Gaurav Thakur

Gaurav Thakur, Eugene Brevdo, Neven S. Fučkar et al.

We analyze the stability properties of the Synchrosqueezing transform, a time-frequency signal analysis method that can identify and extract oscillatory components with time-varying frequency and amplitude. We show that Synchrosqueezing is robust to bounded perturbations of the signal and to Gaussian white noise. These results justify its applicability to noisy or nonuniformly sampled data that is ubiquitous in engineering and the natural sciences. We also describe a practical implementation of Synchrosqueezing and provide guidance on tuning its main parameters. As a case study in the geosciences, we examine characteristics of a key paleoclimate change in the last 2.5 million years, where Synchrosqueezing provides significantly improved insights.

Gaurav Thakur, Hau-Tieng Wu

We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multi-component AM-FM signal. We describe an algorithm to recover these instantaneous frequencies from the uniform or nonuniform samples of the signal and show that our method is robust to noise. We also consider an alternative approach based on the conventional, Hilbert transform-based notion of instantaneous frequency to compare to our new method. We use these methods on several test cases and apply our results to a signal analysis problem in electrocardiography.

Gaurav Thakur

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases.

Gagan Choudhury, David Lynch, Gaurav Thakur et al.

We describe two applications of machine learning in the context of IP/Optical networks. The first one allows agile management of resources at a core IP/Optical network by using machine learning for short-term and long-term prediction of traffic flows and joint global optimization of IP and optical layers using colorless/directionless (CD) flexible ROADMs. Multilayer coordination allows for significant cost savings, flexible new services to meet dynamic capacity needs, and improved robustness by being able to proactively adapt to new traffic patterns and network conditions. The second application is important as we migrate our metro networks to Open ROADM networks, to allow physical routing without the need for detailed knowledge of optical parameters. We discuss a proof-of-concept study, where detailed performance data for wavelengths on a current flexible ROADM network is used for machine learning to predict the optical performance of each wavelength. Both applications can be efficiently implemented by using a SDN (Software Defined Network) controller.

Gaurav Thakur

A statistical algorithm for categorizing different types of matches and fraud in image databases is presented. The approach is based on a generative model of a graph representing images and connections between pairs of identities, trained using properties of a matching algorithm between images.

Gaurav Thakur

This paper develops a mathematical and computational framework for analyzing the expected performance of Bayesian data fusion, or joint statistical inference, within a sensor network. We use variational techniques to obtain the posterior expectation as the optimal fusion rule under a deterministic constraint and a quadratic cost, and study the smoothness and other properties of its classification performance. For a certain class of fusion problems, we prove that this fusion rule is also optimal in a much wider sense and satisfies strong asymptotic convergence results. We show how these results apply to a variety of examples with Gaussian, exponential and other statistics, and discuss computational methods for determining the fusion system's performance in more general, large-scale problems. These results are motivated by studying the performance of fusing multi-modal radar and acoustic sensors for detecting explosive substances, but have broad applicability to other Bayesian decision problems.

Gaurav Thakur

We describe a methodology for modeling the performance of decision-level data fusion between different sensor configurations, implemented as part of the JIEDDO Analytic Decision Engine (JADE). We first discuss a Bayesian network formulation of classical probabilistic data fusion, which allows elementary fusion structures to be stacked and analyzed efficiently. We then present an extension of the Wald sequential test for combining the outputs of the Bayesian network over time. We discuss an algorithm to compute its performance statistics and illustrate the approach on some examples. This variant of the sequential test involves multiple, distinct stages, where the evidence accumulated from each stage is carried over into the next one, and is motivated by a need to keep certain sensors in the network inactive unless triggered by other sensors.