The inverse hyperbolic tangent function and Jacobian sine function

Wang, Gendi

doi:10.1016/j.jmaa.2016.11.002

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…The information in the source images is redundant and complementary for the image fusion shown in Figure 1. The hyperbolic tangent function is one of the hyperbolic functions, and derives from hyperbolic sine function and hyperbolic cosine function [32]. It can be calculated as follows:…”

Section: Adaptive Dictionary Learningmentioning

confidence: 99%

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Remote Sensing Image Fusion Based on Sparse Representation and Guided Filtering

Liu

et al. 2019

Electronics

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In this paper, a remote sensing image fusion method is presented since sparse representation (SR) has been widely used in image processing, especially for image fusion. Firstly, we used source images to learn the adaptive dictionary, and sparse coefficients were obtained by sparsely coding the source images with the adaptive dictionary. Then, with the help of improved hyperbolic tangent function (tanh) and l 0 − max , we fused these sparse coefficients together. The initial fused image can be obtained by the image fusion method based on SR. To take full advantage of the spatial information of the source images, the fused image based on the spatial domain (SF) was obtained at the same time. Lastly, the final fused image could be reconstructed by guided filtering of the fused image based on SR and SF. Experimental results show that the proposed method outperforms some state-of-the-art methods on visual and quantitative evaluations.

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Section: Adaptive Dictionary Learningmentioning

confidence: 99%

“…From Figure 2a,b we can see that tanh is symmetrical around the origin point. As x increases, the difference between the value of the The hyperbolic tangent function is one of the hyperbolic functions, and derives from hyperbolic sine function and hyperbolic cosine function [32]. It can be calculated as follows:…”

Section: Adaptive Dictionary Learningmentioning

confidence: 99%

Remote Sensing Image Fusion Based on Sparse Representation and Guided Filtering

Liu

et al. 2019

Electronics

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“…The study of the convexity/concavity with respect to Hölder means, or simply H p;q -convexity/concavity, of special functions has attracted attentions of many researchers, see [2,6,7,[9][10][11][13][14][15][16][17]. In particular, the convexity/concavity of the inverse hyperbolic tangent and sine functions has been studied in [9] and [11], respectively.…”

Section: Introductionmentioning

confidence: 99%

Generalized convexity of the inverse hyperbolic cosine function

He¹,

Wang²

2018

MMN

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Shafer–Fink type inequalities for arc lemniscate functions

Wei

Wang

2020

RACSAM

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In this paper, we investigate the monotonicity and inequalities for some functions involving the arc lemniscate and the hyperbolic arc lemniscate functions. In particular, sharp Shafer-Fink type inequalities for the arc lemniscate and the hyperbolic arc lemniscate functions are proved.Keywords. arc lemniscate functions, hyperbolic arc lemniscate functions, lemniscate functions, hyperbolic lemniscate functions, Shafer-Fink type inequalities Mathematics Subject Classification (2010). 26D07, 33E05

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The inverse hyperbolic tangent function and Jacobian sine function

Cited by 6 publications

References 13 publications

Remote Sensing Image Fusion Based on Sparse Representation and Guided Filtering

Remote Sensing Image Fusion Based on Sparse Representation and Guided Filtering

Generalized convexity of the inverse hyperbolic cosine function

Shafer–Fink type inequalities for arc lemniscate functions

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