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R. M. Willett, R. D. Nowak (Rice University), E. D. Kolaczyk (Boston University)
The nonparametric multiscale algorithms presented here are powerful new tools for photon-limited signal and image denoising and reconstruction. Unlike traditional wavelet-based multiscale methods, these algorithms are both well suited to processing Poisson data and capable of preserving image edges. At the heart of these new algorithms lie multiscale signal decompositions based on polynomials in one dimension and multiscale image decompositions based on platelets in two dimensions. Platelets are defined by the authors as localized atoms at various locations, scales and orientations that can produce highly accurate, piecewise linear approximations to images consisting of smooth regions separated by smooth boundaries. Polynomial- and platelet-based maximum penalized likelihood methods for signal and image analysis are both tractable and computationally efficient. Simulations establish the practical effectiveness of these methods in applications such as Gamma Ray Burst intensity estimation and astronomical image reconstruction; statistical risk bounds establish the theoretical near-optimality of these methods.
Supported by the National Science Foundation, grant nos. BCS 0079077 and MIP-9701692, the Office of Naval Research, grant nos. N00014-99-1-0219 and N00014-00-1-0390, and the Army Research Office, grant no. DAAD19-99-1-0290.
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The author(s) of this abstract have provided an email address for comments about the abstract: willett@rice.edu, nowak@rice.edu, kolaczyk@math.bu.edu
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Bulletin of the American Astronomical Society, 34, #4
© 2002. The American Astronomical Soceity.