John R. Kender, Rick Kjeldsen
IEEE Transactions on Pattern Analysis and Machine Intelligence
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This article investigates an important class of inverse problems—the estimation of the initial condition of a spatio-temporal advection-diffusion process using spatially sparse data streams. Three spatial sampling schemes are considered, including irregular, nonuniform and shifted uniform sampling. The irregular sampling scheme is the general scenario, while computationally efficient solutions are available in the spectral domain for nonuniform and shifted uniform sampling. For each sampling scheme, the inverse problem is formulated as a regularized convex optimization problem that minimizes the distance between forward model outputs and observations. The optimization problem is solved by the Alternating Direction Method of Multipliers algorithm, which also handles the situation when a linear inequality constraint (e.g., non-negativity) is imposed on the model output. Numerical examples are presented, code is made available on GitHub, and discussions are provided to generate some useful insights of the proposed inverse modeling approaches.
John R. Kender, Rick Kjeldsen
IEEE Transactions on Pattern Analysis and Machine Intelligence
A. Grill, B.S. Meyerson, et al.
Proceedings of SPIE 1989
Fausto Bernardini, Holly Rushmeier
Proceedings of SPIE - The International Society for Optical Engineering
Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007