Related papers: Compression Spectrum: Where Shannon meets Fourier
Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical…
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random…
How the human brain processes information during different cognitive tasks is one of the greatest questions in contemporary neuroscience. Understanding the statistical properties of brain signals during specific activities is one promising…
Spectroscopy sampling along delay time is typically performed with uniform delay spacing, which has to be low enough to satisfy the Nyquist-Shannon sampling theorem. The sampling theorem puts the lower bound for the sampling rate to ensure…
Signal processing over graphs has recently attracted significant attentions for dealing with structured data. Normal graphs, however, only model pairwise relationships between nodes and are not effective in representing and capturing some…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
The task of compression of data -- as stated by the source coding theorem -- is one of the cornerstones of information theory. Data compression usually exploits statistical redundancies in the data according to its prior distribution.…
A finite-energy signal is represented by a square-integrable, complex-valued function $t\mapsto s(t)$ of a real variable $t$, interpreted as time. Similarly, a noisy signal is represented by a random process. Time-frequency analysis, a…
Donoho and Stark have shown that a precise deterministic recovery of missing information contained in a time interval shorter than the time-frequency uncertainty limit is possible. We analyze this signal recovery mechanism from a physics…
Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these…
Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$…
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or…
Objective: To characterize the irregularity of the spectrum of a signal, spectral entropy is a widely adopted measure. However, such a metric is invariant under any permutation of the estimations of the powers of individual frequency…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
This paper introduces a novel technique to preserve spectral features in lossy compression based on a novel fast Fourier correction algorithm\added{ for regular-grid data}. Preserving both spatial and frequency representations of data is…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…