On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

Sinusoidal transforms such as the DCT are known to be optimal-that is, asymptotically equivalent to the Karhunen-Loeve transform (KLT)-for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains applicable for non-Gaussian signals, it loses optimality and, is outperformed by the independent-component analysis (ICA), which aims at producing the most-decoupled representation. In this paper, we consider an extension of the classical AR(1) model that is driven by symmetric-alpha-stable (S alpha S) noise which is either Gaussian (alpha = 2) or sparse (0 < alpha < 2). For the sparse (non-Gaussian) regime, we prove that an expansion in a proper wavelet basis (including the Haar transform) is much closer to the optimal orthogonal ICA solution than the classical Fourier-type representations. Our criterion for optimality, which favors independence, is the Kullback-Leibler divergence between the joint pdf of the original signal and the product of the marginals in the transformed domain. We also observe that, for very sparse AR(1) processes (alpha <= 1), the operator-like wavelet transform is indistinguishable from the ICA solution that is determined through numerical optimization.

Published in:
2013 Ieee International Conference On Acoustics, Speech And Signal Processing (Icassp), 5598-5602
Presented at:
IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, CANADA, MAY 26-31, 2013
New York, Ieee

 Record created 2014-06-02, last modified 2019-06-17

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