This talk presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of the subspace. The algorithm is derived …
The arithmetic-geometric mean inequality states that the arithmetic mean of a set of positive numbers is always greater than the geometric mean unless all of the numbers are equal to one another. Does a similar inequality hold for positive definite matrices? The answer is not straightforward as positive definite matrices …
One of the major driving forces in the area of applied and computational harmonic analysis during the last two decades is the development and the analysis of redundant systems that produce sparse approximations for classes of functions of interest. Such redundant systems include wavelet frames, ridgelets, curvelets and shearlets, to …
The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. In this talk, I introduce a simple algorithm, termed one-step thresholding (OST) algorithm, for model-order agnostic model selection in linear inference problems. I …
Learning the structure of graphical models from data is a fundamental task in many scientific domains. I will describe analysis and applications of learning graphical models. We analyze the theoretical properties of a well-known structure learning algorithm known as the Chow-Liu algorithm (1968). The Chow-Liu algorithm learns the maximum-likelihood (ML) …
In wireless communications and networks, the average delay packets experience is an important quality of service criterion. Therefore, it is imperative to design advanced transmission schemes to jointly address the goals of reliability, high rates and low delay. I will first talk about the delay-optimal rate allocation in a multiple …
This week, we’ll hear belated summaries from three graduate students about their internships over the summer. Each presenter will speak for about 15 minutes. John Brady — NASA Langley Research Center. John worked on testing and modifying a communications protocol for use in the Climate Absolute Radiance and Refractivity Observatory …
The Discrete Fourier Transform (DFT) is one of the most important operators in computational mathematics.The DFT operator acts on the n-dimenional Hilbert Space of complex valued functions on the group of integers modulo-n. It becames very useful in the last century due to the Cooley–Tukey algorithm that computes this transform …
Given the proliferation of wireless communication devices, the need for increased power and bandwidth efficiencyin emerging technologies is getting ever more pronounced. Two echnological trends offer new opportunities for addressing these challenges: mm-wave systems (60-100GHz) that afford large bandwidths, and multi-antenna (MIMO) transceivers that exploit the spatial dimension. In particular, …
Phase retrieval is the recovery of signals from Fourier transform magnitude with wide applications in crystallography, microscopy, optics, and astronomy. Although a unique solution almost always exists for two or higher dimensional signals, there is no known algorithm with guaranteed recovery. An iterative algorithm for recovering nonnegative real signals, based …