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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE015465596
Author(s):
Plemmons, Robert J.; Pauca, Victor P.:
Shorttitle:
Problems arising in adaptive optical imaging
Source:
J. Comput. Appl. Math. 123, No. 1-2, 467-487 (2000).
Classification:
94A08Image processing compression, reconstruction, etc.
94B60Other types of codes
93C40Adaptive control
78M25Other numerical methods
93C83Control problems involving computers process control, etc.
85A99Miscellaneous topics
93B25Algebraic methods
65F15Eigenvalues, eigenvectors
65R10Integral transforms
49J40Variational methods including variational inequalities
49K35Minimax problems
Primary Classification:
Secondary Classification:
Keywords:
imaging through turbulence, adaptive optics control, covariance matrix computations, fast Hankel transform, structured matrices, trace maximization problem
Review:


Paper enters new terrain. It is full of applicability remarks (on
the real-time ``subtraction" of the influence of turbulent
atmosphere on telescope images etc) but, basically, it
concentrates on some important questions arising in connection
with the fast Hankel transformation (for computation of the
covariance matrix) and with the Jacobi-type methods needed in
adaptive optics for the control of the deformable mirrors with
multiple bandwiths. The latter task is formulated as a
maximization of a sum of traces for a set of certain k matrices
and its sample computations reveal that the performance of the
available algorithms can still be greatly improved. The success of
a ``maximal simultaneous diagonalization" of these (mutually not
quite commuting) matrices can be sought by a hill-climbing scheme
with respect to the matrix pairs in a way which resembles the
Jacobi diagonalization method. New ideas are also shown needed in
the latter set of challenges where still exists a room for
reduction in computation costs.
Remarks to the editors: