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De-Noising with the traditional (orthogonal, maximally-decimated) wavelet transform sometimes exhibits visual artifacts; we attribute some of these { for example , Gibbs phenomena in the neighborhood of discontinuities { to the lack of translation invariance of the wavelet basis. One method to suppress such artifacts, termed \cycle spinning" by Coifman, is(More)
We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to(More)
We define a notion of Radon Transform for data in an n by n grid. It is based on summation along lines of absolute slope less than 1 (as a function either of x or of y), with values at non-Cartesian locations defined using trigonometric interpolation on a zero-padded grid. The definition is geometrically faithful: the lines exhibit no 'wraparound effects'.(More)
In a wide range of applied problems of 2-D and 3-D imaging a continuous formulation of the problem places great emphasis on obtaining and manipulating the Fourier transform in Polar coordinates. However , the translation of continuum ideas into practical work with data sampled on a Cartesian grid is problematic. In this article we develop a fast high(More)
We provide a framework for structural multiscale geometric organization of graphs and subsets of R n. We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to(More)
The integral L 0 e iνφ(s,t) f (s) ds with a highly oscillatory kernel (large ν, ν is up to 2000) is considered. This integral is accurately evaluated with an improved trapezoidal rule and effectively transcribed using local Fourier basis and adaptive multiscale local Fourier basis. The representation of the oscillatory kernel in these bases is sparse. The(More)
In the companion article, a framework for structural multiscale geometric organization of subsets of R(n) and of graphs was introduced. Here, diffusion semigroups are used to generate multiscale analyses in order to organize and represent complex structures. We emphasize the multiscale nature of these problems and build scaling functions of Markov matrices(More)
The Ridgelet Packets library provides a large family of or-thonormal bases for functions f (x, y) in L 2 (dxdy) which includes or-thonormal ridgelets as well as bases deriving from tilings reminiscent from the theory of wavelets and the study of oscillatory Fourier integrals. An intuitively appealing feature: many of these bases have elements whose envelope(More)
This is a short summary of a talk given at the Frontier Science in EEG Symposium, Continuous Waveform Analysis, held on 9 October 1993 in New Orleans. We describe some new libraries of waveforms well-adapted to various numerical analysis and signal processing tasks. The main point is that by expanding a signal in a library of waveforms which are(More)
DESIGN: We have developed and applied a unique tuned light source based on a Digital Mirror Device (DMD) (Plain Sight Systems Inc.) which transmits any combination of light frequencies, range 450 nm – 850 nm, transilluminating H&E stained micro-array tissue sections of normal and malignant colon through a Nikon Biophot microscope. Hyper-spectral pictures of(More)