In this paper, we present an efficient and optimal method for optimization of Hahn parameters a and b using the Artificial Bee Colony algorithm (ABC) in order to improve the quality of reconstruction and the compression of bio-signals and 2D / 3D color images of large sizes. The proposed methods are essentially based on two concepts: the development of a recursive calculation of the initial terms of Hahn polynomials in order to avoid the problems of instability of polynomial values and the use of ABC algorithm to optimize the values of the parameters a and b of the discrete orthogonal Hahn polynomials ( HPs ) during the reconstruction and the compression of bio-signals and 2D / 3D color images. The simulation results performed on bio-signals and on large size 2D / 3D color images clearly show the efficiency and superiority of the proposed methods over conventional methods in terms of reconstruction of signals and images.

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