Pub Date : 2022-03-07DOI: 10.1142/s0219691322500059
F. Shah, Huzaifa L. Qadri, Waseem Z. Lone
{"title":"Free metaplectic wavelet transform in L2(ℝn)","authors":"F. Shah, Huzaifa L. Qadri, Waseem Z. Lone","doi":"10.1142/s0219691322500059","DOIUrl":"https://doi.org/10.1142/s0219691322500059","url":null,"abstract":"","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125046776","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 : 2022-03-07DOI: 10.1142/s0219691322500072
L. K. Vashisht
{"title":"Duality for matrix-valued wave packet frames in L2(ℝd, ℂs×r)","authors":"L. K. Vashisht","doi":"10.1142/s0219691322500072","DOIUrl":"https://doi.org/10.1142/s0219691322500072","url":null,"abstract":"","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129851532","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 : 2022-02-20DOI: 10.1142/s0219691322500084
Youngmi Hur
Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any prescribed directions. There are two types of wavelet filters in our tight wavelet filter bank. One type is entirely determined by the prescribed information about the directionality and makes the wavelet filter bank directional. The other type helps the wavelet filter bank to be tight. In addition to the flexibility in choosing the directions, our construction method has other useful properties. It works for any multidimension, and it allows the user to have any prescribed number of vanishing moments along the chosen directions. Furthermore, our tight wavelet filter banks have fast algorithms for analysis and synthesis. Concrete examples are given to illustrate our construction method and properties of resulting tight wavelet filter banks.
{"title":"Tight Wavelet Filter Banks with Prescribed Directions","authors":"Youngmi Hur","doi":"10.1142/s0219691322500084","DOIUrl":"https://doi.org/10.1142/s0219691322500084","url":null,"abstract":"Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any prescribed directions. There are two types of wavelet filters in our tight wavelet filter bank. One type is entirely determined by the prescribed information about the directionality and makes the wavelet filter bank directional. The other type helps the wavelet filter bank to be tight. In addition to the flexibility in choosing the directions, our construction method has other useful properties. It works for any multidimension, and it allows the user to have any prescribed number of vanishing moments along the chosen directions. Furthermore, our tight wavelet filter banks have fast algorithms for analysis and synthesis. Concrete examples are given to illustrate our construction method and properties of resulting tight wavelet filter banks.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114994084","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 : 2022-02-11DOI: 10.1142/s0219691322500540
Guanglong Xu, Zhensheng Hu, Jia Cai
Zero-shot sketch-based image retrieval (ZSSBIR), as a popular studied branch of computer vision, attracts wide attention recently. Unlike sketch-based image retrieval (SBIR), the main aim of ZSSBIR is to retrieve natural images given free hand-drawn sketches that may not appear during training. Previous approaches used semantic aligned sketch-image pairs or utilized memory expensive fusion layer for projecting the visual information to a low dimensional subspace, which ignores the significant heterogeneous cross-domain discrepancy between highly abstract sketch and relevant image. This may yield poor performance in the training phase. To tackle this issue and overcome this drawback, we propose a Wasserstein distance based cross-modal semantic network (WAD-CMSN) for ZSSBIR. Specifically, it first projects the visual information of each branch (sketch, image) to a common low dimensional semantic subspace via Wasserstein distance in an adversarial training manner. Furthermore, identity matching loss is employed to select useful features, which can not only capture complete semantic knowledge, but also alleviate the over-fitting phenomenon caused by the WAD-CMSN model. Experimental results on the challenging Sketchy (Extended) and TU-Berlin (Extended) datasets indicate the effectiveness of the proposed WAD-CMSN model over several competitors.
{"title":"WAD-CMSN: Wasserstein Distance based Cross-Modal Semantic Network for Zero-Shot Sketch-Based Image Retrieval","authors":"Guanglong Xu, Zhensheng Hu, Jia Cai","doi":"10.1142/s0219691322500540","DOIUrl":"https://doi.org/10.1142/s0219691322500540","url":null,"abstract":"Zero-shot sketch-based image retrieval (ZSSBIR), as a popular studied branch of computer vision, attracts wide attention recently. Unlike sketch-based image retrieval (SBIR), the main aim of ZSSBIR is to retrieve natural images given free hand-drawn sketches that may not appear during training. Previous approaches used semantic aligned sketch-image pairs or utilized memory expensive fusion layer for projecting the visual information to a low dimensional subspace, which ignores the significant heterogeneous cross-domain discrepancy between highly abstract sketch and relevant image. This may yield poor performance in the training phase. To tackle this issue and overcome this drawback, we propose a Wasserstein distance based cross-modal semantic network (WAD-CMSN) for ZSSBIR. Specifically, it first projects the visual information of each branch (sketch, image) to a common low dimensional semantic subspace via Wasserstein distance in an adversarial training manner. Furthermore, identity matching loss is employed to select useful features, which can not only capture complete semantic knowledge, but also alleviate the over-fitting phenomenon caused by the WAD-CMSN model. Experimental results on the challenging Sketchy (Extended) and TU-Berlin (Extended) datasets indicate the effectiveness of the proposed WAD-CMSN model over several competitors.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"1103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116052433","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 : 2021-12-15DOI: 10.1142/s0219691321500594
Zhihua Zhang
Frequency domain of bandlimited frame multiresolution analyses (MRAs) plays a key role when derived framelets are applied into narrow-band signal processing and data analysis. In this study, we give a characterization of frequency domain of weakly translation invariant frame scaling functions [Formula: see text] with frequency domain [Formula: see text]. Based on it, we further study convex and ball-shaped frequency domains. If frequency domain of bandlimited frame scaling function [Formula: see text] is convex and completely symmetric about the origin, then it must be weakly invariant and [Formula: see text]. If [Formula: see text] has a ball-shaped frequency domain, the ball radius must be bounded by [Formula: see text]. These frequency domain characters are owned uniquely by frame scaling functions and not by orthogonal scaling functions.
{"title":"Frequency domain of weakly translation invariant frame MRAs","authors":"Zhihua Zhang","doi":"10.1142/s0219691321500594","DOIUrl":"https://doi.org/10.1142/s0219691321500594","url":null,"abstract":"Frequency domain of bandlimited frame multiresolution analyses (MRAs) plays a key role when derived framelets are applied into narrow-band signal processing and data analysis. In this study, we give a characterization of frequency domain of weakly translation invariant frame scaling functions [Formula: see text] with frequency domain [Formula: see text]. Based on it, we further study convex and ball-shaped frequency domains. If frequency domain of bandlimited frame scaling function [Formula: see text] is convex and completely symmetric about the origin, then it must be weakly invariant and [Formula: see text]. If [Formula: see text] has a ball-shaped frequency domain, the ball radius must be bounded by [Formula: see text]. These frequency domain characters are owned uniquely by frame scaling functions and not by orthogonal scaling functions.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126694565","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 : 2021-12-04DOI: 10.1142/s0219691321500582
Hengjie Chen, Zhong Li
By applying fundamental mathematical knowledge, this paper proves that the function [Formula: see text] is an integer no less than [Formula: see text] has the property that the difference between the function value of middle point of arbitrarily two adjacent equidistant distribution nodes on [Formula: see text] and the mean of function values of these two nodes is a constant depending only on the number of nodes if and only if [Formula: see text] By them, we establish an important result about deep neural networks that the function [Formula: see text] can be interpolated by a deep Rectified Linear Unit (ReLU) network with depth [Formula: see text] on the equidistant distribution nodes in interval [Formula: see text] and the error of approximation is [Formula: see text] Then based on the main result that has just been proven and the Chebyshev orthogonal polynomials, we construct a deep network and give the error estimate of approximation to polynomials and continuous functions, respectively. In addition, this paper constructs one deep network with local sparse connections, shared weights and activation function [Formula: see text] and discusses its density and complexity.
{"title":"A note on the applications of one primary function in deep neural networks","authors":"Hengjie Chen, Zhong Li","doi":"10.1142/s0219691321500582","DOIUrl":"https://doi.org/10.1142/s0219691321500582","url":null,"abstract":"By applying fundamental mathematical knowledge, this paper proves that the function [Formula: see text] is an integer no less than [Formula: see text] has the property that the difference between the function value of middle point of arbitrarily two adjacent equidistant distribution nodes on [Formula: see text] and the mean of function values of these two nodes is a constant depending only on the number of nodes if and only if [Formula: see text] By them, we establish an important result about deep neural networks that the function [Formula: see text] can be interpolated by a deep Rectified Linear Unit (ReLU) network with depth [Formula: see text] on the equidistant distribution nodes in interval [Formula: see text] and the error of approximation is [Formula: see text] Then based on the main result that has just been proven and the Chebyshev orthogonal polynomials, we construct a deep network and give the error estimate of approximation to polynomials and continuous functions, respectively. In addition, this paper constructs one deep network with local sparse connections, shared weights and activation function [Formula: see text] and discusses its density and complexity.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134316912","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 : 2021-11-29DOI: 10.1142/s0219691321500600
Anis Zeglaoui, A. Mabrouk, O. Kravchenko
{"title":"Wavelet neural networks functional approximation and application","authors":"Anis Zeglaoui, A. Mabrouk, O. Kravchenko","doi":"10.1142/s0219691321500600","DOIUrl":"https://doi.org/10.1142/s0219691321500600","url":null,"abstract":"","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120881582","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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