Publication

How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

Michaël Unser, Thierry Blu, Philippe Thévenaz
2002
Conference Papers

Abstract

We present a simple, original method to improve piecewise linear interpolation with uniform knots: We shift the sampling knots by a fixed amount, while enforcing the interpolation property. Thanks to a theoretical analysis, we determine the optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and it is close to 1 ⁄ 5. We confirm our theoretical findings by performing a cumulative rotation experiment, which shows a significant increase of the quality of the shifted method with respect to the standard one. Most interesting is the fact that we get a quality similar to that of high-quality cubic convolution at the computational cost of linear interpolation.

Official source

https://infoscience.epfl.ch/entities/publication/204a1c4e-3015-4873-87e0-b03c4a560182

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Michaël Unser, Thierry Blu, Philippe Thévenaz
2002
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/204a1c4e-3015-4873-87e0-b03c4a560182

About this result

Related concepts (32)

Interpolation

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.

Bilinear interpolation

In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in another direction.

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How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

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