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

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.