Available online at www.sciencedirect.com Journal of the Franklin Institute ] (]]]]) ]]]–]]] Non-separable local polynomial regression cell-average multiresolution operators. Application to compression of images $ Francesc Aràndiga a , Dionisio F. Yáñez b,c,n a Departament de Matemàtica Aplicada, Universitat de València, Spain b Campus Capacitas, Universidad Católica de Valencia, Spain c Departamento de Matemáticas, CC. NN. y CC. SS. aplicadas a la educación, Universidad Católica de Valencia, Spain Received 1 November 2014; accepted 12 December 2015 Abstract Cell-average multiresolution Harten's algorithms have been satisfactorily used to compress data. These schemes are based on two operators: decimation and prediction. The accuracy of the method depends on the prediction operator. In order to design a precise function, local polynomial regression has been used in the last years. This paper is devoted to construct a family of non-separable two-dimensional linear prediction operators approximating the real values with this procedure. Some properties are proved as the order of the scheme and the stability. Some numerical experiments are performed comparing the new methods with the classical linear method. & 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. 1. Introduction Harten's multiresolution (MR) has been developed in data processing for compression and impainting of digital images and signals (see, e.g., [19,22,12,4,1]). These algorithms are based on two operators: decimation and prediction. Decimation operator indicates the nature of the data. In www.elsevier.com/locate/jfranklin http://dx.doi.org/10.1016/j.jfranklin.2015.12.006 0016-0032/& 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. ☆ This research was partially supported by Spanish MCINN MTM 2011-22741 and MTM 2014-54388. n Corresponding author at: Departamento de Matemáticas, CC. NN., CC. SS. aplicadas a la educación, Universidad Católica de Valencia, Spain. E-mail addresses: arandiga@uv.es (F. Aràndiga), dionisiofelix.yanez@ucv.es (D.F. Yáñez). Please cite this article as: F. Aràndiga, D.F. Yáñez, Non-separable local polynomial regression cell-average multiresolution operators. Application to compression of images, Journal of the Franklin Institute. (2016), http: //dx.doi.org/10.1016/j.jfranklin.2015.12.006