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Journal articles on the topic 'Fractional Fourier entropy'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Li, Shu-Nan, and Bing-Yang Cao. "On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations." Entropy 21, no. 2 (February 21, 2019): 204. http://dx.doi.org/10.3390/e21020204.

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Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

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2

Tao, Ran, Xudong Zhao, Wei Li, Heng-Chao Li, and Qian Du. "Hyperspectral Anomaly Detection by Fractional Fourier Entropy." IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 12, no. 12 (December 2019): 4920–29. http://dx.doi.org/10.1109/jstars.2019.2940278.

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3

Yan, Yan. "Gingivitis detection by fractional Fourier entropy with optimization of hidden neurons." International Journal of Cognitive Computing in Engineering 1 (June 2020): 36–44. http://dx.doi.org/10.1016/j.ijcce.2020.09.003.

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4

Wang, Shuihua, Yudong Zhang, Xiaojun Yang, Ping Sun, Zhengchao Dong, Aijun Liu, and Ti-Fei Yuan. "Pathological Brain Detection by a Novel Image Feature—Fractional Fourier Entropy." Entropy 17, no. 12 (December 17, 2015): 8278–96. http://dx.doi.org/10.3390/e17127877.

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5

Zhang, Lili, Jiachen Ma, Baozhi Cheng, and Fang Lin. "Fractional Fourier Transform-Based Tensor RX for Hyperspectral Anomaly Detection." Remote Sensing 14, no. 3 (February 8, 2022): 797. http://dx.doi.org/10.3390/rs14030797.

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Anomaly targets in a hyperspectral image (HSI) are often multi-pixel, rather than single-pixel, objects. Therefore, algorithms using a test point vector may ignore the spatial characteristics of the test point. In addition, hyperspectral anomaly detection (AD) algorithms usually use original spectral signatures. In a fractional Fourier transform (FrFT), the signals in the fractional Fourier domain (FrFD) possess complementary characteristics of both the original reflectance spectrum and its Fourier transform. In this paper, a tensor RX (TRX) algorithm based on FrFT (FrFT-TRX) is proposed for hyperspectral AD. First, the fractional order of FrFT is selected by fractional Fourier entropy (FrFE) maximization. Then, the HSI is transformed into the FrFD by FrFT. Next, TRX is employed in the FrFD. Finally, according to the optimal spatial dimensions of the target and background tensors, the optimal AD result is achieved by adjusting the fractional order. TRX employs a test point tensor, making better use of the spatial characteristics of the test point. TRX in the FrFD exploits the complementary advantages of the intermediate domain to increase discrimination between the target and background. Six existing algorithms are used for comparison in order to verify the AD performance of the proposed FrFT-TRX over five real HSIs. The experimental results demonstrate the superiority of the proposed algorithm.

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6

NAGHSH, Mohammad Mahdi, and Mahmood MODARRES-HASHEMI. "ISAR Image Formation Based on Minimum Entropy Criterion and Fractional Fourier Transform." IEICE Transactions on Communications E92-B, no. 8 (2009): 2714–22. http://dx.doi.org/10.1587/transcom.e92.b.2714.

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7

Zhang, Yudong, Xiaojun Yang, Carlo Cattani, Ravipudi Rao, Shuihua Wang, and Preetha Phillips. "Tea Category Identification Using a Novel Fractional Fourier Entropy and Jaya Algorithm." Entropy 18, no. 3 (February 27, 2016): 77. http://dx.doi.org/10.3390/e18030077.

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8

Lopes, António M., and J. A. Tenreiro Machado. "Application of Fractional Techniques in the Analysis of Forest Fires." International Journal of Nonlinear Sciences and Numerical Simulation 17, no. 7-8 (December 1, 2016): 381–90. http://dx.doi.org/10.1515/ijnsns-2016-0026.

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Abstract:In this paper we study the global behavior of forest fires (FFs) in the Continental United States for the period 1984–2013. The data are obtained from a public domain catalog maintained by the Monitoring Trends in Burn Severity project. First we adopt clustering analysis to reduce the information dimensionality. Then we adopt mathematical tools commonly used in the analysis of dynamical systems, namely fractal dimension, entropy and fractional Fourier transform. The fractional techniques unveil FF patterns embedded in the data.

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9

Wang, Shui-Hua, Hong Cheng, Preetha Phillips, and Yu-Dong Zhang. "Multiple Sclerosis Identification Based on Fractional Fourier Entropy and a Modified Jaya Algorithm." Entropy 20, no. 4 (April 5, 2018): 254. http://dx.doi.org/10.3390/e20040254.

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10

Guo, ZhiPeng, Yi Xin, and YiZhang Zhao. "Cancer classification using entropy analysis in fractional Fourier domain of gene expression profile." Biotechnology & Biotechnological Equipment 32, no. 4 (December 19, 2017): 1042–46. http://dx.doi.org/10.1080/13102818.2017.1413596.

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11

Chen, Hua Li, and Yun Lian Sun. "Power Quality Disturbance Research of Grid-Connected Wind Generation Based on Fractional Fourier Transform with Wavelet Entropy." Applied Mechanics and Materials 130-134 (October 2011): 1600–1604. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.1600.

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In the process of connected wind generation with the power grid, the classification and recognition of power quality disturbance signals which are researched by the scholars at home and abroad are always the hot issues in Power System. A new method using Fractional Fourier Transform (FRFT) with Wavelet Entropy is presented for recognizing the signals of PQ disturbance based on the characteristics of power quality (PQ) signals. FRFT have better time-frequency aggregation and can choose better domain instead of and make PQ disturbance recognize more accurately with wavelet entropy. Simulation results demonstrate its effectiveness.

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12

Wang, Wantian, Yong Zhu, Ziyue Tang, Yichang Chen, Zhenbo Zhu, Yongjian Sun, and Chang Zhou. "Efficient Rotational Angular Velocity Estimation of Rotor Target via Modified Short-Time Fractional Fourier Transform." Remote Sensing 13, no. 10 (May 18, 2021): 1970. http://dx.doi.org/10.3390/rs13101970.

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As a special micro-motion feature of rotor target, rotational angular velocity can provide a discriminant basis for target classification and recognition. In this paper, the authors focus on an efficient rotational angular velocity estimation method of the rotor target is based on the combination of the time–frequency analysis algorithm and Hough transform. In order to avoid the problems of low time–frequency resolution and cross-term interference in short-time Fourier transform and Wigner–Ville distribution algorithm, a modified short-time fractional Fourier transform (M-STFRFT) is proposed to obtain the time-FRFT domain (FRFD)-frequency spectrum with the highest time–FRFD–frequency resolution. In particular, an orthogonal matching pursuit (OMP)-based algorithm is proposed to reduce the computational complexity when estimating the matched transform order in the proposed M-STFRFT algorithm. Firstly, partial transform order candidates are selected randomly from the complete candidates. Then, a partial entropy vector corresponding to partial transform order candidates is calculated from the FRFT results and utilized to reconstruct the complete entropy vector via the OMP algorithm, and the matched transform order can be estimated by searching minimum entropy. Based on the estimated matched transform order, STFRFT is performed to obtain the time–FRFD–frequency spectrum. Moreover, Hough transform is employed to obtain the energy accumulation spectrum, and the micro-Doppler parameter of rotational angular velocity can be estimated by searching the peak value from the energy accumulation spectrum. Both simulated data and measured data collected by frequency modulated continuous wave radar validate the effectiveness of the proposed algorithm.

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13

Zhang, Lili, and Baozhi Cheng. "A combined model based on stacked autoencoders and fractional Fourier entropy for hyperspectral anomaly detection." International Journal of Remote Sensing 42, no. 10 (February 14, 2021): 3611–32. http://dx.doi.org/10.1080/01431161.2020.1868605.

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14

Wang, Shui-Hua, Xin Zhang, and Yu-Dong Zhang. "DSSAE: Deep Stacked Sparse Autoencoder Analytical Model for COVID-19 Diagnosis by Fractional Fourier Entropy." ACM Transactions on Management Information Systems 13, no. 1 (March 31, 2022): 1–20. http://dx.doi.org/10.1145/3451357.

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( Aim ) COVID-19 has caused more than 2.28 million deaths till 4/Feb/2021 while it is still spreading across the world. This study proposed a novel artificial intelligence model to diagnose COVID-19 based on chest CT images. ( Methods ) First, the two-dimensional fractional Fourier entropy was used to extract features. Second, a custom deep stacked sparse autoencoder (DSSAE) model was created to serve as the classifier. Third, an improved multiple-way data augmentation was proposed to resist overfitting. ( Results ) Our DSSAE model obtains a micro-averaged F1 score of 92.32% in handling a four-class problem (COVID-19, community-acquired pneumonia, secondary pulmonary tuberculosis, and healthy control). ( Conclusion ) Our method outperforms 10 state-of-the-art approaches.

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Wang, Shui-Hua, Xin Zhang, and Yu-Dong Zhang. "DSSAE: Deep Stacked Sparse Autoencoder Analytical Model for COVID-19 Diagnosis by Fractional Fourier Entropy." ACM Transactions on Management Information Systems 13, no. 1 (March 31, 2022): 1–20. http://dx.doi.org/10.1145/3451357.

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( Aim ) COVID-19 has caused more than 2.28 million deaths till 4/Feb/2021 while it is still spreading across the world. This study proposed a novel artificial intelligence model to diagnose COVID-19 based on chest CT images. ( Methods ) First, the two-dimensional fractional Fourier entropy was used to extract features. Second, a custom deep stacked sparse autoencoder (DSSAE) model was created to serve as the classifier. Third, an improved multiple-way data augmentation was proposed to resist overfitting. ( Results ) Our DSSAE model obtains a micro-averaged F1 score of 92.32% in handling a four-class problem (COVID-19, community-acquired pneumonia, secondary pulmonary tuberculosis, and healthy control). ( Conclusion ) Our method outperforms 10 state-of-the-art approaches.

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16

Ma, Jie, and Lei Jiao. "Fault Diagnosis of Planetary Gear Based on FRWT and 2D-CNN." Mathematical Problems in Engineering 2022 (February 10, 2022): 1–14. http://dx.doi.org/10.1155/2022/4648653.

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The fault signals of planetary gears are nonstationary and nonlinear signals. It is difficult to extract weak fault features under strong background noise. This paper adopts a new filtering method, fractional Wavelet transform (FRWT). Compared with the traditional fractional Fourier transform (FRFT), it can improve the effect of noise reduction. This paper adopts a planetary gear fault diagnosis method combining fractional wavelet transform (FRWT) and two-dimensional convolutional neural network (2D-CNN). Firstly, several intrinsic mode component functions (IMFs) are obtained from the original vibration signal by AFSA-VMD decomposition, and the two components with the largest correlation coefficient are selected for signal reconstruction. Then, the reconstructed signal is filtered in fractional wavelet domain. By analyzing the wavelet energy entropy of the filtered signal, a two-dimensional normalized energy characteristic matrix is constructed and the two-dimensional features are input into the two-dimensional convolution neural network model for training. The simulation results show that the training effect of this method is better than that of FRFT-2D-CNN. Through the verification of the test set, we can know that the fault diagnosis of planetary gears can be realized accurately based on FRWT and 2D-CNN.

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17

Sheikh, Nadeem Ahmad, Dennis Ling Chuan Ching, Ilyas Khan, and Hamzah bin Sakidin. "Generalization of the Convective Flow of Brinkman-Type Fluid Using Fourier’s and Fick’s Laws: Exact Solutions and Entropy Generation." Mathematical Problems in Engineering 2020 (December 29, 2020): 1–13. http://dx.doi.org/10.1155/2020/8896555.

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A new scheme to formulating the Caputo time-fractional model for the flow of Brinkman-type fluid between the plates was introduced by using the generalized laws of Fourier and Fick. Within a channel, free convection flow of the electrically conducted Brinkman-type fluid was considered. A newly generated transformation was applied to the heat and mass concentration equations. The governing equations were solved by the techniques of Fourier sine and the Laplace transforms. In terms of the special function, namely, the Mittag-Leffler function, final solutions were obtained. The entropy generation and Bejan number are also calculated for the given flow. To explain the conceptual arguments of the embedded parameters, separate plots are represented in figures and are often quantitatively computed and presented in tables. It is worth noting that for increasing the values of the Brinkman-type fluid parameter, the velocity profile decreases. The regression analysis shows that the variation in the velocity for time parameter is statistically significant.

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18

Zhang, Yu-Dong, and Junding Sun. "Preliminary study on angiosperm genus classification by weight decay and combination of most abundant color index with fractional Fourier entropy." Multimedia Tools and Applications 77, no. 17 (September 2, 2017): 22671–88. http://dx.doi.org/10.1007/s11042-017-5146-3.

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19

Wang, Shuihua, Ming Yang, Jianwu Li, Xueyan Wu, Hainan Wang, Bin Liu, Zhengchao Dong, and Yudong Zhang. "Texture Analysis Method Based on Fractional Fourier Entropy and Fitness-scaling Adaptive Genetic Algorithm for Detecting Left-sided and Right-sided Sensorineural Hearing Loss." Fundamenta Informaticae 151, no. 1-4 (March 11, 2017): 505–21. http://dx.doi.org/10.3233/fi-2017-1507.

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20

Guanlei, Xu, Wang Xiaotong, and Xu Xiaogang. "Generalized entropic uncertainty principle on fractional Fourier transform." Signal Processing 89, no. 12 (December 2009): 2692–97. http://dx.doi.org/10.1016/j.sigpro.2009.05.014.

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21

Yan, Yan. "Gingivitis detection by Fractional Fourier Entropy and Particle Swarm Optimization." EAI Endorsed Transactions on e-Learning, April 28, 2021, 169424. http://dx.doi.org/10.4108/eai.28-4-2021.169424.

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22

WANG, SHUI-HUA, YELIZ KARACA, XIN ZHANG, and YU-DONG ZHANG. "SECONDARY PULMONARY TUBERCULOSIS RECOGNITION BY ROTATION ANGLE VECTOR GRID-BASED FRACTIONAL FOURIER ENTROPY." Fractals 30, no. 01 (November 9, 2021). http://dx.doi.org/10.1142/s0218348x22400473.

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Aim: Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis bacteria. This study plans to build a novel deep learning-based model for the accurate recognition of tuberculosis. Methods: We propose a novel model — rotation angle vector grid-based fractional Fourier entropy and deep stacked sparse autoencoder (RAVG-FrFE–DSSAE) — which uses RAVG-FrFE as a feature extractor and harnesses DSSAE as the classifier. Moreover, an 18-way MDA is introduced on the training set to avoid overfitting. Results: Experimental results of 10 runs of 10-fold CV showcase that this proposed RAVG-FrFE–DSSAE algorithm yields a reasonable performance including of 93.68[Formula: see text]±[Formula: see text]1.11% sensitivity, 94.38[Formula: see text]±[Formula: see text]1.11% specificity, 94.35[Formula: see text]±[Formula: see text]1.04% precision, 94.03[Formula: see text]±[Formula: see text]0.69% accuracy, 94.01[Formula: see text]±[Formula: see text]0.70% [Formula: see text]-score, 88.07[Formula: see text]±[Formula: see text]1.38% MCC, 94.01[Formula: see text]±[Formula: see text]0.70% FMI, and 0.9725 AUC, respectively. Conclusions: Our result outperforms the eight state-of-the-art approaches. Besides, the result shows the effectiveness of the 18-way MDA.

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23

Zhang, Yudong, Yi Sun, Preetha Phillips, Ge Liu, Xingxing Zhou, and Shuihua Wang. "A Multilayer Perceptron Based Smart Pathological Brain Detection System by Fractional Fourier Entropy." Journal of Medical Systems 40, no. 7 (June 2, 2016). http://dx.doi.org/10.1007/s10916-016-0525-2.

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24

Zhang, Yu‐Dong, Suresh Chandra Satapathy, and Shui‐Hua Wang. "Fruit category classification by fractional Fourier entropy with rotation angle vector grid and stacked sparse autoencoder." Expert Systems, April 8, 2021. http://dx.doi.org/10.1111/exsy.12701.

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25

Khan, Dolat, Kanayo Kenneth Asogwa, Nevzat Akkurt, Poom Kumam, Wiboonsak Watthayu, and Kanokwan Sitthithakerngkiet. "Development of generalized Fourier and Fick’s law of electro-osmotic MHD flow of sodium alginate based Casson nanofluid through inclined microchannel: exact solution and entropy generation." Scientific Reports 12, no. 1 (November 4, 2022). http://dx.doi.org/10.1038/s41598-022-21854-5.

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AbstractElectro-osmotic flow via a microchannel has numerous uses in the contemporary world, including in the biochemical and pharmaceutical industries. This research explores the electroosmotic flow of Casson-type nanofluid with Sodium Alginate nanoparticles through a vertically tilted microchannel. In addition, the transverse magnetic field is also considered. In this flowing fluid, the influence of heat and mass transmission is also explored. The aforementioned physical process is represented by partial differential equations. Utilizing suitable dimensionless variables for nondimensionalized. Furthermore, the non—dimensional classical system is fractionalized with the use of generalized Fourier and Fick's law. Generalizations are made using the Caputo derivative's description. The analytical solution of the velocity, temperature, and concentration profiles is obtained by combining the methods of Laplace and Fourier. Interestingly, the influence of several physical characteristics such as the fractional parameter, Casson fluid parameter, the thermal and mass Grashof numbers, and the zeta potential parameter is displayed. Moreover, the results show that the volume fractional of nanoparticles enhances the rate of heat transfer up to 39.90%, Skin friction up to 38.05%, and Sherwood number up to 11.11%. Also, the angle of inclination enhances the fluid velocity.

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26

Shrivastava, Aarushi, Janki Ballabh Sharma, and Sunil Dutt Purohit. "Image encryption based on Fractional wavelet transform, Arnold transform with the double random phases in HSV color domain." Recent Advances in Computer Science and Communications 13 (September 18, 2020). http://dx.doi.org/10.2174/2666255813999200918123535.

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Objective: In the recent multimedia technology images play an integral role in communication. Here in this paper, we propose a new color image encryption method using FWT (Fractional Wavelet transform), double random phases and Arnold transform in HSV color domain. Methods: Firstly the image is changed into the HSV domain and the encoding is done using the FWT which is the combination of the fractional Fourier transform with wavelet transform and the two random phase masks are used in the double random phase encoding. In this one inverse DWT is taken at the end in order to obtain the encrypted image. To scramble the matrices the Arnold transform is used with different iterative values. The fractional order of FRFT, the wavelet family and the iterative numbers of Arnold transform are used as various secret keys in order to enhance the level of security of the proposed method. Results: The performance of the scheme is analyzed through its PSNR and SSIM values, key space, entropy, statistical analysis which demonstrates its effectiveness and feasibility of the proposed technique. Stimulation result verifies its robustness in comparison to nearby schemes. Conclusion: This method develops the better security, enlarged and sensitive key space with improved PSNR and SSIM. FWT reflecting time frequency information adds on to its flexibility with additional variables and making it more suitable for secure transmission.

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