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Statistics
 

New developments in probabilistic image analysis: boundary detection and image reconstruction

Colloquium

Statistics

By: Meng Li
Visiting Assistant Professor
From: Duke University
When: Friday, January 20, 2017
11:00 AM - 12:00 PM
Where: Keck Hall
102
Abstract: Images (2D, 3D, or even higher dimensional) are a fundamental data type. The area of image analysis is undergoing a dramatic transformation to utilize the power of statistical modeling, which provides a unique way to describe uncertainties and leads to model-based solutions. We exemplify this by two critical and challenging problems, boundary detection and image reconstruction, in a comprehensive way from theory, methodology to application. We view the boundary as a closed smooth lower-dimensional manifold, and propose a nonparametric Bayesian approach based on priors indexed by the unit sphere. The proposed method achieves four goals of guaranteed geometric restriction, (nearly) minimax optimal rate adapting to the smoothness level, convenience for joint inference and computational efficiency. We introduce a probabilistic model-based technique using wavelets with adaptive random partitioning to reconstruct images. We represent multidimensional signals by a mixture of one-dimensional wavelet decompositions in the form of randomized recursive partitioning on the space of wavelet coefficient trees, where the decomposition adapts to the geometric features of the signal. State-of-the-art performances of proposed methods are demonstrated using simulations and applications including neuroimaging in brain oncology. R/Matlab packages/toolboxes and interactive shiny applications are available for routine implementation.