AAS 201st Meeting, January, 2003
Session 63. Making it Work: Principled ``Model Free Deconvolution" via Multiscale Methods
Special, Tuesday, January 7, 2003, 10:00-11:30am, 613-614

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[63.01] Multiscale Analysis of Photon-Limited Astronomical Signals and Images

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.

If you would like more information about this abstract, please follow the link to http://www.ece.rice.edu/~willett/. This link was provided by the author. When you follow it, you will leave the Web site for this meeting; to return, you should use the Back comand on your browser.

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.