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13
TIMEFREQUENCY LOCALIZATION FROM SPARSITY CONSTRAINTS
"... In the case of multicomponent AMFM signals, the idealized representation which consists of weighted trajectories on the timefrequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploitin ..."
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Cited by 8 (2 self)
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In the case of multicomponent AMFM signals, the idealized representation which consists of weighted trajectories on the timefrequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the WignerVille distribution neighbouring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum l1norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical
Multitaper timefrequency reassignment for nonstationary spectrum estimation and chirp enhancement
 IEEE Transactions on Signal Processing
"... Abstract—A method is proposed for obtaining timefrequency distributions of chirp signals embedded in nonstationary noise, with the twofold objective of a sharp localization for the chirp components and a reduced level of statistical fluctuations for the noise. The technique consists in combining t ..."
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Cited by 7 (2 self)
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Abstract—A method is proposed for obtaining timefrequency distributions of chirp signals embedded in nonstationary noise, with the twofold objective of a sharp localization for the chirp components and a reduced level of statistical fluctuations for the noise. The technique consists in combining timefrequency reassignment with multitapering, and two variations are proposed. The first one, primarily aimed at nonstationary spectrum estimation, is based on sums of estimates with different tapers, whereas the second one makes use of differences between the same estimates for the sake of chirp enhancement. The principle of the technique is outlined, its implementation based on Hermite functions is justified and discussed, and some examples are provided for supporting the efficiency of the approach, both qualitatively and quantitatively. Index Terms—Chirps, multitapers, reassignment, timefrequency. I.
INFORMATIONTHEORETIC SIGNAL PROCESSING ON THE TIMEFREQUENCY PLANE AND APPLICATIONS
"... Timefrequency analysis is a major tool in representing the energy distribution of timevarying signals. There has been a lot of research on various properties of these representations. However, there is a general lack of quantitative measures in describing the amount of information encoded into a t ..."
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Cited by 3 (0 self)
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Timefrequency analysis is a major tool in representing the energy distribution of timevarying signals. There has been a lot of research on various properties of these representations. However, there is a general lack of quantitative measures in describing the amount of information encoded into a timefrequency distribution. Recently, informationtheoretic measures such as entropy and divergence have been adapted to the timefrequency plane to quantify the complexity of individual signals as well as the difference between signals. In this paper, we present a variety of informationtheoretic measures and their definitions on the timefrequency plane. The properties of these measures and how they can be applied to signal classification problems are discussed in detail. We then present an application of informationtheoretic signal processing to the analysis of event related brain potentials. 1.
Information Theoretic Measures for Quantifying the Integration of Neural Activity
"... Abstract — In recent years, there has been a growing interest in quantifying the interaction and integration between different neuronal activities in the brain. One problem of interest has been to quantify how different neuronal sites communicate with each other. For this purpose, different measures ..."
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Abstract — In recent years, there has been a growing interest in quantifying the interaction and integration between different neuronal activities in the brain. One problem of interest has been to quantify how different neuronal sites communicate with each other. For this purpose, different measures of functional integration such as spectral coherence, phase synchrony and mutual information have been proposed. In this paper, we introduce informationtheoretic measures such as entropy and divergence to quantify the interaction between different neuronal sites. The informationtheoretic measures introduced in this paper are adapted to the timefrequency domain to account for the dynamic nature of neuronal activity. Timefrequency distributions are twodimensional energy density functions of time and frequency, and can be treated in a way similar to probability density functions. Since timefrequency distributions are not always positive, information measures such as Renyi entropy and JensenRenyi divergence are adapted to this new domain instead of the wellknown Shannon entropy. In this paper, we first discuss some properties of these modified measures and then illustrate their application to neural signals. The proposed measures are applied to multiple electrode recordings of electroencephalogram (EEG) data to quantify the interaction between different neuronal sites and between different cognitive states. I.
QUANTITATIVE EVALUATION OF CONCENTRATED TIMEFREQUENCY DISTRIBUTIONS
"... This work objectively evaluates and presents a quantitative analysis of concentrated timefrequency distributions (TFDs) obtained through Network of Expert Neural Networks (NENNs). The objective methods include the ratio of norms based measures, Shannon & Rényi entropy measures, normalized Rényi ent ..."
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This work objectively evaluates and presents a quantitative analysis of concentrated timefrequency distributions (TFDs) obtained through Network of Expert Neural Networks (NENNs). The objective methods include the ratio of norms based measures, Shannon & Rényi entropy measures, normalized Rényi entropy measure and Jubisa measure. The introduction of these measures allows quantifying the quality of TFDs instead of relying solely on visual inspection of their plots. Performance comparison with various other quadratic TFDs is provided too. 1.
Abstract On Some Entropy Functionals derived from Rényi Information Divergence
, 805
"... We consider the maximum entropy problems associated with Rényi Qentropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the generalized expectation as encountered in nonextensive statistics. The op ..."
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We consider the maximum entropy problems associated with Rényi Qentropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the generalized expectation as encountered in nonextensive statistics. The optimum maximum entropy probability distributions, which can exhibit a powerlaw behaviour, are derived and characterized. The Rényi entropy of the optimum distributions can be viewed as a function of the constraint. This defines two families of entropy functionals in the space of possible expected values. General properties of these functionals, including nonnegativity, minimum, convexity, are documented. Their relationships as well as numerical aspects are also discussed. Finally, we work out some specific cases for the reference measure Q(x) and recover in a limit case some wellknown entropies. Key words: Rényi entropy, Rényi divergences, maximum entropy principle, nonextensivity, Tsallis distributions
Weighted Norms of Ambiguity Functions and Wigner Distributions
"... Abstract — In this article new bounds on weighted pnorms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl–Heisenberg signaling in widesense stationary uncorrelated scattering channels fo ..."
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Abstract — In this article new bounds on weighted pnorms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl–Heisenberg signaling in widesense stationary uncorrelated scattering channels for example it is a key step to find the optimal waveforms for a given scattering statistics which is a problem also well known in radar and sonar waveform optimizations. The same situation arises in quantum information processing and optical communication when optimizing pure quantum states for communicating in bosonic quantum channels, i.e. find optimal channel input states maximizing the pure state channel fidelity. Due to the nonconvex nature of this problem the optimum and the maximizers itself are in general difficult find, numerically and analytically. Therefore upper bounds on the achievable performance are important which will be provided by this contribution. Based on a result due to E. Lieb [1], the main theorem states a new upper bound which is independent of the waveforms and becomes tight only for Gaussian weights and waveforms. A discussion of this particular important case, which tighten recent results on Gaussian quantum fidelity and coherent states, will be given. Another bound is presented for the case where scattering is determined only by some arbitrary region in phase space. I.
TimeFrequency Energy Distributions Meet Compressed Sensing
, 2010
"... Abstract—In the case of multicomponent signals with amplitude and frequency modulations, the idealized representation which consists of weighted trajectories on the timefrequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revis ..."
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Abstract—In the case of multicomponent signals with amplitude and frequency modulations, the idealized representation which consists of weighted trajectories on the timefrequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the WignerVille distribution neighbouring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum ℓ1norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased. Index Terms—timefrequency, localization, sparsity. EDICS Category: SSPNSSP
ON SCALE AND CONCENTRATION INVARIANCE IN ENTROPIES
"... Rényi entropies are compared to generalized logFisher information and variational entropies in the context of translation, scale and concentration invariance. It is proved that the Rényi entropies occupy a special place amongst these entropies. It is also shown that Shannon entropy is centrally pos ..."
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Rényi entropies are compared to generalized logFisher information and variational entropies in the context of translation, scale and concentration invariance. It is proved that the Rényi entropies occupy a special place amongst these entropies. It is also shown that Shannon entropy is centrally positioned amidst the Rényi entropies.
EURASIP Journal on Applied Signal Processing 2003:5, 422–429 c ○ 2003 Hindawi Publishing Corporation CT Image Reconstruction Approaches Applied to TimeFrequency Representation of Signals
, 2002
"... The mathematical formulation used in tomography has been successfully applied to timefrequency analysis, which represents an important “imaging modality ” of the structure of signals. Based on the interrelation between CT and timefrequency analysis, new methods have been developed for the latter. ..."
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The mathematical formulation used in tomography has been successfully applied to timefrequency analysis, which represents an important “imaging modality ” of the structure of signals. Based on the interrelation between CT and timefrequency analysis, new methods have been developed for the latter. In this paper, an original method for constructing the timefrequency representation of signals from the squared magnitudes of their fractional Fourier transforms is presented. The method uses αnorm minimization with α → 1 which is motivated by Rényi entropy maximization. An iterative optimization method with adaptive estimation of the convergence parameter is elaborated. The proposed method exhibits advantages in the suppression of interference terms for signals with simple timefrequency configurations.