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See detailTwo-dimensional fractional linear prediction
Skovranek, Tomas; Despotovic, Vladimir UL; Peric, Zoran

in Computers and Electrical Engineering (2019), 77

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 ... [more ▼]

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. [less ▲]

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See detailOne-parameter fractional linear prediction
Despotovic, Vladimir UL; Skovranek, Tomas; Peric, Zoran

in Computers and Electrical Engineering (2018), 69

The one-parameter fractional linear prediction (FLP) is presented and the closed-form expressions for the evaluation of FLP coefficients are derived. Contrary to the classical first-order linear ... [more ▼]

The one-parameter fractional linear prediction (FLP) is presented and the closed-form expressions for the evaluation of FLP coefficients are derived. Contrary to the classical first-order linear prediction (LP) that uses one previous sample and one predictor coefficient, the one-parameter FLP model is derived using the memory of two, three or four samples, while not increasing the number of predictor coefficients. The first-order LP is only a special case of the proposed one-parameter FLP when the order of fractional derivative tends to zero. Based on the numerical experiments using test signals (sine test waves), and real-data signals (speech and electrocardiogram), the hypothesis for estimating the fractional derivative order used in the model is given. The one-parameter FLP outperforms the classical first-order LP in terms of the prediction gain, having comparable performance with the second-order LP, although using one predictor coefficient less. [less ▲]

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