Signal Reconstruction using Second Order Tetration Polynomial

Khetkeeree, Suphongsa; Chansamorn, Chapkit

doi:10.1109/itc-cscc.2019.8793435

Cited by 3 publications

(6 citation statements)

References 4 publications

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“…The interpolation results on the left side (0, 1] and the right side [1,2) give the different results (asymmetric property). We can demonstrate four different techniques of asymmetric interpolation as follows.…”

Section: Proposed Methods 21 Asymmetric Tetration Interpolationmentioning

confidence: 99%

“…12, No. 2, April 2022: 1893-1903 1894 mathematics, which is the next mathematical operation after exponentiation in our previous work, for modeling the alternative formulas for signal interpolation [2] as: − Tetration polynomial: the tetration is one of the mathematical operations located after exponentiation but before pentation. It was firstly proposed by Goodstein [37] in 1947.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, it also can be called for a different name such as superexponentiation [40], hyperpower [41]. This mathematical operator was applied in the problem of compacting Church numerals [42], and our previous work [2]. The form of the traditional polynomial function was used to model the tetration polynomial function.…”

Section: Introductionmentioning

confidence: 99%

“…− Existed tetration interpolation: the simple quadratic tetration polynomial was considered in our previous work [2], written as (3):…”

Section: Introductionmentioning

confidence: 99%

“…− Forward and backward operations: The above interpolation formula (3) has the shift variant and asymmetric properties [2]. It gives an individual value for each domain range.…”

Section: Introductionmentioning

confidence: 99%

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Symmetric quadratic tetration interpolation using forward and backward operation combination

Charnsamorn

Khetkeeree

2022

IJECE

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The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.

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Section: Proposed Methods 21 Asymmetric Tetration Interpolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…− Existed tetration interpolation: the simple quadratic tetration polynomial was considered in our previous work [2], written as (3):…”

Section: Introductionmentioning

confidence: 99%

“…− Forward and backward operations: The above interpolation formula (3) has the shift variant and asymmetric properties [2]. It gives an individual value for each domain range.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Symmetric quadratic tetration interpolation using forward and backward operation combination

Charnsamorn

Khetkeeree

2022

IJECE

Self Cite

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Review Study of Image De-Noising on Digital Image Processing and Applications

Abdulah

Rohani²,

Ismail³

et al. 2023

ARASET

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This paper reviews several studies of image de-noising on digital image processing and applications. Noisy images contain different noise that exist either due to environment or electronic interferences. Ergo, de-noising is crucial to eliminate the noise that disturb data collecting process. The impact of de-noising on image processing can result for accurate and precise data collected from the image. Additionally, de-noising process required several crucial steps that help to enhance knowledge on digital image and its application. Hence, study and understanding de-noising can improve multiple aspect such as image quality, data sensitivity and specificity, accuracy of the collected data, and increase the percentage of each parameter.

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Extension of tetration to real and complex heights

Ueda¹

2021

Preprint

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Signal Reconstruction using Second Order Tetration Polynomial

Cited by 3 publications

References 4 publications

Symmetric quadratic tetration interpolation using forward and backward operation combination

Symmetric quadratic tetration interpolation using forward and backward operation combination

Review Study of Image De-Noising on Digital Image Processing and Applications

Extension of tetration to real and complex heights

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