working in wavelet representations. However, analytical estimates can be obtained only for particular combinations of analytical models of signal and noise, thus…

Convolutional neural networks (CNNs) have shown outstanding performance on image denoising with the help of large-scale datasets. Earlier methods naively trained a single CNN with many pairs of clean-noisy images. However, the conditional…

In this paper we propose a method for wavelet denoising of signals contaminated with Gaussian noise when prior information about the $L^2$-energy of the signal is available. Assuming the independence model, according to which the wavelet…

This paper considers a Bayesian view for estimating a sub-network in a Markov random field. The sub-network corresponds to the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the…

In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…

Signal denoising is a key preprocessing step for many applications, as the performance of a learning task is closely related to the quality of the input data. In this paper, we apply a signal processing based deep neural network…

Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from…

We propose a Bayesian shrinkage rule to estimate the wavelet coefficients in a nonparametric regression model with Gaussian errors, based on a mixture of a point mass function at zero and a symmetric, zero-centered raised cosine…

The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes…

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…

The deep image prior was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to…

This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed…

We refine and extend an earlier MDL denoising criterion for wavelet-based denoising. We start by showing that the denoising problem can be reformulated as a clustering problem, where the goal is to obtain separate clusters for informative…

In this contribution, we consider the problem of blind source separation in a Bayesian estimation framework. The wavelet representation allows us to assign an adequate prior distribution to the wavelet coefficients of the sources. MCMC…

We present a novel, general-purpose method for deconvolving and denoising images from gridded radio interferometric visibilities using Bayesian inference based on a Gaussian process model. The method automatically takes into account…