Beyond FRiM, ASAP: a family of sparse approximation for covariance matrices and preconditioners

Éric Thiébaut; Michel Tallon; Samuel Thé; Loïc Denis

doi:10.1117/12.2630192

29 August 2022 Beyond FRiM, ASAP: a family of sparse approximation for covariance matrices and preconditioners

Éric Thiébaut, Michel Tallon, Samuel Thé, Loïc Denis

Proceedings Volume 12185, Adaptive Optics Systems VIII; 121852Q (2022) https://doi.org/10.1117/12.2630192
Event: SPIE Astronomical Telescopes + Instrumentation, 2022, Montréal, Québec, Canada

Abstract

The FRiM fractal operator belongs to a family of operators, called ASAP, defined by an ordered selection of nearest neighbors. This generalization provides means to improve upon the good properties of FRiM. We propose a fast algorithm to build an ASAP operator mimicking the fractal structure of FRiM for pupils of any size and geometry and to learn the sparse coefficients from empirical data. We empirically show the good approximation by ASAP of correlated statistics and the benefits of ASAP for solving phase restoration problems.

Conference Presentation

Citation Download Citation

Éric Thiébaut, Michel Tallon, Samuel Thé, and Loïc Denis "Beyond FRiM, ASAP: a family of sparse approximation for covariance matrices and preconditioners", Proc. SPIE 12185, Adaptive Optics Systems VIII, 121852Q (29 August 2022); https://doi.org/10.1117/12.2630192

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