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- B.A.Sc University of Waterloo
- M.S. - M.I.T.
- PhD - M.I.T.
Dr. Fieguth's interests are in the area of accelerated computational methods applied to large statistical problems in image processing, computer vision, and remote sensing.
Multiscale Statistical Modeling:
An estimation problem involves determining the state of a system (along with associated uncertainties in this state) based on some measurements of the system and a prior model of the physics governing the system of interest.
Although this problem is quite straightforward to formulate mathematically, the solution of such estimation problems becomes computationally totally intractable as the size of the system becomes very large; this research seeks to develop computationally efficient alternatives.
The thrust of this research is the development of novel statistical structures, particularly hierarchical or multiscale ones, which lead to vastly improved computational efficiency. Such methods have been developed, however they are generally subject to a number of limitations which form the foci of this research: the existence of only a limited class of multiscale models, a lack of analytic bounds on the accuracy of the computed estimates, and an inability to model problems which are dynamic (that is, evolving) in time.
The field of remote sensing forms an almost perfect complement of the above research:
There are a wide variety of extremely large estimation problems to be solved.
In general, the statistical knowledge of the system of interest is relatively poor, so the approximations introduced by a multiscale approach are typically not a great concern.
The problems are "real" - i.e., they address significant scientific or environmental questions.
This work is conducted in collaboration with researchers in oceanography who supply physical models, observational data, and the scientific expertise to ensure that meaningful answers are being computed to meaningful problems. Past and ongoing remote sensing efforts include ocean altimetry (production of ocean-surface maps), ocean hydrography (estimation of volumetric temperature fields), acoustic tomography (estimation of large-scale oceanographic features from measurements of sound propagation), and geodesy (determining high-resolution features of the earth's gravitational field from ocean-surface features).