Related papers: Extracting useful information from noisy exponenti…

We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…

In this paper, we study the MUltiple SIgnal Classification (MUSIC) algorithm often used to image small targets when multiple measurement vectors are available. We show that this algorithm may be used when the imaging problem can be cast as…

We theoretically describe how weak signals may be efficiently transmitted throughout more than one frequency range in noisy excitable media by kind of stochastic multiresonance. This serves us here to reinterpret recent experiments in…

We prove exponential estimates for plurisubharmonic functions with respect to Monge-Ampere measures with Holder continuous potential. As an application, we obtain several stochastic properties for the equilibrium measures associated to…

Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…

We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…

In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven…

Functional magnetic resonance imaging (fMRI) is a notoriously noisy measurement of brain activity because of the large variations between individuals, signals marred by environmental differences during collection, and spatiotemporal…

Recent algebraic parametric estimation techniques led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal. In this paper, we extend such differentiation methods by providing a larger choice…

The problem of information extraction from discrete stochastic time series, produced with some finite sampling frequency, using flicker-noise spectroscopy, a general framework for information extraction based on the analysis of the…

For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…

The measurements of very low level signals at low frequency is a very difficult problem, because environmental noise increases in this frequency domain and it is very difficult to filter it efficiently. In order to counteract these major…

Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…

The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…

Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this…

We present a fast and simple algorithm that allows the extraction of multiple exponential signals from the temporal dependence of correlation functions evaluated on the lattice including the statistical fluctuations of each signal and…

Noise is an inherent part of neuronal dynamics, and thus of the brain. It can be observed in neuronal activity at different spatiotemporal scales, including in neuronal membrane potentials, local field potentials, electroencephalography,…

Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…