Publication

Approximation and compression of piecewise smooth functions

Martin Vetterli, Paolo Prandoni
1999
Journal Articles

Abstract

Wavelet or sub–band coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate–distortion (RD) bounds for the wavelet approximation of piecewise smooth functions, and piecewise polynomial functions in particular. We contrast these results with RD bounds achievable using an oracle–based method. We then introduce a practical dynamic programming algorithm, which achieves performance similar to the oracle method, and present experimental results.

Official source

https://infoscience.epfl.ch/entities/publication/cd183428-177a-4318-8d44-03def7dd5b01

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Martin Vetterli, Paolo Prandoni
1999
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/cd183428-177a-4318-8d44-03def7dd5b01

About this result

Related concepts (32)

Approximation algorithm

In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time.

Piecewise

In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself. A distinct, but related notion is that of a property holding piecewise for a function, used when the domain can be divided into intervals on which the property holds.

Spline (mathematics)

In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In the computer science subfields of computer-aided design and computer graphics, the term spline more frequently refers to a piecewise polynomial (parametric) curve.