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The variable projection (VarPro) method is an efficient method to solveseparable nonlinear least squares problems. In this paper, we propose amodified VarPro for large-scale separable nonlinear inverse problems thatpromotes edge-preserving and sparsity properties on the desired solution andenhances the convergence of the parameters that define the forward problem. Weadopt a majorization minimization method that relies on constructing aquadratic tangent majorant to approximate a general $\ell_p$ regularizedproblem by an $\ell_2$ regularized problem that can be solved by the aid ofgeneralized Krylov subspace methods at a relatively low cost compared to theoriginal unprojected problem. In addition, we can use more potential generalregularizers including total variation (TV), framelet, and wavelets operators.The regularization parameter can be defined automatically at each iteration bymeans of generalized cross validation. Numerical examples on large-scaletwo-dimensional imaging problems arising from blind deconvolution are used tohighlight the performance of the proposed approach in both quality of thereconstructed image as well as the reconstructed forward operator.

An $\ell_p$ Variable Projection Method for Large-Scale Separable Nonlinear Inverse Problems