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Minimum Support Interpolators with Optimum Approximation Properties

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Approximating Linear Threshold Predicates

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We study constraint satisfaction problems on the domain {-1,1}, where the given constraints are homogeneous linear threshold predicates. That is, predicates of the form sgn(w_1 x_1 + ... + w_n x_n) for some positive integer weights w_1, ..., w_n. Despite t ...

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Nondyadic and nonlinear multiresolution image approximations

Maria Arrate Munoz Barrutia

This thesis focuses on the development of novel multiresolution image approximations. Specifically, we present two kinds of generalization of multiresolution techniques: image reduction for arbitrary scales, and nonlinear approximations using other metrics ...

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Discretization of the radon transform and of its inverse by spline convolutions

Michaël Unser, Michael Stefan Daniel Liebling, Stefan Horbelt

We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. We apply our results to derive spline-convolution-based algorithms for two closely related prob ...

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MOMS: Maximal-Order Interpolation of Minimal Support

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We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly-supported basis function φ(x). We first give the expression of the φ's that have minimal support for a given accuracy (also known as "approximat ...

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Least-Squares Image Resizing Using Finite Differences

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We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation ...

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Variational Approach to Tomographic Reconstruction

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We formulate the tomographic reconstruction problem in a variational setting. The object to be reconstructed is considered as a continuous density function, unlike in the pixel-based approaches. The measurements are modeled as linear operators (Radon trans ...

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