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

Daoui, Achraf; Karmouni, Hicham; Sayyouri, Mhamed; Qjidaa, Hassan

doi:10.1007/s11042-021-11206-2

Cited by 11 publications

(11 citation statements)

References 47 publications

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“…The results also outperform the introduced algorithm compared to FrGLMs-HM at each order in terms of PSNR and MSE. A comparative investigation of other existing algorithms [8,18,20,36] in reconstruction quality is summarized in Table 4. Figures 7 and 8 A comparative investigation of other existing algorithms [8,18,20,36] in reconstruction quality is summarized in Table 4.…”

Section: Resultsmentioning

confidence: 99%

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Efficient Analysis of Large-Size Bio-Signals Based on Orthogonal Generalized Laguerre Moments of Fractional Orders and Schwarz–Rutishauser Algorithm

Aldakheel,

Khafaga,

Fathi

et al. 2023

Fractal Fract

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Orthogonal generalized Laguerre moments of fractional orders (FrGLMs) are signal and image descriptors. The utilization of the FrGLMs in the analysis of big-size signals encounters three challenges. First, calculating the high-order moments is a time-consuming process. Second, accumulating numerical errors leads to numerical instability and degrades the reconstructed signals’ quality. Third, the QR decomposition technique is needed to preserve the orthogonality of the higher-order moments. In this paper, the authors derived a new recurrence formula for calculating the FrGLMs, significantly reducing the computational CPU times. We used the Schwarz–Rutishauser algorithm as an alternative to the QR decomposition technique. The proposed method for computing FrGLMs for big-size signals is accurate, simple, and fast. The proposed algorithm has been tested using the MIT-BIH arrhythmia benchmark dataset. The results show the proposed method’s superiority over existing methods in terms of processing time and reconstruction capability. Concerning the reconstructed capability, it has achieved superiority with average values of 25.3233 and 15.6507 with the two metrics PSNR and MSE, respectively. Concerning the elapsed reconstruction time, it also achieved high superiority with an efficiency gain of 0.8. The proposed method is suitable for utilization in the Internet of Healthcare Things.

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Section: Resultsmentioning

confidence: 99%

“…We utilized some ECG signals from the MIT-BIH Arrhythmia Dataset in the experiments. The Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) are utilized to evaluate the efficacy of the introduced algorithm [36].…”

Section: Experiments and Discussionmentioning

confidence: 99%

Efficient Analysis of Large-Size Bio-Signals Based on Orthogonal Generalized Laguerre Moments of Fractional Orders and Schwarz–Rutishauser Algorithm

Aldakheel,

Khafaga,

Fathi

et al. 2023

Fractal Fract

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“…Discrete orthogonal moments (DOMs) are regarded as powerful descriptors in the field of digital signal and image processing. DOMs are computed based on discrete orthogonal polynomials (DOPs), like Tchebichef [24], Krawtchouk [2], Hahn [25], Meixner [26], Charlier [27], dual Hahn [28], [29] and Racah polynomials [30]. Lately, some discrete orthogonal polynomials involving fractional order have been introduced in the literature.…”

Section: Related Workmentioning

confidence: 99%

Biomedical Multimedia Encryption by Fractional-Order Meixner Polynomials Map and Quaternion Fractional-Order Meixner Moments

et al. 2022

Self Cite

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Chaotic systems are widely used in signal and image encryption schemes. Therefore, the design of new chaotic systems is always useful for improving the performance of encryption schemes in terms of security. In this work, we first demonstrate the chaotic behavior of fractional order Meixner polynomials (FrMPs) for introducing a new two-dimensional (2D) chaotic system called FrMPs map. This system is very sensitive to any variation by 15 10 − of its control parameters ( and µ β ).Next, we use FrMPs to introduce a new type of orthogonal transforms called quaternion fractional order Meixner moments (QFrMMs). The latter generalize the existing fractional order Meixner moments. To demonstrate the relevance of the proposed FrMPs map and QFrMMs in the field of signal and image processing, they are applied in the development of a new encryption scheme. The main advantage of this scheme is its applicability to the encryption of different types of biomedical data such as multi-biomedical signals, multiple grayscale medical images, color medical image, and grayscale medical image. Several simulation analysis (visual, histogram, runtime, correlation, robustness, etc.) are conducted to verify the efficiency of the proposed scheme. Simulation and comparison results confirm that our encryption method is effective in terms of high security level, high quality of the decrypted information, strong resistance to different types of attacks, etc. These findings support the suitability of the proposed scheme for the secure exchange of biomedical multimedia via a public communication channel.

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“…When these basic functions are polynomials, the resulting numerical characteristics are referred to as moments. The use of orthogonal polynomials is advantageous because it reduces the correlation between moments and improves the numerical stability of both the polynomials and the moments, particularly at higher degrees and orders [3], [4]. (The order of the moment corresponds to the degree of the polynomial.…”

Section: Introductionmentioning

confidence: 99%

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Mahmmod,

Abdulhussain,

Suk

et al. 2023

IEEE Access

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Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision. Racah polynomials were originally introduced by Wilson and later modified by Zhu to be orthogonal on a discrete set of samples. However, when the degree of the polynomial is high, it encounters numerical instability issues. In this paper, we propose a novel algorithm called Improved Stabilization (ImSt) for computing DRP coefficients. The algorithm partitions the DRP plane into asymmetric parts based on the polynomial size and DRP parameters. We have optimized the use of stabilizing conditions in these partitions. To compute the initial values, we employ the logarithmic gamma function along with a new formula. This combination enables us to compute the initial values efficiently for a wide range of DRP parameter values and large polynomial sizes. Additionally, we have derived a symmetry relation for the case when the Racah polynomial parameters are zero (a = 0, α = 0, β = 0). This symmetry makes the Racah polynomials symmetric about the main diagonal, and we present a different algorithm for this specific scenario. We have demonstrated that the ImSt algorithm works for a broader range of parameters and higher degrees compared to existing algorithms. A comprehensive comparison between ImSt and the existing algorithms has been conducted, considering the maximum polynomial degree, computation time, restriction error analysis, and reconstruction error. The results of the comparison indicate that ImSt outperforms the existing algorithms for various values of Racah polynomial parameters.

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

Cited by 11 publications

References 47 publications

Efficient Analysis of Large-Size Bio-Signals Based on Orthogonal Generalized Laguerre Moments of Fractional Orders and Schwarz–Rutishauser Algorithm

Efficient Analysis of Large-Size Bio-Signals Based on Orthogonal Generalized Laguerre Moments of Fractional Orders and Schwarz–Rutishauser Algorithm

Biomedical Multimedia Encryption by Fractional-Order Meixner Polynomials Map and Quaternion Fractional-Order Meixner Moments

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

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