Next: Finite Dimensional Approximation Up: Regularization and Smoothing for Previous: Regularization and Smoothing for . ... As the image is contaminated by noise, the deconvolution of equation ( 1 ) by the usual Fourier methods, that is the Fourier inversion of the solution of the equation . where the notation denotes the Fourier transform of , is not effective. ... A different approach, based on the usual Fourier techniques applied to images previously smoothed, could also be adopted. ...

Next: Introduction Up: No Title Previous: References . ... The continuous wavelet transform . ... The discrete wavelet transform . ... Multiresolution Analysis . ... trous algorithm . ... Pyramidal Algorithm with one Wavelet . ... Visualization of the Wavelet Transform . Visualisation of the first class . ... The Wiener-like filtering in the wavelet space . ... Adaptive filtering from the wavelet transform . ... Regularization in the wavelet space . ... TRANSF/WAVE . ... VISUAL/WAVE . ...

Next: Historical Notes Up: The Chirplet Transform: Previous: The Chirplet Transform: . ... One of these TF methods, the short-time Fourier transform (STFT), has been used extensively for analyzing speech, music, and other non-stationary signals. ... Another time-frequency representation (which might more appropriately be called a time-scale representation) is the well-known wavelet transformheil-walnut,mallat:theory,daubechies:transform,strangwavelets. ... Historical Notes . ...

Next: Deconvolution with CLEAN Up: Image Deconvolution Previous: Image Deconvolution . ... The convolution theorem states that the Fourier transform of the sampled distribution (the dirty image, ) is equal to the convolution of the Fourier transform of the true source visibility distribution (the true image, I ) and the Fourier transform of the sampling function (the dirty beam, ): . where indicates convolution, and indicates the Fourier transform. ...

... Thanks to special permission from Cambridge University Press, we are able to bring you the complete Numerical Recipes in Fortran 77 book On-Line! ... 1.0 Introduction 1 . ... 2.4 Tridiagonal and Band Diagonal Systems of Equations 42 . ... 3.2 Rational Function Interpolation and Extrapolation 104 . ... 7.2 Transformation Method: Exponential and Normal Deviates 277 . ... 9.6 Newton-Raphson Method for Nonlinear Systems of Equations 372 . ... 12.3 FFT of Real Functions, Sine and Cosine Transforms 504 . ...

... Previous: Background Fluctuation Analysis from the Multiscale Entropy . ... A new measure of information is defined which is based on noise modeling and incorporates resolution scale. Properties of this measure are discussed. ... Additionally it allows for image noise modeling, and subsequent noise removal. ... Hence information- and entropy-based processing technologies will be necessary for the effective design and implementation of large, future generation, image databases. ...

... For example, precision of the approximation was calculated for Solar system and 47 Uma star system Kepler orbital elements : Jupiter Saturn 9.537 0.0539 Uranus 19.189 0.0473 Neptune 30.070 0.0086 47 Uma b 2.10 0.032 0.10 3.76 5.83 0.89 47 Uma c 3.60 0 ... rad , rad , rad l, rad 0.0228 1.754 4.801 0.328 0.0434 1.983 5.865 5.591 0.0135 1.291 1.685 2.495 0.0309 2.300 4.636 4.673 Kepler elements for Solar ... Estimation accuracy of disturbing function (h1) expansion is presented. ...

... This can be used to smooth the values in the column. Specifically, for input vector defined from to and convolver defined from to , colsmooth performs the following transformation: . ... These formulae automatically normalise the convolver . ... In fact use of a low-pass filter may be deceptive: the amount of noise may not have decreased very much although the graph looks much better because of the suppression of the more visible high-frequency end of the noise spectrum. ...

... We study in this paper the effect of shock excitation of leaky and surface modes by the p-polarized electromagnetic wave incident on the rapidly ionized gaseous or solid layer. ... For example, if [pic] (solid density, multiple ionized plasma), the basic frequency [pic], [pic], [pic] we find, that the wavelength of leaky wave [pic] is in soft x rays band. ... If [pic] (low density gaseous plasma), the basic frequency [pic], [pic], [pic] we find, that the wavelength of leaky wave [pic] is in THz band...

... IONOSPHERIC DATA IN THE INTERACTIVE SPIDR SYSTEM . ... The Ionosphere The ionosphere is that part of the upper atmosphere where free electrons occur in sufficient density to have an appreciable influence on the propagation of radio frequency electromagnetic waves. ... These regions may be further divided into several regularly occurring layers, such as F1 or F2. ... E Region: The region between about 95 and 150km above the Earth that marks the height of the regular daytime E layer. ...

Next: Historical Background Up: R Coronae Borealis Stars Previous: R Coronae Borealis Stars . R Coronae Borealis stars, or RCB stars, are an important class of VARIABLE STAR . ... RCB stars, remarkably, do both. RCB stars are best known because of their irregular `fades'. ... The fades are caused by enormous clouds of dust which cover a large part of the star's surface. ... As well as irregular fades, the light output from RCBs goes up and down by a few per cent every 40 days or so. ...

Next: The Arecibo Observatory and Up: Astronomer's Guide to the Previous: Astronomer's Guide to the . The 305-m William E. Gordon radio telescope at Arecibo is the largest single-dish radio telescope on our planet, and is available to the global scientific community for astronomical observations at wavelengths between 6 m and 3 cm (frequencies of 47 MHz to 10 GHz). ... In Section 2 of this document, we provide an introduction to the Observatory, the telescope and its instrumentation. ...

... The collecting area is increased by nesting concentric mirror pairs, all having the same focal length. ... Figure shows the largest optical element being ground at HDOS. ... X-ray testing demonstrated that the CXO mirrors are indeed the largest high-resolution X-ray optics ever made; the nominal effective area (based on the ground calibrations) is shown as a function of energy in the left panel of Figure , along with those of their Einstein and ROSAT predecessors. ...

... Report on Cosmic Call 1999 . ... Cosmic Call Sessions . ... This Report outlines methodology, hard- and software, which were developed to transmit first public Interstellar messages from Evpatoria Deep Space Center (EDSC), and describes four Cosmic Call Sessions, which were fulfilled in EDSC on May 24 and June 30 - July 1, 1999. ... Each Cosmic Call consists of two parts. ... Dutil Message, . ... The software for gathering all messages and creating the Cosmic Call stream, was written on C language. ...

Next: False Alarms and Up: Period Determination Previous: Phase Dispersion Minimization . The other period search technique is the periodogram which is based on the prescriptions of Lomb (1976) and Horne & Balinas (1986). The periodogram is essentially a discrete Fourier transform of the input data. Any function of time can be written as a function of frequency: . ... Decomposition of a regularly sampled signal into its Fourier components is straightforward. ...

Subject, Problems and Objects of Theoretical Astrophysics. ... Stellar Photospheres, Their Features. ... Physics of Continuous Radiation Absorption in Stellar Photospheres. ... Continuous Radiation Absorption in Stellar Photospheres of Various Spectral Classes. Solar Type Photospheres. ... Characterisics of Absorption Lines. ... Interstellar Absorption Lines, Their Features. ... Physical and Dynamic Features of Interstellar Medium, Which Follows from Observations of Interstellar Absorption Lines. ...

... During a magnetospheric substorm the cross-tail current is disrupted (e.g., Fairfield and Ness, 1970). A current system called the substorm current wedge (SCW; Atkinson, 1967; McPherron et al., 1973) is formed as this current is diverted through a circuit consisting of earthward (downward) field-aligned currents (FACs) on the eastern side of the wedge, a westward auroral electrojet in the ionosphere , and tailward (upward) FACs on the western side of the wedge. ... Res. ... Geophys. ...

... Circle rotations. ... Symbolic dynamical systems: sequence spaces, Markov chains, adding machines. Birkhoff recurrence theorem. ... Tent map. ... Expanding maps of a circle. ... Topological entropy. ... Finiteness of entropy for Lipschitz self-maps. Entropy for symbolical dynamical systems. ... Entropy for one-dimensional maps. Entropy for expanding maps and the Misiurewicz-Przytycki theorem. ... Structural stability of expanding circle maps. ... SRB measures for expanding maps. ...

... Part B: Theory of Wavelet Transform . ... Part G: Using the Wavelet for analysis of internal Structure of the astrophysical objects + N-Dimensions . ... Comment: Parts of light curves of variable white dwarfs ate investigated by means of a wavelet analysis. ... Comment: The quasi-periodic nature of chromospheric activity variations is not completely compatible with the standard Fourier analysis, so a wavelet analysis is applied to study the nature of regularities in the data. ... 1992) . ...

... For new participaing countries and the countries, starting their activity at the International Astronomy Olympiad (see the Supplementary Instructions N 3 ), presenting the short report is optional. ... May 18 , 2013. moved to 15 weeks before the Olympiad (according to common solution of OAC and LOC): . ... The (age) groups are defined by rules 4.5.2-4., i.e.: . ... Participants of the both groups must be not younger than 14.00 years on December 31, 2013 (i.e. born in 1999 or earlier). ...