Towards the Optimal Representations of Sparse Stochastic Processes
Pedram Pad, EPFL STI LIB

Seminar • 12 November 2012 • BM 4.233

Abstract
We have studied first-order systems driven by the α-stable white noises. For these processes, we have proved that the Haar-type Wavelet Transform (HWT), produces less dependent coefficients than the Fourier transform. In addition, we have observed that for very sparse signals (α < 1), the HWT performs as well as the optimal transform. To evaluate the quality of a transform, we use the Kullback-Leibler Divergence (KLD) and a Stein-based criterion as a measures of the independence of the coefficients. The Stein-based criterion relates to denoising signals embedded in Additive White Gaussian Noise (AWGN). This result is surprising, since we know that the Fourier transform is optimal for decoupling Gaussian processes (it is asymptotically equivalent to the Karhunen-Loeve Transform (KLT)). Also, despite the wide usage of wavelets, this is one of the few results on the optimality of wavelets, especially within a stochastic framework.