Operator-Like Wavelets
John Paul Ward, EPFL STI LIB
In this talk, we propose an innovation model based on a stochastic differential equation. The two defining components of the model are a sparse white noise and a shift-invariant pseudo-differential operator. Within this framework, we construct wavelets that act like the operator so that the sparsity of the noise is transferred to the wavelet coefficients. A description of the construction as well as approximation properties of the wavelets will be discussed. Importantly, each of these properties is determined by conditions on the underlying operator.
John Paul Ward, EPFL STI LIB
Seminar • 23 January 2012
AbstractIn this talk, we propose an innovation model based on a stochastic differential equation. The two defining components of the model are a sparse white noise and a shift-invariant pseudo-differential operator. Within this framework, we construct wavelets that act like the operator so that the sparsity of the noise is transferred to the wavelet coefficients. A description of the construction as well as approximation properties of the wavelets will be discussed. Importantly, each of these properties is determined by conditions on the underlying operator.