BFGS method based variable projection approach for image restoration. Issue 12 (25th May 2021) - Chen, Qiong‐Ying; Huang, Yun‐Zhi; Gan, Min; Chen, C. L. Philip; Chen, Guang‐Yong
Abstract: In this paper, a variable projection approach based on the BFGS (Broyden–Fletcher–Goldfarb–Shanno) method for image reconstruction problems is proposed, which is an alternative to the common alternating minimisation scheme. The image restoration is expressed as a nonlinear least‐squares problem with reduced parameter space. To improve the efficiency of the algorithm, the BFGS method is proposed to be used to optimise the reduced objective function. The large‐scale problem considered in this paper is projected on to a small Krylov subspace using Lanczos bidiagonalisation. The regularisation parameter is selected by a weighted generalised cross validation criterion. Numerical examples demonstrate the efficiency and effectiveness of the proposed algorithm.