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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)
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)
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)
One of the major challenges related to image registration is the estimation of large motions without prior knowledge. This work presents a Fourier-based approach that estimates large translations, scalings, and rotations. The algorithm uses the pseudopolar (PP) Fourier transform to achieve substantial improved approximations of the polar and log-polar(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)
Computing the Fourier transform of a function in polar coordinates is an important building block in many scientific disciplines and numerical schemes. In this paper we present the pseudo-polar Fourier transform that samples the Fourier transform on the pseudo-polar grid, also known as the concentric squares grid. The pseudo-polar grid consists of equally(More)
In this paper we propose a direct method for the solution of the Poisson equation in rectangular regions. It has an arbitrary order accuracy and low CPU requirements which makes it practical for treating large-scale problems. The method is based on a pseudospectral Fourier approximation and a polynomial subtraction technique. Fast convergence of the Fourier(More)
The Radon transform is a fundamental tool in many areas. For example , in reconstruction of an image from its projections (CT scanning). Although it is situated in the core of many modern physical computations, the Radon transform lacks a coherent discrete definition for 2D discrete images which is algebraically exact, invertible, and rapidly computable. We(More)
nonlinear diffusion filtering, operator-splitting schemes, bilateral filtering Efficient numerical schemes for nonlinear diffusion filtering based on additive operator splitting (AOS) were introduced in [15]. AOS schemes are efficient and unconditionally stable, yet their accuracy is limited. Future applications of nonlinear diffusion filtering may require(More)