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Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger, A. Juditsky, A. B. Tsybakov, A. Zeevi (2008)

Annales de l'I.H.P. Probabilités et statistiques

We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

Change-point estimation from indirect observations. 2. Adaptation

A. Goldenshluger, A. Juditsky, A. Tsybakov, A. Zeevi (2008)

Annales de l'I.H.P. Probabilités et statistiques

We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable practical...

Chaotic patterns in aeroelastic signals.

Marques, F.D., Vasconcellos, R.M.G. (2009)

Mathematical Problems in Engineering

Chirps $n$ -dimensionnels et analyse $2$ -microlocale

Y. Meyer (1994/1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution

Ewa Świercz (2010)

International Journal of Applied Mathematics and Computer Science

A new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification...

Coarse quantization for random interleaved sampling of bandlimited signals

Alexander M. Powell, Jared Tanner, Yang Wang, Özgür Yılmaz (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids {kT + Tn} k ∈ Zwith offsets ${T_{n}}_{n = 1}^{N} \subset [0, T]$ T n n = 1 N ⊂ [ 0 ,T ] . If the offsetsTn are chosen independently and uniformly at random from [0,T] and if the sample values of fare quantized with a first order Sigma-Delta algorithm, then with high probability the quantization error $| f (t) - \tilde{f} (t) |$ | f ( t ) − x10ff65;...

Coarse quantization for random interleaved sampling of bandlimited signals∗∗∗

Alexander M. Powell, Jared Tanner, Yang Wang, Özgür Yılmaz (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids {kT + Tn} k ∈ Z with offsets ${T_{n}}_{n = 1}^{N} \subset [0, T]$ . If the offsets Tn are chosen independently and uniformly at random from [0,T] and if the sample values of f are quantized with a first order Sigma-Delta algorithm, then with high probability...

Compression on the digital unit sphere.

Allali, Mohamed (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Construction of sampling and interpolating sequences for multi-band signals. the two-band case

Sergei Avdonin, Anna Bulanova, William Moran (2007)