Lancros algorithm based efficient parameter estimate via generalized cross-validation
Kai Xie · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
Super-resolution image restoration is often known to be an ill-posed inverse and large scale problem. The regularization parameter plays a crucial role in the quality of the restored image. Although generalized cross-validation is a popular tool for computing a regularized parameter, it has been rarely applied to super-resolution image restoration problems until recently. A major difficulty lies in the implementation of generalized cross-validation which requires the costly computation and the evaluation of the trace of an inverse matrix. In this paper numerical approximate techniques are used to reduce the computational complexity. We employ Gauss quadrature to compute approximately the cross-validation function. The evaluation of the trace of the inverse matrix is replaced by stochastic trace so as to alleviate the problem. Further, Lancros algorithm and Galerkin equation is used to evaluate the stochastic trace. Our results show that the method is an effective and robust.