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Time-variant inverse problems are naturally cast as state space problems. In state estimation, using a smoother as the estimator results in a smaller estimation errors than a Kalman-type filter. However, this induces an augmented high-dimensional problem. To deal with this challenge, we construct a reduced state space model incorporating approximation errors. We derive the corresponding fixed-lag smoother and apply to an imaging problem induced by a stochastic advection-diffusion equation with unknown temporal boundary conditions.
This presentation is part of Contributed Presentation “CP11 - Contributed session 11”