Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging

Signals comprised of a stream of short pulses appear in many applications including bio-imaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing sampling schemes are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams from the minimal number of samples. We then design a compactly supported class of filters, satisfying this condition. The periodic solution is extended to finite and infinite streams, and is shown to be numerically stable even for a large number of pulses. High noise robustness is also demonstrated when the delays are sufficiently separated. Finally, we process ultrasound imaging data using our techniques, and show that substantial rate reduction with respect to traditional ultrasound sampling schemes can be achieved.Comment: 14 pages, 13 figure

Zero-One Laws for Sliding Windows and Universal Sketches

Given a stream of data, a typical approach in streaming algorithms is to design a sophisticated algorithm with small memory that computes a specific statistic over the streaming data. Usually, if one wants to compute a different statistic after the stream is gone, it is impossible. But what if we want to compute a different statistic after the fact? In this paper, we consider the following fascinating possibility: can we collect some small amount of specific data during the stream that is "universal," i.e., where we do not know anything about the statistics we will want to later compute, other than the guarantee that had we known the statistic ahead of time, it would have been possible to do so with small memory? This is indeed what we introduce (and show) in this paper with matching upper and lower bounds: we show that it is possible to collect universal statistics of polylogarithmic size, and prove that these universal statistics allow us after the fact to compute all other statistics that are computable with similar amounts of memory. We show that this is indeed possible, both for the standard unbounded streaming model and the sliding window streaming model

Hydrologic drought indices analysis by regionalization methods in southwest of Iran

11 p.International audienceDrought is a recurrent extreme climate event with tremendous hazard for every specter of natural environment and human lives. Drought analysis usually involves characterizing drought severity, duration and intensity. Usually, long-term datasets of hydrometric and hydrochemical information are needed to begin an evaluation of dominant low flow (as hydrologic drought indices) producing processes however, in many catchments, these data are not available. A major research challenge in ungauged basins is to quickly assess the dominant hydrological processes of watersheds. In this paper, for developing regional models, low flow analysis has been performed by 3 regression methods (multivariate regression, low flow index method, regionalization model of frequency formula parameters) and Hybrid low flow model in Karkheh basin (southwestern of Iran). Estimated error for four methods show although hybrid method can also use for low flow regionalization analysis but multivariate regression and low flow index methods are more suitable for this purpose

Estimation of the Degree of Polarization for Hybrid/Compact and Linear Dual-Pol SAR Intensity Images: Principles and Applications

Analysis and comparison of linear and hybrid/compact dual-polarization (dual-pol) synthetic aperture radar (SAR) imagery have gained a wholly new importance in the last few years, in particular, with the advent of new spaceborne SARs such as the Japanese ALOS PALSAR, the Canadian RADARSAT-2, and the German TerraSAR-X. Compact polarimetry, hybrid dual-pol, and quad-pol modes are newly promoted in the literature for future SAR missions. In this paper, we investigate and compare different hybrid/compact and linear dual-pol modes in terms of the estimation of the degree of polarization (DoP). The DoP has long been recognized as one of the most important parameters characterizing a partially polarized electromagnetic wave. It can be effectively used to characterize the information content of SAR data. We study and compare the information content of the intensity data provided by different hybrid/compact and linear dual-pol SAR modes. For this purpose, we derive the joint distribution of multilook SAR intensity images. We use this distribution to derive the maximum likelihood and moment-based estimators of the DoP in hybrid/compact and linear dual-pol modes.We evaluate and compare the performance of these estimators for different modes on both synthetic and real data, which are acquired by RADARSAT-2 spaceborne and NASA/JPL airborne SAR systems, over various terrain types such as urban, vegetation, and ocean

Efficient Triangle Counting in Large Graphs via Degree-based Vertex Partitioning

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important real world applications such as spam detection, uncovering of the hidden thematic structure of the Web and link recommendation. Counting triangles in graphs with millions and billions of edges requires algorithms which run fast, use small amount of space, provide accurate estimates of the number of triangles and preferably are parallelizable. In this paper we present an efficient triangle counting algorithm which can be adapted to the semistreaming model. The key idea of our algorithm is to combine the sampling algorithm of Tsourakakis et al. and the partitioning of the set of vertices into a high degree and a low degree subset respectively as in the Alon, Yuster and Zwick work treating each set appropriately. We obtain a running time $O \left(m + \frac{m^{3/2} \Delta \log{n}}{t \epsilon^2} \right)$ and an $\epsilon$ approximation (multiplicative error), where $n$ is the number of vertices, $m$ the number of edges and $\Delta$ the maximum number of triangles an edge is contained. Furthermore, we show how this algorithm can be adapted to the semistreaming model with space usage $O\left(m^{1/2}\log{n} + \frac{m^{3/2} \Delta \log{n}}{t \epsilon^2} \right)$ and a constant number of passes (three) over the graph stream. We apply our methods in various networks with several millions of edges and we obtain excellent results. Finally, we propose a random projection based method for triangle counting and provide a sufficient condition to obtain an estimate with low variance.Comment: 1) 12 pages 2) To appear in the 7th Workshop on Algorithms and Models for the Web Graph (WAW 2010

Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows

The principal objective is to extend the boundaries within which large eddy simulations (LES) and direct numerical simulations (DNS) can be applied in computational analyses of high speed reacting flows. A summary of work accomplished during the last six months is presented