589 research outputs found
Statistical Analysis of Audio Signals using Time-Frequency Analysis
In this thesis, we provide nonparametric estimation of signals corrupted by stationary noise in the white noise model. We derive adaptive and rate-optimal estimators of signals in modulation spaces by thresholding the coefficients obtained from the Gabor expansion. The rates obtained using the classical oracle inequalities of Donoho and Johnstone (1994) exhibit new features that reflect the inclusion of both time and frequency. The scope of our results is extended to alpha-modulation spaces in the one-dimensional setting, allowing a comparison with Sobolev and Besov spaces. To confirm the practical applicability of our methods, we perform extensive simulations. These simulations evaluate the performance of our methods in comparison to state-of-the-art methods over a range of scenarios
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
Waterfilling Theorems for Linear Time-Varying Channels and Related Nonstationary Sources
The capacity of the linear time-varying (LTV) channel, a continuous-time LTV
filter with additive white Gaussian noise, is characterized by waterfilling in
the time-frequency plane. Similarly, the rate distortion function for a related
nonstationary source is characterized by reverse waterfilling in the
time-frequency plane. Constraints on the average energy or on the squared-error
distortion, respectively, are used. The source is formed by the white Gaussian
noise response of the same LTV filter as before. The proofs of both
waterfilling theorems rely on a Szego theorem for a class of operators
associated with the filter. A self-contained proof of the Szego theorem is
given. The waterfilling theorems compare well with the classical results of
Gallager and Berger. In the case of a nonstationary source, it is observed that
the part of the classical power spectral density is taken by the Wigner-Ville
spectrum. The present approach is based on the spread Weyl symbol of the LTV
filter, and is asymptotic in nature. For the spreading factor, a lower bound is
suggested by means of an uncertainty inequality.Comment: 13 pages, 5 figures; channel model in Section III now restricted to
LTV filters with real-valued kerne
A comparative study on global wavelet and polynomial models for nonlinear regime-switching systems
A comparative study of wavelet and polynomial models for non-linear Regime-Switching (RS) systems is carried out. RS systems, considered in this study, are a class of severely non-linear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to RS caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An Orthogonal Least Squares (OLS) algorithm interfered with by an Error Reduction Ratio (ERR) index and regularised by an Approximate Minimum Description Length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems
Modeling for the Computer-Aided Design of Long Interconnects
L'abstract è presente nell'allegato / the abstract is in the attachmen
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