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We establish in the world of stochastic processes a theoretical relation between sparsity and wavelets. The underlying principle is to treat stochastic processes as generalized functions, which facilitates the study of their properties in a transform domai ...
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in response to streamin ...
We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...
Localised and high-frequency measurements of the global horizontal irradiance (GHI) are a key information to assess the level of power production of distributed photovoltaic generation. The paper presents a supervised machine learning-based procedure to es ...
We investigate the performance of wavelet shrinkage methods for the denoising of symmetric-a-stable (S alpha S) self-similar stochastic processes corrupted by additive white Gaussian noise (AWGN), where a is tied to the sparsity of the process. The wavelet ...
Recently, the type of compound regularizers has become a popular choice for signal reconstruction. The estimation quality is generally sensitive to the values of multiple regularization parameters. In this work, based on BDF algorithm, we develop a data-dr ...
We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show that the signat ...
We propose a new statistical dictionary learning algorithm for sparse signals that is based on an α-stable innovation model. The parameters of the underlying model—that is, the atoms of the dictionary, the sparsity index α and the dispersion of the transfo ...
We study jump-penalized estimators based on least absolute deviations which are often referred to as Potts estimators. They are estimators for a parsimonious piecewise constant representation of noisy data having a noise distribution which has heavier tail ...
Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...
