Speaker
Description
Many imaging inverse problems assume a known linear forward operator, yet practical systems often suffer from uncertainty in acquisition geometry, such as projection angles in computed tomography, sensor positions in photoacoustic tomography. These uncertainties introduce nonlinearity and require joint estimation of both the image and the forward model parameters.
We propose a nonlinear recycled majorization–minimization generalized Krylov subspace (NL-RMM-GKS) framework for large-scale inverse problems with uncertain forward operators. The method extends MM-GKS to nonlinear settings by combining majorization–minimization for nonsmooth regularization with Krylov subspace projection and subspace recycling, ensuring bounded memory usage.
Two complementary formulations are developed: an alternating minimization approach that alternates between image updates and Gauss–Newton parameter estimation, and a variable projection approach that eliminates the image variable and optimizes directly over the parameters using inexact inner solves. We further introduce streaming variants that process data sequentially, enabling reconstruction from large or dynamically acquired datasets without storing the full operator.
We carry out rigorous numerical experiments in fan-beam computed tomography and photoacoustic tomography to demonstrate that our proposed framework achieves high-quality reconstructions with bounded memory requirements, making it suitable for large-scale and dynamic imaging problems with uncertain geometry.