Operator-Like Wavelets with Application to Functional Magnetic Resonance Imaging

@inproceedings{Khalidov2009OperatorLikeWW,
  title={Operator-Like Wavelets with Application to Functional Magnetic Resonance Imaging},
  author={Ildar Khalidov},
  year={2009}
}
We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smoothed version of L{y}. For a linear system characterized by an operator equation L{y} = x, the operator-like wavelet transform essentially deconvolves the system output y and extracts the “innovation” signal x. The main contributions of the… CONTINUE READING

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 81 references

Cardinal exponential splines: part I - theory and filtering algorithms

IEEE Transactions on Signal Processing • 2005
View 7 Excerpts
Highly Influenced

Cardinal exponential splines: part II - think analog, act digital

IEEE Transactions on Signal Processing • 2005
View 8 Excerpts
Highly Influenced

Surfing the brain: An overview of wavelet-based techniques for fMRI data analysis

Dimitri Van De Ville, Thierry Blu, Michael Unser
IEEE Engineering in Medicine and Biology Magazine, vol. 25, no. 2, pp. 65–78, 2006. • 2006
View 4 Excerpts
Highly Influenced

Generalized smoothing splines and the optimal discretization of the Wiener filter

IEEE Transactions on Signal Processing • 2005
View 3 Excerpts
Highly Influenced

Atomic Decomposition by Basis Pursuit

SIAM J. Scientific Computing • 1998
View 3 Excerpts
Highly Influenced

A family of polynomial spline wavelet transforms

Signal Processing • 1993
View 4 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…