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Variational methods for diffusive optical tomography and data clustering

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If you have a question about this talk, please contact Hector Basevi.

Host: Dr Jinming Duan

Abstract: Variational method has been successfully applied to computer vision and image processing tasks, through defining energy functionals on design variables, unknown parameters and image features. Variational method has also been extended to the field of machine learning. This talk is about variational methods developed for solving inverse source problems in medical imaging as well as data clustering problems. It consists of two parts. In the first part, we present a new approach to solve the inverse source problem arising in image reconstruction problems.

First, we find a particular solution called the orthogonal solution that satisfies the data fitting term. Then we add to it a correction function in the kernel space so that the final solution fulfils the regularization and other physical requirements. The key idea is that the correction function in the kernel has no impact to the data fitting, and the regularization is imposed in a smaller space. In addition, we use an efficient basis to represent the source function to form a hybrid strategy using spectral methods and finite element methods in the algorithm. The resulting algorithm can drastically improve the computation speed over the existing methods. As a case study, we apply the proposed method to Fluorescence Tomography (FT).

Second, we report our work on data clustering, in particular semi-supervised clustering method inspire by Pott’s model and Chan-Vese model. The algorithm is proposed as a minimization of a convex functional of the labelling function. The functional combines the total variation of the labelling function and a region-force term. The gradient operator used to define the total variation is based on the nonlocal operator recently arises in nonlocal diffusion problems in computational physics. The region-force term is calculated by the affinity between each data point and the labelled data points, which can be interpreted as the prior probability of each data point belonging to each class. The numerical methods for minimizing this functional is described and is tested on benchmark data sets. Experiments indicate that the accuracy and speed are competitive with the state-of-the-art in multi-class semi-supervised clustering algorithms.


This talk is part of the Artificial Intelligence and Natural Computation seminars series.

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