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Uncertainty principles and ideal atomic decomposition
 IEEE Transactions on Information Theory
, 2001
"... Suppose a discretetime signal S(t), 0 t
Abstract

Cited by 358 (19 self)
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Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discretetime signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time/frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the `1 norm of the coe cients among all decompositions. Here \highly sparse " means that Nt + Nw < p N=2 where Nt is the number of time atoms, Nw is the number of frequency atoms, and N is the length of the discretetime signal.
Vocal Command Signal Segmentation and Phonemes Classification.
, 1999
"... this paper we study a set of vocal command signals recorded in a noisy environment. We describe and use Fang's segmentation algorithm ..."
Abstract

Cited by 1 (0 self)
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this paper we study a set of vocal command signals recorded in a noisy environment. We describe and use Fang's segmentation algorithm
Multivariate Bayes Wavelet Shrinkage and Applications
"... ABSTRACT In recent years, wavelet shrinkage has become a very appealing method for data denoising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive wit ..."
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ABSTRACT In recent years, wavelet shrinkage has become a very appealing method for data denoising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that is elicited on the model parameters describing the wavelet coefficients after applying a Discrete Wavelet Transformation (DWT). In difference to other approaches, the prior proposes a multivariate Normal distribution with a covariance matrix that allows for correlations among Wavelet coefficients corresponding to the same level of detail. In addition, an extra scale parameter is incorporated that permits an additional shrinkage level over the coefficients. The posterior distribution for this shrinkage procedure is not available in closed form but it is easily sampled through Markov chain Monte Carlo (MCMC) methods. Applications on a set of test signals and two noisy signals are presented. KEY WORDS: methods Bayes shrinkage, wavelets, discrete wavelet transformation, data denoising, MCMC