Optimization issues in blind deconvolution algorithms

Details Optimization issues in blind deconvolution algorithms Optimization issues in blind deconvolution algorithms

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002spie.4847..174t&link_type=abstract

Astronomical Data Analysis II. Edited by Starck, Jean-Luc; Murtagh, Fionn D. Proceedings of the SPIE, Volume 4847, pp. 174-1

Astronomy and Astrophysics

Astronomy

6

Scientific paper

Modern blind deconvolution algorithms combine agreement with the data and regularization constraints into a single criteria (a so-called penalizing function) that must be minimized in a restricted parameter space (at least to insure positivity). Numerically speaking, blind deconvolution is a constrained optimization problem which must be solved by iterative algorithms owning to the very large number of parameters that must be estimated. Additional strong difficulties arise because blind deconvolution is intrinsically ambiguous and highly non-quadratic. This prevent the problem to be quickly solved. Various optimizations are proposed to considerably speed up blind deconvolution. These improvements allow the application of blind deconvolution to very large images that are now routinely provided by telescope facilities. First, it is possible to explicitly cancel the normalization ambiguity and therefore improve the condition number of the problem. Second, positivity can be enforced by gradient projection techniques without the need of a non-linear re-parameterization. Finally, superior convergence rates can be obtained by using a small sub-space of ad-hoc search directions derived from the effective behavior of the penalizing function.

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