Related papers: On the usefulness of Meyer wavelets for deconvolut…
We consider density estimation for Besov spaces when each sample is quantized to only a limited number of bits. We provide a noninteractive adaptive estimator that exploits the sparsity of wavelet bases, along with a simulate-and-infer…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
This short study reformulates the statistical Bayesian learning problem using a quantum mechanics framework. Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show…
We give a fairly comprehensive review of wavelets and of their application to density-functional theory (DFT) and to our recent application of a wavelet-based version of linear-response time-dependent DFT (LR-TD-DFT). Our intended audience…
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…
The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score…
The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^2$-risk…
Wavelet functions allow the sparse and efficient representation of a signal at different scales. Recently the application of wavelets to the denoising of maps of cosmic microwave background (CMB) fluctuations has been proposed. The…
Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all methods in the literature are based on Fourier transformation because it is…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…