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A New Optimal Order Preconditioner for High-Resolution Image Reconstruction with Multisensors

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Author(s): Thomas Huckle | Jochen Staudacher

Journal: Sel├žuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 3;
Issue: 2;
Start page: 49;
Date: 2002;
Original page

Keywords: Sparse linear systems | preconditioned conjugate gradients | Kronecker products | inverse problems | Tikhonov regularization | image processing.

ABSTRACT
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.