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We present a new approach to reconstruct volume data by non-discrete models. As a model, we use a family of “near-best” spline quasi-interpolants based on trivariate $C^2$ quartic box splines and obtained by minimizing an upper bound of their infinity norm. We show the uniqueness of the problem solution, that we explicitly give, we discuss the optimal approximation properties of our model and we present some numerical tests and applications with real world volume data.
This presentation is part of Minisymposium “MS2 - Interpolation and Approximation Methods in Imaging (4 parts)”
organized by: Alessandra De Rossi (University of Torino) , Costanza Conti (University of Firenze) , Francesco Dell'Accio (University of Calabria) .