Pub Date : 2021-11-24DOI: 10.1142/s0219691321500533
P. Andrianov
In this paper, the definition of a periodic discrete multiresolution analysis is provided. The characterization of such systems is obtained in terms of properties of scaling sequences. Wavelet systems generated by such multiresolution analyses are defined and described. Decomposition and reconstruction formulas for the associated discrete wavelet transform are provided.
{"title":"Multidimensional periodic discrete wavelets","authors":"P. Andrianov","doi":"10.1142/s0219691321500533","DOIUrl":"https://doi.org/10.1142/s0219691321500533","url":null,"abstract":"In this paper, the definition of a periodic discrete multiresolution analysis is provided. The characterization of such systems is obtained in terms of properties of scaling sequences. Wavelet systems generated by such multiresolution analyses are defined and described. Decomposition and reconstruction formulas for the associated discrete wavelet transform are provided.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126398095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-13DOI: 10.1142/s0219691321500521
A. Prasad, Z. A. Ansari
In this paper, we introduce the concept of linear canonical wave packet transform (LCWPT) based on the idea of linear canonical transform (LCT) and wave packet transform (WPT). Parseval’s identity and some properties of LCWPT are discussed. The inversion formula of LCWPT is formulated. Moreover, the composition of LCWPTs is defined and some properties are studied related to it. The LCWPTs of Mexican hat wavelet function are obtained.
{"title":"The wave packet transform in the framework of linear canonical transform","authors":"A. Prasad, Z. A. Ansari","doi":"10.1142/s0219691321500521","DOIUrl":"https://doi.org/10.1142/s0219691321500521","url":null,"abstract":"In this paper, we introduce the concept of linear canonical wave packet transform (LCWPT) based on the idea of linear canonical transform (LCT) and wave packet transform (WPT). Parseval’s identity and some properties of LCWPT are discussed. The inversion formula of LCWPT is formulated. Moreover, the composition of LCWPTs is defined and some properties are studied related to it. The LCWPTs of Mexican hat wavelet function are obtained.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133531257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-06DOI: 10.1142/s0219691321500491
Pong-Chol Son, Kyong-il Kim, Kyong-Chol Choe, Hyok-Il Kye
Navigation at sea requires accurate velocity measurement of a vehicle relative to the seabed. Correlation velocity measurement techniques are efficiently used to measure the velocity of underwater vehicles because they are not affected by sound speed compared to Doppler techniques, have several advantages such as small size and power consumption and tracking deep seabed. We consider the relationship of maximum correlation coefficient and signal-to-noise ratio (SNR), which are important parameters in correlation velocity measurement and present the maximum correlation coefficient equation according to SNR. Next, we propose a method of the noise robustness enhancement using discrete wavelet transform (DWT) in correlation velocity measurement. In addition, we evaluate the noise robustness of the proposed method and various methods of correlation velocity measurement through simulation, and present the maximum correlation coefficient equation according to SNR of our method. Simulation results show that new method of correlation velocity measurement using wavelet thresholding proposed in this paper improves the noise robustness of correlation velocity measurement more than various methods. In addition, in correlation velocity log (CVL) operating under low SNR below 6 dB, the maximum correlation coefficient of new method increases more than 0.1 than the classical method. Simulation results show that the new method of correlation velocity measurement considerably improved the noise robustness of spatial CVL than classical method, and the noise robustness of new method is highest among various methods of correlation velocity measurement.
{"title":"A method to enhance the noise robustness of correlation velocity measurement using discrete wavelet transform","authors":"Pong-Chol Son, Kyong-il Kim, Kyong-Chol Choe, Hyok-Il Kye","doi":"10.1142/s0219691321500491","DOIUrl":"https://doi.org/10.1142/s0219691321500491","url":null,"abstract":"Navigation at sea requires accurate velocity measurement of a vehicle relative to the seabed. Correlation velocity measurement techniques are efficiently used to measure the velocity of underwater vehicles because they are not affected by sound speed compared to Doppler techniques, have several advantages such as small size and power consumption and tracking deep seabed. We consider the relationship of maximum correlation coefficient and signal-to-noise ratio (SNR), which are important parameters in correlation velocity measurement and present the maximum correlation coefficient equation according to SNR. Next, we propose a method of the noise robustness enhancement using discrete wavelet transform (DWT) in correlation velocity measurement. In addition, we evaluate the noise robustness of the proposed method and various methods of correlation velocity measurement through simulation, and present the maximum correlation coefficient equation according to SNR of our method. Simulation results show that new method of correlation velocity measurement using wavelet thresholding proposed in this paper improves the noise robustness of correlation velocity measurement more than various methods. In addition, in correlation velocity log (CVL) operating under low SNR below 6 dB, the maximum correlation coefficient of new method increases more than 0.1 than the classical method. Simulation results show that the new method of correlation velocity measurement considerably improved the noise robustness of spatial CVL than classical method, and the noise robustness of new method is highest among various methods of correlation velocity measurement.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"20 7-8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125026202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-06DOI: 10.1142/s0219691321500557
Anastassia Gorsanova
In this paper, sufficient conditions on non-stationary periodic wavelet systems to provide good approximation properties of wavelet expansions are established. The approximation error is estimated in terms of modulus of continuity in [Formula: see text]-spaces.
{"title":"Jackson-type theorem on approximation by non-stationary periodic wavelets","authors":"Anastassia Gorsanova","doi":"10.1142/s0219691321500557","DOIUrl":"https://doi.org/10.1142/s0219691321500557","url":null,"abstract":"In this paper, sufficient conditions on non-stationary periodic wavelet systems to provide good approximation properties of wavelet expansions are established. The approximation error is estimated in terms of modulus of continuity in [Formula: see text]-spaces.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"243 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113972319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-06DOI: 10.1142/s021969132150051x
A. Alzubi
The e-learning platform gains significant attraction in the current scenario due to the outbreak of the epidemic COVID-19 as e-learning ensures the students continue their studies in the safest environment while maintaining the educational standard. The performance prediction is one of the significant tasks to be carried out in the e-learning platform to sort out the students who require immediate attention to enhance their grades before the final assessment. This paper proposes a prediction model that effectively predicts the learners’ performance in the e-khool learning management system (e-khool LMS) based on the proposed wolf-swarm optimization dependent Deep Long Short-term (wolf-swarm optimization-based Deep-LSTM) approach. The optimization algorithm tunes the optimal weights of the Deep-LSTM classifier, which inherits the hybrid characteristics of the traitors and particles. Initially, the learner data from the e-khool database is employed for classification based on the proposed wolf-swarm optimization dependent Deep-LSTM classifier. The effectiveness of the proposed prediction model is analyzed in terms of MSE and RMSE with the value of 5.93 and 2.426, respectively.
由于新冠肺炎疫情的爆发，电子学习平台在保持教育标准的同时，确保学生在最安全的环境中继续学习，因此具有很大的吸引力。成绩预测是电子学习平台的一项重要工作，目的是在最终考核前，对需要立即关注的学生进行梳理，提高他们的成绩。基于基于狼群优化的Deep- Long - short(基于狼群优化的Deep- lstm)方法，提出了一种能够有效预测e- kool学习管理系统(e- kool LMS)中学习者表现的预测模型。优化算法对Deep-LSTM分类器的最优权值进行调整，该分类器继承了叛徒和粒子的混合特性。首先，基于基于狼群优化的Deep-LSTM分类器，使用e- kool数据库中的学习者数据进行分类。采用MSE和RMSE分别为5.93和2.426，对所提预测模型的有效性进行了分析。
{"title":"Learner performance prediction in the e-learning platform using the optimized deep long short-term memory classifier","authors":"A. Alzubi","doi":"10.1142/s021969132150051x","DOIUrl":"https://doi.org/10.1142/s021969132150051x","url":null,"abstract":"The e-learning platform gains significant attraction in the current scenario due to the outbreak of the epidemic COVID-19 as e-learning ensures the students continue their studies in the safest environment while maintaining the educational standard. The performance prediction is one of the significant tasks to be carried out in the e-learning platform to sort out the students who require immediate attention to enhance their grades before the final assessment. This paper proposes a prediction model that effectively predicts the learners’ performance in the e-khool learning management system (e-khool LMS) based on the proposed wolf-swarm optimization dependent Deep Long Short-term (wolf-swarm optimization-based Deep-LSTM) approach. The optimization algorithm tunes the optimal weights of the Deep-LSTM classifier, which inherits the hybrid characteristics of the traitors and particles. Initially, the learner data from the e-khool database is employed for classification based on the proposed wolf-swarm optimization dependent Deep-LSTM classifier. The effectiveness of the proposed prediction model is analyzed in terms of MSE and RMSE with the value of 5.93 and 2.426, respectively.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124446754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-30DOI: 10.1142/s021969132150048x
Neil D. Dizon, J. Hogan, J. Lakey
We present an optimization approach to wavelet architecture that hinges on the Zak transform to formulate the construction as a minimization problem. The transform warrants parametrization of the quadrature mirror filter in terms of the possible integer sample values of the scaling function and the associated wavelet. The parameters are predicated to satisfy constraints derived from the conditions of regularity, compact support and orthonormality. This approach allows for the construction of nearly cardinal scaling functions when an objective function that measures deviation from cardinality is minimized. A similar objective function based on a measure of symmetry is also proposed to facilitate the construction of nearly symmetric scaling functions on the line.
{"title":"Optimization in the construction of cardinal and symmetric wavelets on the line","authors":"Neil D. Dizon, J. Hogan, J. Lakey","doi":"10.1142/s021969132150048x","DOIUrl":"https://doi.org/10.1142/s021969132150048x","url":null,"abstract":"We present an optimization approach to wavelet architecture that hinges on the Zak transform to formulate the construction as a minimization problem. The transform warrants parametrization of the quadrature mirror filter in terms of the possible integer sample values of the scaling function and the associated wavelet. The parameters are predicated to satisfy constraints derived from the conditions of regularity, compact support and orthonormality. This approach allows for the construction of nearly cardinal scaling functions when an objective function that measures deviation from cardinality is minimized. A similar objective function based on a measure of symmetry is also proposed to facilitate the construction of nearly symmetric scaling functions on the line.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128747198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1142/s0219691321500478
M. B. Abid, M. B. Slimane, I. Omrane, M. Turkawi
In this paper, we first establish a general lower bound for the multivariate wavelet leaders Rényi dimension valid for any pair [Formula: see text] of functions on [Formula: see text] where [Formula: see text] belongs to the Besov space [Formula: see text] with [Formula: see text] and [Formula: see text] belongs to [Formula: see text] with [Formula: see text]. We then prove the optimality of this result for quasi all pairs [Formula: see text] in the Baire generic sense. Finally, we compute both iso-mixed and upper-multivariate Hölder spectra for all pairs [Formula: see text] in the same [Formula: see text]-set. This allows to prove (respectively, study) the Baire generic validity of the upper-multivariate (respectively, iso-multivariate) multifractal formalism based on wavelet leaders for such pairs.
{"title":"Multivariate wavelet leaders Rényi dimension and multifractal formalism in mixed Besov spaces","authors":"M. B. Abid, M. B. Slimane, I. Omrane, M. Turkawi","doi":"10.1142/s0219691321500478","DOIUrl":"https://doi.org/10.1142/s0219691321500478","url":null,"abstract":"In this paper, we first establish a general lower bound for the multivariate wavelet leaders Rényi dimension valid for any pair [Formula: see text] of functions on [Formula: see text] where [Formula: see text] belongs to the Besov space [Formula: see text] with [Formula: see text] and [Formula: see text] belongs to [Formula: see text] with [Formula: see text]. We then prove the optimality of this result for quasi all pairs [Formula: see text] in the Baire generic sense. Finally, we compute both iso-mixed and upper-multivariate Hölder spectra for all pairs [Formula: see text] in the same [Formula: see text]-set. This allows to prove (respectively, study) the Baire generic validity of the upper-multivariate (respectively, iso-multivariate) multifractal formalism based on wavelet leaders for such pairs.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128420888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1142/s0219691321500508
Amit Verma, B. Gupta
In this paper, we study the continuous fractional wavelet transform (CFrWT) in [Formula: see text]-dimensional Euclidean space [Formula: see text] with scaling parameter [Formula: see text] such that [Formula: see text]. We obtain inner product relation and reconstruction formula for the CFrWT depending on two wavelets along with the reproducing kernel function, involving two wavelets, for the image space of CFrWT. We obtain Heisenberg’s uncertainty inequality and Local uncertainty inequality for the CFrWT. Finally, we prove the boundedness of CFrWT on the Morrey space [Formula: see text] and estimate [Formula: see text]-distance of the CFrWT of two argument functions with respect to different wavelets.
{"title":"A note on continuous fractional wavelet transform in ℝn","authors":"Amit Verma, B. Gupta","doi":"10.1142/s0219691321500508","DOIUrl":"https://doi.org/10.1142/s0219691321500508","url":null,"abstract":"In this paper, we study the continuous fractional wavelet transform (CFrWT) in [Formula: see text]-dimensional Euclidean space [Formula: see text] with scaling parameter [Formula: see text] such that [Formula: see text]. We obtain inner product relation and reconstruction formula for the CFrWT depending on two wavelets along with the reproducing kernel function, involving two wavelets, for the image space of CFrWT. We obtain Heisenberg’s uncertainty inequality and Local uncertainty inequality for the CFrWT. Finally, we prove the boundedness of CFrWT on the Morrey space [Formula: see text] and estimate [Formula: see text]-distance of the CFrWT of two argument functions with respect to different wavelets.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122331852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1142/s0219691321500466
Di Zhang, Yichen Zhou, Jiaqi Zhao, Yong Zhou
The appropriate setting of hyperparameter is a key factor to determine the performance of the deep learning model. Efficient hyperparametric optimization algorithm can not only improve the efficiency and speed of model hyperparametric optimization, but also reduce the application threshold of deep learning model. Therefore, we propose a parameter learning algorithm-based co-evolutionary for remote sensing scene classification. First, a co-evolution framework is proposed to optimize the optimizer’s hyperparameters and weight parameters of the convolutional neural networks (CNNs) simultaneously. Second, with the strategy of co-evolution with two populations, the hyperparameters can learn within the population and the weights of CNN can be updated by utilizing information between the populations. Finally, the parallel computing mechanism is adapted to speed up the learning process, as the two populations can evolve simultaneously. Extensive experiments on three public datasets demonstrate the effectiveness of the proposed approach.
{"title":"Co-evolution-based parameter learning for remote sensing scene classification","authors":"Di Zhang, Yichen Zhou, Jiaqi Zhao, Yong Zhou","doi":"10.1142/s0219691321500466","DOIUrl":"https://doi.org/10.1142/s0219691321500466","url":null,"abstract":"The appropriate setting of hyperparameter is a key factor to determine the performance of the deep learning model. Efficient hyperparametric optimization algorithm can not only improve the efficiency and speed of model hyperparametric optimization, but also reduce the application threshold of deep learning model. Therefore, we propose a parameter learning algorithm-based co-evolutionary for remote sensing scene classification. First, a co-evolution framework is proposed to optimize the optimizer’s hyperparameters and weight parameters of the convolutional neural networks (CNNs) simultaneously. Second, with the strategy of co-evolution with two populations, the hyperparameters can learn within the population and the weights of CNN can be updated by utilizing information between the populations. Finally, the parallel computing mechanism is adapted to speed up the learning process, as the two populations can evolve simultaneously. Extensive experiments on three public datasets demonstrate the effectiveness of the proposed approach.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"4 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131709200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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