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Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…

Robotics · Computer Science 2025-01-13 Miguel Saavedra-Ruiz , Steven A. Parkison , Ria Arora , James Richard Forbes , Liam Paull

We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…

Statistics Theory · Mathematics 2010-09-20 Sebastian Schmutzhard , Alexander Jung , Franz Hlawatsch , Zvika Ben-Haim , Yonina C. Eldar

We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…

Statistics Theory · Mathematics 2011-12-30 Marc Hoffmann , Axel Munk , Johannes Schmidt-Hieber

In this paper we revisit a non-linear filter for {\em non-Gaussian} noises that was introduced in [1]. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed…

Information Theory · Computer Science 2026-01-22 Imon Banerjee , Itai Gurvich

We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…

Statistics Theory · Mathematics 2025-08-20 Akshay Prasadan , Matey Neykov

The removal of blur from a signal, in the presence of noise, is readily accomplished if the blur can be described in precise mathematical terms. However, there is growing interest in problems where the extent of blur is known only…

Statistics Theory · Mathematics 2007-11-06 Peter Hall , Peihua Qiu

In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the…

Methodology · Statistics 2015-03-17 Fabienne Comte , Charles-A. Cuenod , Marianna Pensky , Yves Rozenholc

In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context.…

Statistics Theory · Mathematics 2020-12-25 Christophe Chesneau , Salima El Kolei , Junke Kou , Fabien Navarro

We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…

Statistics Theory · Mathematics 2009-03-06 Anatoli Iouditski , Arkadii S. Nemirovski

In this paper, we present an algorithm for identifying a parametrically described destructive unknown system based on a non-gaussianity measure. It is known that under certain conditions the output of a linear system is more gaussian than…

Computer Vision and Pattern Recognition · Computer Science 2013-09-20 Deborah Pereg , Doron Benzvi

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a…

Statistics Theory · Mathematics 2007-06-13 P. M. Robinson

We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which…

Statistics Theory · Mathematics 2025-08-12 Marc Hoffmann , Kolyan Ray

High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is:…

Signal Processing · Electrical Eng. & Systems 2022-05-06 Guillaume Dalle , Yohann de Castro

Deep learning approaches for black-box modelling of audio effects have shown promise, however, the majority of existing work focuses on nonlinear effects with behaviour on relatively short time-scales, such as guitar amplifiers and…

Sound · Computer Science 2023-05-11 Marco Comunità , Christian J. Steinmetz , Huy Phan , Joshua D. Reiss

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…

Optimization and Control · Mathematics 2008-03-25 François-Xavier Dupé , Jalal Fadili , Jean Luc Starck

We propose strongly consistent algorithms for reconstructing the characteristic function 1_K of an unknown convex body K in R^n from possibly noisy measurements of the modulus of its Fourier transform \hat{1_K}. This represents a complete…

Metric Geometry · Mathematics 2016-05-02 Gabriele Bianchi , Richard J. Gardner , Markus Kiderlen

Deconvolution with a box (square wave) is a key operation for super-resolution with pixel-shift cameras. In general convolution with a box is not invertible. However, we can obtain perfect reconstructions of sparse signals using convex…

Numerical Analysis · Mathematics 2024-07-17 Pedro Felzenszwalb

Nonlinear interference is modeled by a time-varying conditionally Gaussian channel. It is shown that approximating this channel with a time-invariant channel imposes considerable loss in the performance of channel decoding. An adaptive…

Information Theory · Computer Science 2021-02-02 Reza Rafie Borujeny , Frank R. Kschischang

This article introduces cyclic fractional Gaussian noise (cfGn), a stochastic model that integrates second-order cyclostationarity with long-range dependence property. While classical cyclostationary processes are widely discussed in the…

Applications · Statistics 2026-04-28 Hubert Woszczek , Agnieszka Wylomanska

The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is…

Statistics Theory · Mathematics 2025-11-10 Maksym Luz , Mykhailo Moklyachuk