Non-separable local polynomial regression cell-average multiresolution operators. Application to compression of images

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.