Uncertainty relations and sparse decompositions of analog signals

@article{Eldar2008UncertaintyRA,
  title={Uncertainty relations and sparse decompositions of analog signals},
  author={Y. C. Eldar},
  journal={2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel},
  year={2008},
  pages={147-151}
}
  • Y. C. Eldar
  • Published 2008 in
    2008 IEEE 25th Convention of Electrical and…
We consider uncertainty principles for analog signals that lie in a finitely-generated shift-invariant (SI) space. By adapting the notion of coherence defined for finite dictionaries to infinite SI representations, we develop an uncertainty principle similar in spirit to its finite counterpart. Building upon these results and similar work in the finite setting, we show how to find a sparse decomposition of an analog signal in an overcomplete dictionary by solving a convex optimization problem… CONTINUE READING