Broadband chaos generated by an optoelectronic oscillator.

We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.

Detection and Classification of Whale Acoustic Signals

This dissertation focuses on two vital challenges in relation to whale acoustic signals: detection and classification.

In detection, we evaluated the influence of the uncertain ocean environment on the spectrogram-based detector, and derived the likelihood ratio of the proposed Short Time Fourier Transform detector. Experimental results showed that the proposed detector outperforms detectors based on the spectrogram. The proposed detector is more sensitive to environmental changes because it includes phase information.

In classification, our focus is on finding a robust and sparse representation of whale vocalizations. Because whale vocalizations can be modeled as polynomial phase signals, we can represent the whale calls by their polynomial phase coefficients. In this dissertation, we used the Weyl transform to capture chirp rate information, and used a two dimensional feature set to represent whale vocalizations globally. Experimental results showed that our Weyl feature set outperforms chirplet coefficients and MFCC (Mel Frequency Cepstral Coefficients) when applied to our collected data.

Since whale vocalizations can be represented by polynomial phase coefficients, it is plausible that the signals lie on a manifold parameterized by these coefficients. We also studied the intrinsic structure of high dimensional whale data by exploiting its geometry. Experimental results showed that nonlinear mappings such as Laplacian Eigenmap and ISOMAP outperform linear mappings such as PCA and MDS, suggesting that the whale acoustic data is nonlinear.

We also explored deep learning algorithms on whale acoustic data. We built each layer as convolutions with either a PCA filter bank (PCANet) or a DCT filter bank (DCTNet). With the DCT filter bank, each layer has different a time-frequency scale representation, and from this, one can extract different physical information. Experimental results showed that our PCANet and DCTNet achieve high classification rate on the whale vocalization data set. The word error rate of the DCTNet feature is similar to the MFSC in speech recognition tasks, suggesting that the convolutional network is able to reveal acoustic content of speech signals.

Inter-site and inter-scanner diffusion MRI data harmonization.

We propose a novel method to harmonize diffusion MRI data acquired from multiple sites and scanners, which is imperative for joint analysis of the data to significantly increase sample size and statistical power of neuroimaging studies. Our method incorporates the following main novelties: i) we take into account the scanner-dependent spatial variability of the diffusion signal in different parts of the brain; ii) our method is independent of compartmental modeling of diffusion (e.g., tensor, and intra/extra cellular compartments) and the acquired signal itself is corrected for scanner related differences; and iii) inter-subject variability as measured by the coefficient of variation is maintained at each site. We represent the signal in a basis of spherical harmonics and compute several rotation invariant spherical harmonic features to estimate a region and tissue specific linear mapping between the signal from different sites (and scanners). We validate our method on diffusion data acquired from seven different sites (including two GE, three Philips, and two Siemens scanners) on a group of age-matched healthy subjects. Since the extracted rotation invariant spherical harmonic features depend on the accuracy of the brain parcellation provided by Freesurfer, we propose a feature based refinement of the original parcellation such that it better characterizes the anatomy and provides robust linear mappings to harmonize the dMRI data. We demonstrate the efficacy of our method by statistically comparing diffusion measures such as fractional anisotropy, mean diffusivity and generalized fractional anisotropy across multiple sites before and after data harmonization. We also show results using tract-based spatial statistics before and after harmonization for independent validation of the proposed methodology. Our experimental results demonstrate that, for nearly identical acquisition protocol across sites, scanner-specific differences can be accurately removed using the proposed method.