title: Deconvolution by thresholding in mirror wavelet bases.
abstract: The deconvolution of signals is studied with thresholding estimators that decompose signals in an orthonormal basis and threshold the resulting coefficients. A general criterion is established to choose the orthonormal basis in order to minimize the estimation risk. Wavelet bases are highly sub-optimal to restore signals and images blurred by a low-pass filter whose transfer function vanishes at high frequencies. A new orthonormal basis called mirror wavelet basis is constructed to minimize the risk for such deconvolutions. An application to the restoration of satellite images is shown.
authors.affiliation: Centre de Math. Appliquees, Ecole Polytechnique, Palaiseau, France.
authors.forename: Jérôme
authors.initials: J
authors.lastname: Kalifa
authors.forename: Stéphane
authors.initials: S
authors.lastname: Mallat
authors.forename: Bernard
authors.initials: B
authors.lastname: Rougé