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

Thomas Huckle, Jochen Staudacher

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.

Keywords


Sparse linear systems; preconditioned conjugate gradients; Kronecker products; inverse problems; Tikhonov regularization; image processing

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