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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 paper 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)

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 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)

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)

Although naturally at the heart of many fundamental physical computations, and potentially useful in many important image processing tasks, the Radon transform lacks a coherent discrete definition for two-dimensional (2D) discrete images which is algebraically exact, invertible, and rapidly computable. We define a notion of 2D discrete Radon transforms for… (More)

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to… (More)

One of the major challenges related to image registration is the estimation of large motions without prior knowledge. This paper presents a Fourier based approach that estimates large translation, scale and rotation motions. The algorithm uses the pseudo-polar transform to achieve substantial improved approximations of the polar and log-polar Fourier… (More)

A new multigrid algorithm is constructed for the solution of linear systems of equations which arise from the discretization of elliptic PDEs. It is defined in terms of the difference scheme on the fine grid only, and no rediscretization of the PDE is required. Numerical experiments show that this algorithm gives high convergence rates for several classes… (More)