2016 Summer Project Week/Uncertainty-aware Information Fusion

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Key Investigators

Uncertainty-aware Information Fusion for Real-time Soft Tissue Motion Estimation. This is part of Bojan's PhD thesis.

Need to fuse motion prior and observations/measurements in an uncertainty-aware fashion.
Stochastic processes are a very nice formal mathematical framework which allows for that.
Estimating the motion signal value at a given location in the domain requires conditioning the motion prior on the observations.
The conditioning requires the inversion of an n X n matrix (n is the number of observations).
Time complexity O(n^3)

Identify appropriate formalisms and, if needed, approximation approaches to make calculations fast enough for interventional use.

Investigated reduced-rank approximations of the Gram matrix.
Looked into a general strategy for greedy approximations.
Looked into methods for approximating the regression problem, in particular we investigated the Nyström method, the subset of data points, the subset of regressors, the Bayesian comittee machine, the projected process approximation, and the iterative solution of linear systems.
Performed literature search about comparison of the above methods in terms of performance.
Devised, implemented, and performed initial tests of a faster mechanism for regression, which relies on the matrix inversion lemma.
Strengthened the collaboration among the project members.
Identified follow-up projects that we intend to pursue soon after the NA-MIC project week.
Had numerous fruitful, enjoyable, and particularly very motivating discussions.