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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. [ABSTRACT FROM AUTHOR]

Linear prediction is extensively used in modeling, compression, coding, and generation of speech signal. Various formulations of linear prediction are available, both in time and frequency domain, which start from different assumptions but result in the same solution. In this letter, we propose a novel, generalized formulation of the optimal low-order linear prediction using the fractional (non-integer) derivatives. The proposed fractional derivative formulation allows for the definition of predictor with versatile behavior based on the order of fractional derivative. We derive the closed-form expressions of the optimal fractional linear predictor with restricted memory, and prove that the optimal first-order and the optimal second-order linear predictors are only its special cases. Furthermore, we empirically prove that the optimal order of fractional derivative can be approximated by the inverse of the predictor memory, and thus, it is a priori known. Therefore, the complexity is reduced by optimizing and transferring only one predictor coefficient, i.e., one parameter less in comparison to the second-order linear predictor, at the same level of performance. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Fractional linear prediction (FLP), as a generalization of conventional linear prediction (LP), was recently successfully applied in different fields of research and engineering, such as biomedical signal processing, speech modeling and image processing. The FLP model has a similar design as the conventional LP model, i.e., it uses a linear combination of "fractional terms" with different orders of fractional derivative. Assuming only one "fractional term" and using limited number of previous samples for prediction, FLP model with "restricted memory" is presented in this paper and the closed-form expressions for calculation of FLP coefficients are derived. This FLP model is fully comparable with the widely used low-order LP, as it uses the same number of previous samples, but less predictor coefficients, making it more efficient. Two different datasets, MIDI Aligned Piano Sounds (MAPS) and Orchset, were used for the experiments. Triads representing the chords composed of three randomly chosen notes and usual Western musical chords (both of them from MAPS dataset) served as the test signals, while the piano recordings from MAPS dataset and orchestra recordings from the Orchset dataset served as the musical signal. The results show enhancement of FLP over LP in terms of model complexity, whereas the performance is comparable. [ABSTRACT FROM AUTHOR]