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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Leah Martell                                      February 15, 2001
Department of Mathematical Sciences               304 Whitehead Hall
The Johns Hopkins University                      Preseminar: 3:00 p.m.
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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   MODEL SELECTION AND DATA REDUCTION WITH THE WAVELET TRANSFORM

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                             ABSTRACT

Wavelet transforms have a relatively short history but a large area of
applications, such as signal and image processing and data compression.  In
this talk I will give a brief introduction to wavelets and point out some
of their most widely used implementations.

In the second half of the talk I will focus on a particular problem
concerning model selection and data reduction.  I will introduce a new
wavelet shrinkage rule and mention some of its properties.  The proposed
shrinkage rule has two advantages.  First, it is adaptive to the smoothness
of the signal regardless of whether it has a sparse wavelet representation,
since we consider both the deterministic and the stochastic cases.  Second,
the proposed method allows for fine "tuning" based on the particular data
at hand.  Our simulation study shows that the methods based on the model
selection criterion have better mean squared error (MSE) than the methods
currently known.

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