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

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 $L^1$-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.

KEYWORDS:

• Subdivision
• compression image
• nonlinear operators
• PPH method
• stability

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 65S05

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.