Efficient computation of high-order Meixner moments for large-size signals and images analysis

Daoui, Achraf; Sayyouri, Mhamed; Qjidaa, Hassan

doi:10.1007/s11042-020-09739-z

Cited by 14 publications

(21 citation statements)

References 42 publications

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“…This problem is discussed by Camacho-bello et al in [ 5 ] when computing high-order Tchebichef polynomials. To overcome the encountered problem for Tchebichef, Meixner and Hahn polynomials, the modified Gram-Schmidt orthonormalization process (GSOP) is used [ 5 , 8 , 9 , 12 ]. However, the correction of numerical instability by GSOP is very time-consuming because GSOP involves a complex calculation process [ 5 , 12 ].…”

Section: Conventional and Proposed Computation Of Hpsmentioning

confidence: 99%

“…To overcome the encountered problem for Tchebichef, Meixner and Hahn polynomials, the modified Gram-Schmidt orthonormalization process (GSOP) is used [ 5 , 8 , 9 , 12 ]. However, the correction of numerical instability by GSOP is very time-consuming because GSOP involves a complex calculation process [ 5 , 12 ]. This problem limits the fast reconstruction of large-size signals and images by high-order HPs.…”

Section: Conventional and Proposed Computation Of Hpsmentioning

confidence: 99%

“…The second test presents a comparison in terms of reconstruction errors (MSE and PSNR) by using the moments of Tchebichef (TMs) [5], Krawtchouk (KMs) [47], Meixner (MMs) Fig. 9 Set of reconstructed "Lena" image by different moment types of order up to (1024, 1024) [12], Charlier (CMs) [12] and HMs (based on algorithm 3). Indeed, Fig.…”

Section: Large-size Image Reconstruction By Higher-order Hmsmentioning

confidence: 99%

“…This method succeeded to ensure the numerical stability of higher-order Tchebichef polynomials. More recently, GSOP method is used by Daoui et al to introduce a numerically stable computation of Hahn [ 9 ], Charlier [ 8 ] and Meixner [ 12 ] polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…Applications of DOMs include signal and image reconstruction [8,9,50], image classification [3,16,20,39], face recognition [33], image watermarking [24,41,44], signal zero-watermarking [10], edge detection [35], image encryption [43], signal compression [11,2] and image compression [13,42]. The computation of DOMs involves the computation of kernel discrete orthogonal polynomials (DOPs) such as Tchebichef [27,28], Krawtchouk [45,47], Hahn [46,50], Meixner [12,21], Charlier [8,19,34], dual Hahn [20,48], Racah [49] and Shmaliy [26] polynomials.…”

Section: Introductionmentioning

confidence: 99%

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Fast and stable computation of higher-order Hahn polynomials and Hahn moment invariants for signal and image analysis

Daoui

Karmouni

Sayyouri

et al. 2021

Multimed Tools Appl

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This article presents, on the one hand, new algorithms for the fast and stable computation of discrete orthogonal Hahn polynomials of high order (HPs) based on the elimination of all gamma and factorial functions that cause the numerical fluctuations of HPs, and based on the use of appropriate stability conditions. On the other hand, a new method for the fast and numerically stable computation of Hahn moment invariants (HMIs) is also proposed. This method is mainly based on the use of new recursive relations of HPs and of matrix multiplications when calculating HMIs. To validate the efficiency of the algorithms proposed for the calculation of HPs, several signals and large images (≥4000 × 4000) are reconstructed by Hahn moments (HMs) up to the last order with a reconstruction error tending towards zero ( MSE ≃ 10 −10 ). The efficiency of the proposed method for calculating HMIs is demonstrated on large medical images (2048 × 2048) with a very low relative error ( RE ≃ 10 −10 ). Finally, comparisons with some recent work in the literature are provided.

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