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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE015465596  
Author(s):  
Plemmons, Robert J.; Pauca, Victor P.:  
Shorttitle:  
Problems arising in adaptive optical imaging  
Source:  
J. Comput. Appl. Math. 123, No. 12, 467487 (2000).  
Classification:  
 
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 realtime ``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 Jacobitype 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 hillclimbing 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:  