Optimization issues in blind deconvolution algorithms

Eric Thiebaut

doi:10.1117/12.461151

19 December 2002 Optimization issues in blind deconvolution algorithms

Eric Thiebaut

Proceedings Volume 4847, Astronomical Data Analysis II; (2002) https://doi.org/10.1117/12.461151
Event: Astronomical Telescopes and Instrumentation, 2002, Waikoloa, Hawai'i, United States

Abstract

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.

Citation Download Citation

Eric Thiebaut "Optimization issues in blind deconvolution algorithms", Proc. SPIE 4847, Astronomical Data Analysis II, (19 December 2002); https://doi.org/10.1117/12.461151

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