Hybrid projection methods for large-scale inverse problems with mixed Gaussian priors

Abstract When solving ill-posed inverse problems, a good choice of the prior is critical for computation reasonable solution. A common approach to include Gaussian prior, which defined by mean vector and symmetric positive definite covariance matrix, use iterative projection methods solve corresponding regularized problem. However, main challenge many these that matrix must be known fixed (up constant) before starting solution process. In this paper, we develop hybrid problems with mixed priors where convex combination matrices mixing parameter regularization do not need in advance. Such scenarios may arise when data used generate sample (e.g., assimilation) or different are needed capture qualities The proposed based on Golub–Kahan process, an extension generalized bidiagonalization, distinctive feature both weighting can estimated automatically during Furthermore, training available, various data-driven (including those learned kernels) easily incorporated. Numerical examples from tomographic reconstruction demonstrate potential methods.