Selçuk Journal of Applied Mathematics

www.selcuk.edu.tr




 Selçuk Journal of
  Applied Mathematics

  Summer-Autumn, 2002
  Volume  3
  Number 2

 
Research Center of 
  Applied Mathematics


 SJAM Summer-Autumn 2002, Volume 3 - Number 2

A new optimal order preconditioner for high-resolution image reconstruction with multisensors

Thomas Huckle and Jochen Staudacher

Institut für Informatik, TU München, Boltzmannstr. 3, 85748 Garching, Germany
   email : huckle@in.tum.de ;
   email: staudacj@in.tum.de

Received: August 17, 2002
 

Summary
This paper is devoted to the problem of high-resolution image reconstruction with multisensors: There a high-resolution image is reconstructed from four undersampled, shifted, degraded and noisy low-resolution images. Previously R. Chan, T. Chan, M. Ng and their collaborators had been proposing very successful fast cosine transform based preconditioners for the arising linear systems.On the other hand, no O(n) preconditioners for these sparse problems had been developed. We present a simple and effective O(n) preconditioner based on the structure of the linear systems: The idea is that the system matrices allow for a helpful "analytic factorization". Various numerical experiments underline that our preconditioner leads in fact to an efficient optimal order performance.

 

Key words
sparse linear systems, preconditioned conjugate gradients, Kronecker products, inverse problems, Tikhonov regularization, image processing.
 

2000 Mathematics Subject Classification : 65F10, 65F22, 65F50
 

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