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In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of the optimization process. In the context of absorption imaging in diffuse optical tomography, de Sturler et al., [SIAM J. Sci. Compute., 37 (2015), pp. B495--B517] addres this bottleneck by using parametrized reduced order models, since the forward problem, typically posed in the frequency domain, is essentially the transfer function of a high-dimensional differential algebraic system. Although this approach drastically reduces the number of large linear systems to be solved, the construction of a candidate global basis for parametrized reduced models still requires the solution of many full order problems, the discretized PDE for multiple right-hand sides, and multiple parameter vectors. This step is followed by a rank-revealing factorization to compress the candidate...

Computing Reduced Order Models via Inner-Outer Krylov Recycling in Diffuse Optical Tomography