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

翻译：变量投影法( VarPro) 是解决可分的非线性最小平方问题的有效方法。 在本文中, 我们建议对大规模可分的非线性反向问题采用修改的 VarPro, 以相对原未预测的问题而言成本相对较低的方式解决大规模可分非线性非线性反向问题, 从而在理想的解决方案上促进边缘保留和宽度特性, 并增强界定远期问题的参数的趋同性。 我们采用了一个主要最小化方法, 依靠构建一个四面正向性主要模型, 以近似一般的 $\ ell_ p$ 正规化问题。 使用数字性实例, 说明在重建后的图像质量方面以及作为重建前方操作器的拟议方法的性能。