Pub Date : 2021-10-06DOI: 10.1142/s0219691321500442
Hirofumi Hashimoto, T. Kinoshita
We are concerned with the orthonormal wavelet [Formula: see text] in the Hardy space [Formula: see text] which is a closed subspace of [Formula: see text] without negative frequency components. It is well known that there does not exist an [Formula: see text]-wavelet such that [Formula: see text] is continuous on [Formula: see text] and satisfies [Formula: see text] for some [Formula: see text]. The aim of this paper is to find a critical decay rate in the existing [Formula: see text]-wavelet under the condition that [Formula: see text] is continuous on [Formula: see text]. Moreover, we also construct a concrete [Formula: see text]-wavelet having infinite vanishing moments.
{"title":"On the construction of the orthonormal wavelet in the Hardy space H2(ℝ)","authors":"Hirofumi Hashimoto, T. Kinoshita","doi":"10.1142/s0219691321500442","DOIUrl":"https://doi.org/10.1142/s0219691321500442","url":null,"abstract":"We are concerned with the orthonormal wavelet [Formula: see text] in the Hardy space [Formula: see text] which is a closed subspace of [Formula: see text] without negative frequency components. It is well known that there does not exist an [Formula: see text]-wavelet such that [Formula: see text] is continuous on [Formula: see text] and satisfies [Formula: see text] for some [Formula: see text]. The aim of this paper is to find a critical decay rate in the existing [Formula: see text]-wavelet under the condition that [Formula: see text] is continuous on [Formula: see text]. Moreover, we also construct a concrete [Formula: see text]-wavelet having infinite vanishing moments.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"420 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":"115926825","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 : 2021-10-05DOI: 10.1142/s0219691321500454
Jaime Navarro, David Elizarraraz
The local convergence of the continuous shearlet transform (CST) in two dimensions is used to prove the local regularity of functions [Formula: see text]. Moreover, by means of the regularity theorem of distributions [Formula: see text] and the results for functions in [Formula: see text], the local regularity of distributions [Formula: see text] with compact support is also proved via the local convergence of any derivative of the CST.
{"title":"On the regularity of distributions via the convergence of the continuous shearlet transform in two dimensions","authors":"Jaime Navarro, David Elizarraraz","doi":"10.1142/s0219691321500454","DOIUrl":"https://doi.org/10.1142/s0219691321500454","url":null,"abstract":"The local convergence of the continuous shearlet transform (CST) in two dimensions is used to prove the local regularity of functions [Formula: see text]. Moreover, by means of the regularity theorem of distributions [Formula: see text] and the results for functions in [Formula: see text], the local regularity of distributions [Formula: see text] with compact support is also proved via the local convergence of any derivative of the CST.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125197621","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 : 2021-10-04DOI: 10.1142/s0219691321500545
Kuldoshbay Avazov, A. Abdusalomov, Mukhriddin Mukhiddinov, Nodirbek Baratov, Fazliddin Makhmudov, Y. Cho
{"title":"An improvement for the automatic classification method for ultrasound images used on CNN","authors":"Kuldoshbay Avazov, A. Abdusalomov, Mukhriddin Mukhiddinov, Nodirbek Baratov, Fazliddin Makhmudov, Y. Cho","doi":"10.1142/s0219691321500545","DOIUrl":"https://doi.org/10.1142/s0219691321500545","url":null,"abstract":"","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122468177","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 : 2021-10-02DOI: 10.1142/s0219691321500430
N. Chandra, K. Reddy, G. Sushanth, S. Sujatha
Agriculture is one of the primary occupations in many countries. Tomatoes are grown by many farmers in countries where the water resource is available in abundance. Improper methods of cultivation and failure to identify the diseases when it is in the nascent stage results in the reduction of crop yield thus affecting the outcome of cultivation. This paper proposes a novel method of early identification of diseases in tomato plants by making use of convolutional neural networks (CNN) and image processing. Dataset from an open repository was considered for training and testing and the algorithm was capable of identifying nine different varieties of diseases that affect the tomato plant at its early stages. The images of tomato leaves were fed for identification through processing and classification. An optimum model was developed by analyzing various architectures of CNN including the VGG, ResNet, Inception, Xception, MobileNet and DenseNet. The performance of each of these architectures was compared and various metrics like the accuracy, loss, precision, recall and area under the curve (AUC) were analyzed.
{"title":"A versatile approach based on convolutional neural networks for early identification of diseases in tomato plants","authors":"N. Chandra, K. Reddy, G. Sushanth, S. Sujatha","doi":"10.1142/s0219691321500430","DOIUrl":"https://doi.org/10.1142/s0219691321500430","url":null,"abstract":"Agriculture is one of the primary occupations in many countries. Tomatoes are grown by many farmers in countries where the water resource is available in abundance. Improper methods of cultivation and failure to identify the diseases when it is in the nascent stage results in the reduction of crop yield thus affecting the outcome of cultivation. This paper proposes a novel method of early identification of diseases in tomato plants by making use of convolutional neural networks (CNN) and image processing. Dataset from an open repository was considered for training and testing and the algorithm was capable of identifying nine different varieties of diseases that affect the tomato plant at its early stages. The images of tomato leaves were fed for identification through processing and classification. An optimum model was developed by analyzing various architectures of CNN including the VGG, ResNet, Inception, Xception, MobileNet and DenseNet. The performance of each of these architectures was compared and various metrics like the accuracy, loss, precision, recall and area under the curve (AUC) were analyzed.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129143888","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 : 2021-09-09DOI: 10.1142/s0219691321500417
Yimo Qin, Bin Zou, Jingjing Zeng, Zhifei Sheng, Lei Yin
In this paper, we consider the online regularized pairwise learning (ORPL) algorithm with least squares loss function for non-independently and identically distribution (non-i.i.d.) observations. We first establish new Bennett’s inequalities for [Formula: see text]-mixing sequence, geometrically [Formula: see text]-mixing sequence, [Formula: see text]-geometrically ergodic Markov chain and uniformly ergodic Markov chain. Then we establish the convergence rates for the last iterate of the ORPL algorithm with the polynomially decaying step sizes and varying regularization parameters for non-i.i.d. observations. These established results in this paper extend the previously known results of ORPL from i.i.d. observations to the case of non-i.i.d. observations, and the established result of ORPL for [Formula: see text]-mixing can be nearly optimal rate of ORPL for i.i.d. observations with [Formula: see text]-norm.
{"title":"Online regularized pairwise learning with non-i.i.d. observations","authors":"Yimo Qin, Bin Zou, Jingjing Zeng, Zhifei Sheng, Lei Yin","doi":"10.1142/s0219691321500417","DOIUrl":"https://doi.org/10.1142/s0219691321500417","url":null,"abstract":"In this paper, we consider the online regularized pairwise learning (ORPL) algorithm with least squares loss function for non-independently and identically distribution (non-i.i.d.) observations. We first establish new Bennett’s inequalities for [Formula: see text]-mixing sequence, geometrically [Formula: see text]-mixing sequence, [Formula: see text]-geometrically ergodic Markov chain and uniformly ergodic Markov chain. Then we establish the convergence rates for the last iterate of the ORPL algorithm with the polynomially decaying step sizes and varying regularization parameters for non-i.i.d. observations. These established results in this paper extend the previously known results of ORPL from i.i.d. observations to the case of non-i.i.d. observations, and the established result of ORPL for [Formula: see text]-mixing can be nearly optimal rate of ORPL for i.i.d. observations with [Formula: see text]-norm.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127487554","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 : 2021-09-09DOI: 10.1142/s0219691321500405
Yan Zhang, Yun‐Zhang Li
In wavelet analysis, refinable functions are the bases of extension principles for constructing (weak) dual wavelet frames for [Formula: see text] and its reducing subspaces. This paper addresses refinable function-based dual wavelet frames construction in Walsh reducing subspaces of [Formula: see text]. We obtain a Walsh–Fourier transform domain characterization for weak [Formula: see text]-adic nonhomogeneous dual wavelet frames; and present a mixed oblique extension principle for constructing weak [Formula: see text]-adic nonhomogeneous dual wavelet frames in Walsh reducing subspaces of [Formula: see text].
{"title":"Weak nonhomogeneous wavelet dual frames for Walsh reducing subspace of L2(ℝ+)","authors":"Yan Zhang, Yun‐Zhang Li","doi":"10.1142/s0219691321500405","DOIUrl":"https://doi.org/10.1142/s0219691321500405","url":null,"abstract":"In wavelet analysis, refinable functions are the bases of extension principles for constructing (weak) dual wavelet frames for [Formula: see text] and its reducing subspaces. This paper addresses refinable function-based dual wavelet frames construction in Walsh reducing subspaces of [Formula: see text]. We obtain a Walsh–Fourier transform domain characterization for weak [Formula: see text]-adic nonhomogeneous dual wavelet frames; and present a mixed oblique extension principle for constructing weak [Formula: see text]-adic nonhomogeneous dual wavelet frames in Walsh reducing subspaces of [Formula: see text].","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132977717","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 : 2021-08-30DOI: 10.1142/s0219691321500363
Lina Yang, Yang Liu, Huiwu Luo, Xichun Li, Y. Tang
The function of pseudoknots cannot be ignored in the RNA secondary structure. Existing methods for analyzing RNA secondary structures with pseudoknots exhibit many shortcomings. This paper presents a novel RNA secondary structure visualization method in the case of a joint analysis of RNA primary structures and secondary structures. The way is based on the page number representation of the RNA secondary structure. It innovatively uses five vectors to represent bases, which are sequentially connected to outline the characteristics of the RNA secondary structure. The method covers almost all the constituent elements of the RNA secondary structure and extracts features completely. Experiments are based on the available techniques for large-scale annotation of RNA secondary structures, using a combination method of discrete wavelet transform and fractal dimension. The classification effect is compared with the previous RNA secondary structure representation methods. Experimental results show that the RNA secondary structure visualization method proposed in this paper has good application prospects in RNA secondary structure classification.
{"title":"Visualization of RNA secondary structure with pseudoknots","authors":"Lina Yang, Yang Liu, Huiwu Luo, Xichun Li, Y. Tang","doi":"10.1142/s0219691321500363","DOIUrl":"https://doi.org/10.1142/s0219691321500363","url":null,"abstract":"The function of pseudoknots cannot be ignored in the RNA secondary structure. Existing methods for analyzing RNA secondary structures with pseudoknots exhibit many shortcomings. This paper presents a novel RNA secondary structure visualization method in the case of a joint analysis of RNA primary structures and secondary structures. The way is based on the page number representation of the RNA secondary structure. It innovatively uses five vectors to represent bases, which are sequentially connected to outline the characteristics of the RNA secondary structure. The method covers almost all the constituent elements of the RNA secondary structure and extracts features completely. Experiments are based on the available techniques for large-scale annotation of RNA secondary structures, using a combination method of discrete wavelet transform and fractal dimension. The classification effect is compared with the previous RNA secondary structure representation methods. Experimental results show that the RNA secondary structure visualization method proposed in this paper has good application prospects in RNA secondary structure classification.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"2008 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127309800","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 : 2021-08-11DOI: 10.1142/s0219691321500387
Chao Ma, Lijun Shen, Hao Deng, Jialin Li
It is well known that neurons communicate through synapses in the nervous system, and the size, morphology, and connectivity of synapses determine the functional properties of the neural network. Therefore, synapses have always been one of the key objects of neuroscience. Due to the technical advance in electron microscope (EM), the physical structure of synapses can be observed at high resolution. Nevbarheless, to date, the automatic analysis of the synapse in EM images is still a challenging task. In this paper, we proposed a fractal dimension-based segmentation method for synaptic clef of mouse cortex on EM image stack. Our method does not require a lot of groundtruth to train the model, and shows better adaptive anti-noise performance. That should be ascribed to the stability of segmentation-related key parameters in the data from same tissue. In this way, we only need to give initial values, and then gradually adjust these key parameters. Experiments reveal that our method achieves the desired results, and reduces the time in artificial annotating, so that researchers can focus more on the analysis of segmentation results.
{"title":"Synaptic clef segmentation method based on fractal dimension for ATUM-SEM image of mouse cortex","authors":"Chao Ma, Lijun Shen, Hao Deng, Jialin Li","doi":"10.1142/s0219691321500387","DOIUrl":"https://doi.org/10.1142/s0219691321500387","url":null,"abstract":"It is well known that neurons communicate through synapses in the nervous system, and the size, morphology, and connectivity of synapses determine the functional properties of the neural network. Therefore, synapses have always been one of the key objects of neuroscience. Due to the technical advance in electron microscope (EM), the physical structure of synapses can be observed at high resolution. Nevbarheless, to date, the automatic analysis of the synapse in EM images is still a challenging task. In this paper, we proposed a fractal dimension-based segmentation method for synaptic clef of mouse cortex on EM image stack. Our method does not require a lot of groundtruth to train the model, and shows better adaptive anti-noise performance. That should be ascribed to the stability of segmentation-related key parameters in the data from same tissue. In this way, we only need to give initial values, and then gradually adjust these key parameters. Experiments reveal that our method achieves the desired results, and reduces the time in artificial annotating, so that researchers can focus more on the analysis of segmentation results.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130723743","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 : 2021-07-31DOI: 10.1142/s0219691321500272
M. Bahri, A. K. Amir, R. Ashino
This paper deals with the linear canonical wavelet transform. It is a non-trivial generalization of the ordinary wavelet transform in the framework of the linear canonical transform. We first present a direct relationship between the linear canonical wavelet transform and ordinary wavelet transform. Based on the relation, we provide an alternative proof of the orthogonality relation for the linear canonical wavelet transform. Some of its essential properties are also studied in detail. Finally, we explicitly derive several versions of inequalities associated with the linear canonical wavelet transform.
{"title":"Linear canonical wavelet transform: Properties and inequalities","authors":"M. Bahri, A. K. Amir, R. Ashino","doi":"10.1142/s0219691321500272","DOIUrl":"https://doi.org/10.1142/s0219691321500272","url":null,"abstract":"This paper deals with the linear canonical wavelet transform. It is a non-trivial generalization of the ordinary wavelet transform in the framework of the linear canonical transform. We first present a direct relationship between the linear canonical wavelet transform and ordinary wavelet transform. Based on the relation, we provide an alternative proof of the orthogonality relation for the linear canonical wavelet transform. Some of its essential properties are also studied in detail. Finally, we explicitly derive several versions of inequalities associated with the linear canonical wavelet transform.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127875477","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 : 2021-07-26DOI: 10.1142/s0219691321500375
Haoyang Cheng, Wenquan Cui
Heteroscedasticity often appears in the high-dimensional data analysis. In order to achieve a sparse dimension reduction direction for high-dimensional data with heteroscedasticity, we propose a new sparse sufficient dimension reduction method, called Lasso-PQR. From the candidate matrix derived from the principal quantile regression (PQR) method, we construct a new artificial response variable which is made up from top eigenvectors of the candidate matrix. Then we apply a Lasso regression to obtain sparse dimension reduction directions. While for the “large [Formula: see text] small [Formula: see text]” case that [Formula: see text], we use principal projection to solve the dimension reduction problem in a lower-dimensional subspace and projection back to the original dimension reduction problem. Theoretical properties of the methodology are established. Compared with several existing methods in the simulations and real data analysis, we demonstrate the advantages of our method in the high dimension data with heteroscedasticity.
{"title":"Sparse sufficient dimension reduction with heteroscedasticity","authors":"Haoyang Cheng, Wenquan Cui","doi":"10.1142/s0219691321500375","DOIUrl":"https://doi.org/10.1142/s0219691321500375","url":null,"abstract":"Heteroscedasticity often appears in the high-dimensional data analysis. In order to achieve a sparse dimension reduction direction for high-dimensional data with heteroscedasticity, we propose a new sparse sufficient dimension reduction method, called Lasso-PQR. From the candidate matrix derived from the principal quantile regression (PQR) method, we construct a new artificial response variable which is made up from top eigenvectors of the candidate matrix. Then we apply a Lasso regression to obtain sparse dimension reduction directions. While for the “large [Formula: see text] small [Formula: see text]” case that [Formula: see text], we use principal projection to solve the dimension reduction problem in a lower-dimensional subspace and projection back to the original dimension reduction problem. Theoretical properties of the methodology are established. Compared with several existing methods in the simulations and real data analysis, we demonstrate the advantages of our method in the high dimension data with heteroscedasticity.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134010880","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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