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Deconvolution by thresholding in mirror wavelet bases

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3 Author(s)
Kalifa, J. ; Centre de Math. Appliquees, Ecole Polytechnique, Palaiseau, France ; Mallat, S. ; Rouge, B.

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.

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Image Processing, IEEE Transactions on  (Volume:12 ,  Issue: 4 )