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We introduce and analyse univariate, linear, and stationary subdivision schemes for refining noisy data, by fitting local least squares polynomials. We first present primal schemes, based on fitting linear polynomials to the data, and study…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
Methods have previously been developed for the approximation of Lyapunov functions using radial basis functions. However these methods assume that the evolution equations are known. We consider the problem of approximating a given Lyapunov…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in each iteration. In this…
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
Spectral estimation is a fundamental task in signal processing. Recent algorithms in quantum phase estimation are concerned with the large noise, large frequency regime of the spectral estimation problem. The recent work in…
We describe here an iterative method for jointly estimating the noise power spectrum from a scanning experiment's time-ordered data, together with the maximum-likelihood map. We test the robustness of this method on simulated datasets with…
With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…
In this paper, we address the problem of simultaneous classification and estimation of hidden parameters in a sensor network with communications constraints. In particular, we consider a network of noisy sensors which measure a common…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
We show how to achieve full spectral characterization of general multiaxis additive noise. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable even to models where a large…
We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when…
Reconstructions of past climates are based on the calibration of available proxy data. This calibration is usually achieved by means of linear regression models. In the recent paleo-climate literature there is an ongoing discussion on the…
An effective way to increase the noise robustness of automatic speech recognition is to label noisy speech features as either reliable or unreliable (missing) prior to decoding, and to replace the missing ones by clean speech estimates. We…
An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…
We describe a new method for estimating the direction of sound in a reverberant environment from basic principles of sound propagation. The method utilizes SNR-adaptive features from time-delay and energy of the directional components after…