Related papers: Wavelet invariants for statistically robust multi-…
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…
Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the differing associations between those predictors and responses. Here we…
We present the applications of variational--wavelet approach for the analytical/numerical treatment of the effects of insertion devices on beam dynamics. We investigate the dynamical models which have polynomial nonlinearities and variable…
Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…
Classical representation systems such as Fourier series, wavelets, and fixed dictionaries provide analytically tractable basis expansions, but they are not intrinsically adapted to the empirical structure of modern high-dimensional data.…
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…
Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this work we show that those properties uniquely define an {\em intrinsic wavelet} and present a suitable…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
The dynamic range is an important parameter which measures the spread of sound power, and for music signals it is a measure of recording quality. There are various descriptive measures of sound power, none of which has strong statistical…
We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales,…
This paper investigates unsupervised anomaly detection in multivariate time-series data using reinforcement learning (RL) in the latent space of an autoencoder. A significant challenge is the limited availability of anomalous data, often…
The conceptual picture underlying resolvent analysis(RA) is that the nonlinear term in the Navier-Stokes(NS) equations provides an intrinsic forcing to the linear dynamics, a description inspired by control theory. The inverse of the linear…
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
This paper investigates the asymptotic distribution of a wavelet-based NKK periodogram constructed from least absolute deviations (LAD) harmonic regression at a fixed resolution level. Using a wavelet representation of the underlying time…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for…