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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big SPECIAL SEMINAR}
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\centerline{4:15 p.m., Wednesday, January 19, 2000}
\centerline{Sequoia Hall Rm. 200}

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\centerline{\sl Stephane Mallat}
\centerline{\sl Ecole Polytechnique}
\centerline{\sl Paris.}
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\centerline{\bf Minimax Deconvolution in Mirror Wavelet Bases}
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Thresholding algorithms in an orthonormal basis are studied to estimate
signals degraded by a linear operator whose inverse is not bounded.
Deconvolutions with transfer functions having a zero at high frequencies
are examples of such unstable inverse problems. A ``mirror wavelet'' basis
is constructed to obtain a deconvolution risk asymptotically equivalent to
the minimax risk for bounded variation signals.
This mirror wavelet thresholding estimator is currently used by the French
spatial agency to restore 
satellite images.


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