Title:  Spatial Random Trees and Modeling of Multidimensional Signals

Speaker: Ilya Pollak, Electrical and Computer Engineering, Purdue

Abstract:
In this talk, I will introduce a new class of hierarchical
stochastic models for multidimensional signals, called spatial
random trees (SRTs).  Compared to previous efforts which model
images with stochastic processes on quadtrees, our key innovation
is that the tree structure itself is random, (specifically, a branching
process), and is generated by a probabilistic context-free grammar.
We develop exact procedures for likelihood calculation, MAP
estimation of the processes, and parameter estimation.  These
recursive algorithms, collectively called the center-surround
algorithm, can be applied to learning the hierarchical structure
of a set of images, as well as to image parsing and classification.
In addition, these algorithms can be adapted to solve certain
best-basis search problems where a dictionary of orthogonal bases
is given and the task is to find the basis that represents a
given signal the best according to some cost.