On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

@article{Fageot2014OnTC,
  title={On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling},
  author={Julien Fageot and Arash Amini and Michael Unser},
  journal={Journal of Fourier Analysis and Applications},
  year={2014},
  volume={20},
  pages={1179-1211}
}
The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specifies the probability distribution of its corresponding random variable. Our goal in this work is to lay the foundations of the innovation model, a (possibly) non-Gaussian probabilistic model for sparse signals. This is achieved by using the… CONTINUE READING

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