L-curve curvature via Arnoldi process with application to super-resolution image reconstruction

Kai Xie

doi:10.1117/12.790838

19 February 2008 L-curve curvature via Arnoldi process with application to super-resolution image reconstruction

Kai Xie

Proceedings Volume 6625, International Symposium on Photoelectronic Detection and Imaging 2007: Related Technologies and Applications; 66250M (2008) https://doi.org/10.1117/12.790838
Event: International Symposium on Photoelectronic Detection and Imaging: Technology and Applications 2007, 2007, Beijing, China

Abstract

The L-curve and its curvature are often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations in super-resolution image reconstruction. However, the computation of the L-curve and its curvature is quite costly. In this paper both L-curve and its curvature can be computed fairly inexpensively by partial Arnoldi process applied to the matrix of the given linear system of equations in super-resolution image reconstruction. Through the Arnoldi process the techniques can generate orthogonal bases for the Krylov subspaces, which is a small and condensed Hessenberg matrix. The paper presents the simple solution in super-resolution image reconstruction by the Hessenberg matrix and presents the method for quickly computing L-curve and its curvature.

Citation Download Citation

Kai Xie "L-curve curvature via Arnoldi process with application to super-resolution image reconstruction", Proc. SPIE 6625, International Symposium on Photoelectronic Detection and Imaging 2007: Related Technologies and Applications, 66250M (19 February 2008); https://doi.org/10.1117/12.790838

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