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Original Articles

On the use of generalized harmonic means in image processing using multiresolution algorithms

, , , &
Pages 455-466 | Received 03 Oct 2018, Accepted 27 Jun 2019, Published online: 01 Aug 2019
 

ABSTRACT

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new family of nonlinear schemes conserve the numerical properties of the linear schemes, such as the L1-stability, the order of accuracy or compression rate but avoiding Gibbs phenomenon close to the discontinuities. The generalized harmonic mean was introduced in the framework of point-values in [A. Guessab, M. Moncayo, and G. Schmeisser, A class of nonlinear four-point subdivision schemes. Properties in terms of conditions, Adv. Comput. Math. 37 (2012), pp. 151–190] in order to improve the results of the harmonic mean. However, in the cell-average setting our conclusion is that, from a numerical point of view, the advantage of using the new mean is not clear.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research supported in part by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18, by Spanish MINECO projects MTM2015-64382-P (MINECO/FEDER) and by MTM2017-83942-P and by PGC2018-095896-B-C21.

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