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- A Averbuch, R R Coifman, D L Donoho, M Israeli, J Waldén
- 2001

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)

- Yosi Keller, Amir Averbuch, Moshe Israeli
- IEEE Transactions on Image Processing
- 2005

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)

- Amir Averbuch, Ronald R. Coifman, David L. Donoho, Moshe Israeli, Yoel Shkolnisky
- SIAM J. Scientific Computing
- 2008

Abstract. 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… (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)

- Amir Averbuch, Ronald R. Coifman, David L. Donoho, Moshe Israeli, Yoel Shkolnisky, Ilya Sedelnikov
- SIAM J. Scientific Computing
- 2008

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)

- Avram Sidi, Moshe Israeli
- J. Sci. Comput.
- 1988

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)

- Gil Aharoni, Amir Averbuch, Ronald R. Coifman, Moshe Israeli
- Journal of Mathematical Imaging and Vision
- 1993

This paper presents the local cosine transform (LCT) as a new method for the reduction and smoothing of the blocking effect that appears at low bit rates in image coding algorithms based on the discrete cosine transform (DCT). In particular, the blocking effect appears in the JPEG baseline sequential algorithm. Two types of LCT were developed: LCT-IV is… (More)

- MOSHE ISRAELI
- 2003

Radiation boundary conditions appear in a wide variety of physical problems involving wave propagation [ 1,2]. For these problems, boundary conditions should be specified for dynamical quantities propagating on characteristics entering the domain of integration, while no boundary conditions are necessary for quantities propagating on characteristics leaving… (More)

We present a direct solver for the Poisson and Laplace equations in a 3D rectangular box. The method is based on the application of the discrete Fourier transform accompanied by a subtraction technique which allows reducing the errors associated with the Gibbs phenomenon and achieving any prescribed rate of convergence. The algorithm requires O(N 3 log N )… (More)

- Amir Averbuch, Moshe Israeli, Lev Vozovoi
- SIAM J. Scientific Computing
- 1998

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)