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We construct an adaptive wavelet estimator that attains minimax near-optimal rates in a wide range of Besov balls. The convergence rates are affected only by the weakest dependence amongst the channels, and take into account both noise…
The motivation of this paper is to introduce a novel framework for the restoration of images corrupted by mixed Gaussian-impulse noise. To this aim, first, an adaptive curvelet thresholding criterion is proposed which tries to adaptively…
Standard methodologies for the extraction of the stochastic gravitational wave background (SGWB) from auto- or cross-correlation of interferometric signals often involve the use of a filter function. The standard optimal filter maximizes…
Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…
Lacking rich and realistic data, learned single image denoising algorithms generalize poorly to real raw images that do not resemble the data used for training. Although the problem can be alleviated by the heteroscedastic Gaussian model…
Recently, a new Signal processing method, named Semi-Classical Signal Analysis (SCSA), has been proposed for denoising Magnetic Resonance Spectroscopy (MRS) signals. It is based on the Schr\"odinger Operator's eigenspectrum. It allows an…
We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…
The present paper proposes a bayesian approach for wavelet shrinkage with the use of a shrinkage prior based on the generalized secant hyperbolic distribution symmetric around zero in a nonparemetric regression problem. This shrinkage prior…
Recent diffusion models have achieved promising performances in audio-denoising tasks. The unique property of the reverse process could recover clean signals. However, the distribution of real-world noises does not comply with a single…
In this paper we are concerned with a sequence of univariate random variables with piecewise polynomial means and independent sub-Gaussian noise. The underlying polynomials are allowed to be of arbitrary but fixed degrees. All the other…
Finding a sparse representation of a possibly noisy signal can be modeled as a variational minimization with l_q-sparsity constraints for q less than one. Especially for real-time, on-line, or iterative applications, in which problems of…
This work concerns noise reduction for one-dimensional spectra in the case that the signal is corrupted by an additive white noise. The proposed method starts with mapping the noisy spectrum to a partial circulant matrix. In virtue of…
Analysis and denoising of Cosmic Microwave Background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on $12^{\circ}.8\times 12^{\circ}.8$ maps with resolution resembling the experimental one expected…
In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the…
In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the…
We study the graph signal denoising problem by estimating a piecewise constant signal over an undirected graph. We propose a new Bayesian approach that first converts a general graph to a chain graph via the depth-first search algorithm,…
A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$…
Wavelets are waveform functions that describe transient and unstable variations, such as noises. In this work, we study the advantages of discrete and continuous wavelet transforms (DWT and CWT) of microlensing data to denoise them and…
We study the well-known problem of estimating a sparse $n$-dimensional unknown mean vector $\theta = (\theta_1, ..., \theta_n)$ with entries corrupted by Gaussian white noise. In the Bayesian framework, continuous shrinkage priors which can…
The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster…