Redundant time-frequency marginals for chirplet decomposition

Abstract

This paper presents the foundations of a novel method for chirplet signal decomposition. In contrast to basispursuit techniques on over-complete dictionaries, the proposed method uses a reduced set of adaptive parametric chirplets. The estimation criterion corresponds to the maximization of the likelihood of the chirplet parameters from redundant time-frequency marginals. The optimization algorithm that results from this scenario combines Gaussian mixture models and Huber's robust regression in an iterative fashion. Simulation results support the proposed avenue.Index Terms-Complex Gaussian chirplet, sparse signal decomposition, maximum likelihood.

Fitting sparse Gaussian function mixtures on power spectra

“…In case of the unvoiced segment, the final mixture is more sparse, this indicating the presence of non-tonal components. The proposed technique is planned to be used within the method [24], proposed recently by one of the authors, to detect and to quantify chirp-tonal/stochastic signal components for audio analysis and coding.…”

Sparse Multivariate Gaussian Mixture Regression

“…Given the low number of Gaussian functions (K = 40), the final utilization results in 100%. LS-SVR performance in this scenario is also excellent, 10 : in the noiseless case its learning capabilities are somewhat ahead of the proposed GFM, but in the regression test, SVR shows signs of overfitting, falling slightly behind GFM. However, the major difference arises when comparing the number of parameters to estimate: the proposed GFM deals with only KN = 600 parameters, while SVR complexity is equal to the size of the dataset L = 2401.…”

“…where φ k corresponds to the vectorization of matrix Φ k (10). As the relevance ρ k (x) depends on all Gaussian parameters to be found, the null of the gradient results in a complicated system of nonlinear equations.…”

“…Fitting a Gaussian function mixture (GFM) on data has proven very useful in selected problems of signal and information processing [3]- [10]. Despite function approximation and data regression with GFM counts with solid foundations [11]- [14], several questions still remain open, such as the update of the Gaussian variance, or the development of mechanisms that promote sparsity in the mixture.…”