Alan Muriithi

My research lies at the interface of inverse problems, optimisation, and deep learning, with a focus on the mathematical foundations of learning-based reconstruction for nonlinear and ill-posed inverse problems under model uncertainty. I study settings in which the forward operator is only approximately known, analysing how operator uncertainty affects identifiability, stability, robustness, and solution selection of learned reconstruction schemes and gradient-based algorithms. 

A focus of my work is the development of structural and compatibility conditions that incorporate analytic information from approximate forward models into learning-based methods, ensuring that learned corrections respect the observable and stable components of the inverse problem. 

My work draws on variational analysis, stochastic and spectral methods, and regularisation theory, with applications in computational imaging, and aims to establish principled connections between classical inverse problem theory and modern operator- and learning-based approaches.