On multi-dimensional sampling and interpolation

Optimal Sampling and Interpolation

Multi-dimensional Hermite Interpolation and Approximation for Modelling and Visualization

In this paper we use some well known theorems of algebraic geometry in reducing polynomial Hermite interpolation and approximation in any dimension to the solution of linear systems. We present a mix of symbolic and numerical algorithms for low degree curve ts through points in the plane, surface ts through points and curves in space, and in general, hypersuface ts through points, curves, surfa...

Designing Sampling Schemes for Multi-Dimensional Data

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramér-Rao lower bound for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an a...

Multi-dimensional Boltzmann Sampling of Languages

This paper addresses the uniform random generation of words from a context-free language (over an alphabet of size k), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional extension of Boltzmann samplers [7]. We show that, under mostly strong-connectivity hypotheses, our samplers return a word of size in [(1− ε)n, (1 + ε)n] and exact...

Discrete Sampling and Interpolation: Orthogonal Interpolation for Discrete Bandlimited Signals

We study the problem of finding unitary submatrices of the discrete Fourier transform matrix. This problem is related to a diverse set of questions on idempotents on ZN , tiling ZN , difference graphs and maximal cliques. Each of these is related to the problem of interpolating a discrete bandlimited signal using an orthogonal basis.