A fast truncated Lagrange method for large-scale image restoration problems

In this work, we present a new method for the restoration of images degraded by noise and spatially invariant blur. In the proposed method, the original image restoration problem is replaced by an equality constrained minimization problem. A quasi-Newton method is applied to the first-order optimality conditions of the constrained problem. In each quasi-Newton iteration, the hessian of the Lagrangian is approximated by a circulant matrix and the Fast Fourier Transform is used to compute the quasi-Newton step. The quasi-Newton iteration is terminated according to the discrepancy principle. Results of numerical experiments are presented to illustrate the effectiveness and usefulness of the proposed method.