Related papers: De-noising by thresholding operator adapted wavele…
This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…
The practice of compressed sensing suffers importantly in terms of the efficiency/accuracy trade-off when acquiring noisy signals prior to measurement. It is rather common to find results treating the noise affecting the measurements,…
We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we…
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 transforms. Our key…
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…
Conventional wavelet-domain methods for room impulse response denoising rely on thresholding detail coefficients, which is unsuited for low frequencies. In this work, we introduce a wavelet-based post-processing algorithm that extends…
Assume that $(X_t)_{t\in\Z}$ is a real valued time series admitting a common marginal density $f$ with respect to Lebesgue's measure. Donoho {\it et al.} (1996) propose a near-minimax method based on thresholding wavelets to estimate $f$ on…
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters $\theta_1,\dots,\theta_N$, is larger than the number $n$ of samples: $N>n$. A useful heuristics relates the statistical properties of…
An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq…
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…
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…
In the present paper we consider the problem of Laplace deconvolution with noisy discrete observations. The study is motivated by Dynamic Contrast Enhanced imaging using a bolus of contrast agent, a procedure which allows considerable…
We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…
We propose a PDE-constrained optimization approach for the determination of noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
We propose a method that achieves near-optimal rates for smooth stochastic convex optimization and requires essentially no prior knowledge of problem parameters. This improves on prior work which requires knowing at least the initial…
Time-frequency localization operators (with Gaussian window) $L_F:L^2(\mathbb{R}^d)\to L^2(\mathbb{R}^d)$, where $F$ is a weight in $\mathbb{R}^{2d}$, were introduced in signal processing by I. Daubechies in 1988, inaugurating a new,…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…