Deconvolution by thresholding in mirror wavelet bases.
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.
Kalifa
Jérôme
J
Centre de Math. Appliquees, Ecole Polytechnique, Palaiseau, France.
Mallat
Stéphane
S
Rougé
Bernard
B