Abstract
Hahn’s discrete orthogonal moments are powerful tools for image and signal analysis. Several methods have been proposed to implement Hahn’s moments, but their implementation remains limited for high orders by the problem of the propagation of numerical errors. This problem is due to rounding errors during recursive computations of Hahn’s polynomials under machine (using Matlab, C++, Java…). In this paper, we propose a stable computation of Hahn polynomials at high orders based on the modified Gram-Schmidt orthonormalization process. the proposed method significantly reduces the propagation of numerical errors and therefore preserves the orthonormality property of Hahn polynomials. The results obtained show the stability of Hahn moments obtained by the proposed method for the reconstruction of large 1D signals.
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