Amara L. Graps

Bio: Amara L. Graps is an academic researcher from INAF. The author has contributed to research in topics: Jovian & Jupiter. The author has an hindex of 21, co-authored 50 publications receiving 4149 citations. Previous affiliations of Amara L. Graps include University of Colorado Boulder & Stanford University.

An introduction to wavelets

Abstract: Wavelets were developed independently by mathematicians, quantum physicists, electrical engineers and geologists, but collaborations among these fields during the last decade have led to new and varied applications. What are wavelets, and why might they be useful to you? The fundamental idea behind wavelets is to analyze according to scale. Indeed, some researchers feel that using wavelets means adopting a whole new mind-set or perspective in processing data. Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. Most of the basic wavelet theory has now been done. The mathematics have been worked out in excruciating detail, and wavelet theory is now in the refinement stage. This involves generalizing and extending wavelets, such as in extending wavelet packet techniques. The future of wavelets lies in the as-yet uncharted territory of applications. Wavelet techniques have not been thoroughly worked out in such applications as practical data analysis, where, for example, discretely sampled time-series data might need to be analyzed. Such applications offer exciting avenues for exploration. >

The Cassini Cosmic Dust Analyzer

Abstract: The Cassini-Huygens Cosmic Dust Analyzer (CDA) is intended to provide direct observations of dust grains with masses between 10-19 and 10-9 kg in interplanetary space and in the jovian and satumian systems, to investigate their physical, chemical and dynamical properties as functions of the distances to the Sun, to Jupiter and to Saturn and its satellites and rings, to study their interaction with the saturnian rings, satellites and magnetosphere. Chemical composition of interplanetary meteoroids will be compared with asteroidal and cometary dust, as well as with Saturn dust, ejecta from rings and satellites. Ring and satellites phenomena which might be effects of meteoroid impacts will be compared with the interplanetary dust environment. Electrical charges of particulate matter in the magnetosphere and its consequences will be studied, e.g. the effects of the ambient plasma and the magnetic field on the trajectories of dust particles as well as fragmentation of particles due to electrostatic disruption.

Solar cycle study of interplanetary Lyman-alpha variations: Pioneer venus orbiter sky background results

Abstract: PVO observations of the interplanetary Ly-alpha (IPL) background, obtained over an entire solar cycle (SC) from 1979 to 1985, are compiled and analyzed statistically, along with data from other instruments and earlier solar cycles. The results are presented in extensive tables and graphs and characterized in detail. Findings reported include SC variation of 1.8 for the longitudinally averaged IPL intensity (in agreement with the variation of the 27-d disk-averaged integrated solar Ly-alpha flux), yearly averaged ecliptic H-atom lifetime at 1 AU equal to 1.0 Ms at solar minimum and 1.5 Ms at solar maximum, interplanetary H density equal to 0.07 + or - 0.01/cu cm, and interplanetary H/He within the heliopause but far from the sun of 7 + or - 3.

Io as a source of the jovian dust streams

Abstract: Streams of dust emerging from the direction of Jupiter were discovered in 1992 during the flyby of the Ulysses spacecraft1,2, but their precise origin within the jovian system remained unclear2. Further data3,4,5 collected by the Galileo spacecraft, which has been orbiting Jupiter since December 1995, identified the possible sources of dust as Jupiter's main ring6, its gossamer ring7, comet Shoemaker–Levy 9 (ref. 8) and Io. All but Jupiter's gossamer ring and Io have since been ruled out4,9,10,11,12,13,14. Here we find that the dominant source of the jovian dust streams is Io, on the basis of periodicities in the dust impact signal. Io's volcanoes, rather than impact ejecta, are the dust sources.

Photometry from Voyager 2: Initial Results from the Uranian Atmosphere, Satellites, and Rings

Abstract: The results of Voyager 2 photopolarimetry (PPS) surveys of Uranus, the ring system, occultation experiments and observations of the Uranian moons are reported. Dual-channel photometry and polarimetry data obtained of the atmosphere at various emission and phase angles are delineated and compared with characteristics of the Saturn and Jupiter atmospheres. The results of temperature, UV absorption and density profile calculations are also discussed. Extensive ring dimensional data, based on two occultation experiments, are provided in tabular form noting that the rings contain no dust. Finally, the geometric albedos of the five major moons and the phase curve of the moon Titania are presented. The latter data indicate that Titanian surface features are not the result of recent events such as volcanism or ice slurry outflows.

A wavelet tour of signal processing

Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

Ideal spatial adaptation by wavelet shrinkage

Abstract: SUMMARY With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels; however, it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone. We describe a new principle for spatially-adaptive estimation: selective wavelet reconstruction. We show that variable-knot spline fits and piecewise-polynomial fits, when equipped with an oracle to select the knots, are not dramatically more powerful than selective wavelet reconstruction with an oracle. We develop a practical spatially adaptive method, RiskShrink, which works by shrinkage of empirical wavelet coefficients. RiskShrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so. A new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n, where n is the sample size. Moreover no estimator can give a better guarantee than this. Within the class of spatially adaptive procedures, RiskShrink is essentially optimal. Relying only on the data, it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle. In contrast, it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone.

Wavelets and Subband Coding

Abstract: First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book.

The lifting scheme: A construction of second generation wavelets

Abstract: We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.

Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering

Abstract: This study introduces a new method for detecting and sorting spikes from multiunit recordings The method combines the wavelet transform, which localizes distinctive spike features, with superparamagnetic clustering, which allows automatic classification of the data without assumptions such as low variance or gaussian distributions Moreover, an improved method for setting amplitude thresholds for spike detection is proposed We describe several criteria for implementation that render the algorithm unsupervised and fast The algorithm is compared to other conventional methods using several simulated data sets whose characteristics closely resemble those of in vivo recordings For these data sets, we found that the proposed algorithm outperformed conventional methods