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

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... r 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.