27th Conference of the International Linear Algebra Society (ILAS 2026)

Separable Nonlinear Bayesian Inverse Problems

May 20, 2026, 11:50 AM

25m

Torgersen Hall 1030

Minisymposium Talk Inverse Problems and Uncertainty Quantification through the Lens of Numerical Linear Algebra Inverse Problems and Uncertainty Quantification through the Lens of Numerical Linear Algebra

Speaker

Malena Espanol (Arizona State University)

Description

Separable nonlinear inverse problems arise in many applications where a forward model depends linearly on some unknowns and nonlinearly on others, including semi-blind deconvolution. We adopt a Bayesian framework with Gaussian noise and Gaussian priors on the linear variables, leading to regularized formulations of the inverse problem. We examine prior models for the nonlinear parameters and show that maximum a posteriori (MAP) estimation yields regularized separable nonlinear least squares problems that can be efficiently solved using variable projection (VarPro) methods, as demonstrated through numerical examples.