Two-dimensional fractional linear prediction

Linear prediction (LP) has been applied with great success in coding of one-dimensional, time-varying signals, such as speech or biomedical signals. In case of two-dimensional signal representation (e.g. images) the model can be extended by applying one-dimensional LP along two space directions (2D LP). Fractional linear prediction (FLP) is a generalisation of standard LP using the derivatives of non-integer (arbitrary real) order. While FLP was successfully applied to one-dimensional signals, there are no reported implementations in multidimensional space. In this paper two variants of two-dimensional FLP (2D FLP) are proposed and optimal predictor coefficients are derived. The experiments using various grayscale images confirm that the proposed 2D FLP models are able to achieve comparable performance in comparison to 2D LP using the same support region of the predictor, but with one predictor coefficient less, enabling potential compression.