| Paper: | SS-10.4 | ||
| Session: | Manifolds and Geometry in Signal Processing | ||
| Time: | Friday, May 21, 10:30 - 10:50 | ||
| Presentation: | Special Session Lecture | ||
| Topic: | Special Sessions: Manifolds and Geometry in Signal Processing | ||
| Title: | COARSE-TO-FINE MANIFOLD LEARNING | ||
| Authors: | Rui Castro; Rice University | ||
| Rebecca Willett; Rice University | |||
| Robert Nowak; University of Wisconsin-Madison | |||
| Abstract: | In this paper we consider a sequential, coarse-to-fine, estimation of a piecewise constant function with smooth boundaries. For two dimensions this class of functions is very relevant, since it constitutes a simple model for edges in images. In general, the algorithms needed to achieve the nearly optimal (minimax) performance rates require exhaustive searches over large dictionaries that grow exponentially with dimension. The task that drives the above rates is the estimation of the manifold describing the boundary. This computational burden of the search hinders the use of such techniques in practice, and motivates our work. We consider a sequential, coarse-to-fine, approach that involves first examining the data on a coarse grid, and then refining the analysis and approximation in regions of interest. Specifically, our estimators involve a linear-time (in two dimensions), sequential search over the dictionary, and converge at the same near-optimal rate as estimators based on exhaustive searches. | ||
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