Related papers: Deconvolution of repeated measurements corrupted b…
We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations.…
We consider a model where a signal (discrete or continuous) is observed with an additive Gaussian noise process. The signal is issued from a linear combination of a finite but increasing number of translated features. The features are…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
We formally map the problem of sampling from an unknown distribution with a density in $\mathbb{R}^d$ to the problem of learning and sampling a smoother density in $\mathbb{R}^{Md}$ obtained by convolution with a fixed factorial kernel: the…
In this paper we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
In this paper we analyze the blind deconvolution of an image and an unknown blur in a coded imaging system. The measurements consist of subsampled convolution of an unknown blurring kernel with multiple random binary modulations (coded…
Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…
A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually…
This study focuses on statistical inference for compound models of the form $X=\xi_1+\ldots+\xi_N$, where $N$ is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…
This paper studies the problem of recovering a discrete complex measure on the torus from a finite number of corrupted Fourier samples. We assume the support of the unknown discrete measure satisfies a minimum separation condition and we…
A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…
Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…
In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…