Adaptive Data Representation and Analysis

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.