Monotone cubic interpolation

About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.

A Comparative Study of the Use of Linear and Modified Cubic Spline Interpolation for Image Reconstruction

Abstract: Image reconstruction is the process of recovering a function of two variables from experimentally obtained estimates of its integrals alone certain lines. An important version in medicine is the recovery of the density distribution within a cross-section of the human body from a number of X-ray projections. A computationally efficient technique for image reconstruction is the so-called convolution method. It consists of two steps: (i) data obtained by each of the projections of the cross-section are separately (discrete) convolved with a fixed function; (ii) the density of the function at any point in the cross-section is estimated as the sum of values (one from each projection) of the convolved projection data. A difficulty is that part (ii) usually requires values of the convolved projection data at points other than where they have been calculated during part (i). This is usually resolved by interpolation between the calculated values. In this paper we report on a computer experimental study which compares the efficacy of two methods of interpolation (linear interpolation and a modified cubic spline interpolation) when used with the convolution reconstruction method. The two interpolation techniques are examined for their mathematical properties and are compared from the points of view of resolution of fine details, smoothness of the reconstructed cross-sections, sensitivity to noise in the data, the overall nearness of the original and reconstructed objects, and the cost of implementation. Both methods are illustrated on reconstructions of a mathematically described cross-section of the human head from computer simulated X-ray data.

Fisher Information and Spline Interpolation

Abstract: It is shown that among all cumulative distribution functions passing through $k \geqq 2$ given points there is a unique one with minimal Fisher information; it is obtained by a curious type of spline interpolation. This answers some questions raisd by D. G. Kendall and J. W. Tukey.

Monotone and convex cubic spline interpolation

Abstract: Given a set of monotone and convex data, we present a necessary and sufficient condition for the existence of cubic differentiable interpolating splines which are monotone and convex. Further, we discuss their approximation properties when applied to the interpolation of functions having preassigned degree of smoothness.

Discrete cubic spline interpolation

Abstract: Defining equations, a best approximation property, and error bounds are given for a discrete cubic spline interpolant. Furthermore the distance between two cubic spline interpolants is estimated, and numerical examples are provided.