Adaptive Data Representation and Analysis

dc.contributor.advisor

Xu, Jieren

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Xu, Jieren

dc.date.accessioned

2018-09-21T16:09:11Z

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2019-02-28T09:17:08Z

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2018

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Mathematics

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This dissertation introduces and analyzes algorithms that aim to adaptively handle complex datasets arising in the real-world applications. It contains two major parts. The first part describes an adaptive model of 1-dimensional signals that lies in the field of adaptive time-frequency analysis. It explains a current state-of-the-art work, named the Synchrosqueezed transform, in this field. Then it illustrates two proposed algorithms that use non-parametric regression to reveal the underlying os- cillatory patterns of the targeted 1-dimensional signal, as well as to estimate the instantaneous information, e.g., instantaneous frequency, phase, or amplitude func-

tions, by a statistical pattern driven model.

The second part proposes a population-based imaging technique for human brain

bundle/connectivity recovery. It applies local streamlines as novelly adopted learn- ing/testing features to segment the brain white matter and thus reconstruct the whole brain information. It also develops a module, named as the streamline diffu- sion filtering, to improve the streamline sampling procedure.

Even though these two parts are not related directly, they both rely on an align- ment step to register the latent variables to some coordinate system and thus to facilitate the final inference. Numerical results are shown to validate all the pro- posed algorithms.

dc.identifier.uri

https://hdl.handle.net/10161/17503

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Applied mathematics

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Medical imaging

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adaptive data analysis

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mode decomposition

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non-parametric regression

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signal processing

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statistical learning

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structural connectivity analysis

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Adaptive Data Representation and Analysis

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Dissertation

duke.embargo.months

5

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