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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)
High-accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euter Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are subsequently used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm(More)
The effect of ageing and suicide on mu opioid receptors was studied in the human brain postmortem. Quantitative autoradiography with [3H]DAGO revealed region specific increases in mu receptor density with age. Suicide was accompanied by a significant increase, up to 9-fold, in mu receptor density in the young, but not the old, subjects as compared 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 this article we develop a fast high accuracy Polar FFT. For a given two-dimensional signal of size N × N , the proposed algorithm's complexity is O(N 2 log N), just like in a Cartesian 2D-FFT. A special feature of our approach is that it involves only 1-D equispaced FFT's and 1D interpolations. A central tool in our approach is the pseudo-polar FFT, an(More)
Quantitative autoradiographic analysis of serotonin 5-HT1A receptors in the human brain, using [3H]8-OH-DPAT as a ligand, reveals region-specific decreases in receptor labeling with age in several cortical and hippocampal regions and in the raphe nuclei. This is due to a change in receptor density (Bmax) with no apparent change in affinity (Kd) as affirmed(More)
Schemes for image compression of black-and-white images based on the wavelet transform are presented. The multiresolution nature of the discrete wavelet transform is proven as a powerful tool to represent images decomposed along the vertical and horizontal directions using the pyramidal multiresolution scheme. The wavelet transform decomposes the image into(More)
The Fourier transform of a continuous function, evaluated at frequencies expressed in polar coordinates, is an important conceptual tool for understanding physical continuum phenomena. An analogous tool, suitable for computations on discrete grids, could be very useful; however, no exact analogue exists in the discrete case. In this paper we present the(More)