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Graph theoretic uncertainty principles 图论测不准原理
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148912
J. Benedetto, Paul J. Koprowski
{"title":"Graph theoretic uncertainty principles","authors":"J. Benedetto, Paul J. Koprowski","doi":"10.1109/SAMPTA.2015.7148912","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148912","url":null,"abstract":"We develop a graph theoretic set of uncertainty principles with tight bounds for difference estimators acting simultaneously in the graph domain and the frequency domain. We show that the eigenfunctions of a modified graph Laplacian operator dictate the upper and lower bounds for the inequalities.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122637541","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}
引用次数: 17
Cardinal sine series: Oversampling and non-existence 基数正弦级数:过采样和不存在性
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148842
B. A. Bailey, W. Madych
{"title":"Cardinal sine series: Oversampling and non-existence","authors":"B. A. Bailey, W. Madych","doi":"10.1109/SAMPTA.2015.7148842","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148842","url":null,"abstract":"Growth conditions are given on the samples f(n), n = 0, ±1, ±2, ..., of an entire function f(z) of exponential type less than π that imply that the corresponding cardinal sine series converges. These conditions are the least restrictive of their kind that are possible. Furthermore, an example is provided of an entire function f(z) of exponential type π that is bounded on the real axis and whose corresponding cardinal sine series fails to converge.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121423090","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}
引用次数: 1
The dual frame induced by an invertible frame multiplier 由可逆帧乘法器诱导的双帧
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148859
Diana T. Stoeva, P. Balázs
{"title":"The dual frame induced by an invertible frame multiplier","authors":"Diana T. Stoeva, P. Balázs","doi":"10.1109/SAMPTA.2015.7148859","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148859","url":null,"abstract":"The inverse of an invertible frame multiplier can be represented as a multiplier with reciprocal symbol and sequences dual to the original frames. One of the duals is unique with the property that the other one can be arbitrarily chosen, which is shown in this paper for several cases. We also show when the dual induced by the invertible frame multiplier is the canonical dual and when it has the same structure as the original dual.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114787384","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}
引用次数: 12
Sampling and recovery using multiquadrics 使用多重二次抽样和恢复
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148864
Keaton Hamm
{"title":"Sampling and recovery using multiquadrics","authors":"Keaton Hamm","doi":"10.1109/SAMPTA.2015.7148864","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148864","url":null,"abstract":"We survey recent results in the subject of interpolating bandlimited functions from their samples at both uniform and nonuniform sets via translates of a family of multiquadrics. Recovery of the original function is considered by means of a limiting process which changes a shape parameter associated with the multiquadric function. We also discuss some ways in which approximation rates can be found as well as extensions of the results to interpolation schemes which use other radial basis functions.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127682753","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}
引用次数: 3
A general approach for convergence analysis of adaptive sampling-based signal processing 基于自适应采样的信号处理收敛分析的一般方法
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148882
H. Boche, U. Monich
{"title":"A general approach for convergence analysis of adaptive sampling-based signal processing","authors":"H. Boche, U. Monich","doi":"10.1109/SAMPTA.2015.7148882","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148882","url":null,"abstract":"It is well-known that there exist bandlimited signals for which certain sampling series are divergent. One possible way of circumventing the divergence is to adapt the sampling series to the signals. In this paper we study adaptivity in the number of summands that are used in each approximation step, and whether this kind of adaptive signal processing can improve the convergence behavior of the sampling series. We approach the problem by considering approximation processes in general Banach spaces and show that adaptivity reduces the set of signals with divergence from a residual set to a meager or empty set. Due to the non-linearity of the adaptive approximation process, this study cannot be done by using the Banach-Steinhaus theory. We present examples from sampling based signal processing, where recently strong divergence, which is connected to the effectiveness of adaptive signal processing, has been observed.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115783369","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}
引用次数: 3
Regular operator sampling for parallelograms 平行四边形的正则算子抽样
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148847
G. Pfander, D. Walnut
{"title":"Regular operator sampling for parallelograms","authors":"G. Pfander, D. Walnut","doi":"10.1109/SAMPTA.2015.7148847","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148847","url":null,"abstract":"Operator sampling considers the question of when operators of a given class can be distinguished by their action on a single probing signal. The fundamental result in this theory shows that the answer depends on the area of the support S of the so-called spreading function of the operator (i.e., the symplectic Fourier transform of its Kohn-Nirenberg symbol). |S| <; 1 then identification is possible and when |S| > 1 it is impossible. In the critical case when |S| = 1, the picture is less clear. In this paper we characterize when regular operator sampling (that is, when the probing signal is a periodically-weighted delta train) is possible when S is a parallelogram of area 1.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121650926","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}
引用次数: 1
Analysis of generalized ridge functions in high dimensions 高维广义脊函数的分析
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148892
Sandra Keiper
{"title":"Analysis of generalized ridge functions in high dimensions","authors":"Sandra Keiper","doi":"10.1109/SAMPTA.2015.7148892","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148892","url":null,"abstract":"The approximation of functions in many variables suffers from the so-called “curse of dimensionality”. Namely, functions on RN with smoothness of order s can be recovered at most with an accuracy of n-s/N applying n-dimensional spaces for linear or nonlinear approximation. However, there is a common belief that functions arising as solutions of real world problems have more structure than usual TV-variate functions. This has led to the introduction of different models for those functions. One of the most popular models is that of so-called ridge functions, which are of the form RN ⊇ Ω ∋ x → f(x) = g(Ax) (1) where A ε Rm, N is a matrix and m is considerably smaller than N. The approximation of such functions was for example studied in [1], [2], [3], and [4]. However, by considering functions of the form (1), we assume that real world problems can be described by functions that are constant along certain linear subspaces. Such assumption is quite restrictive and we, therefore, want to study a more generalized form of ridge functions, namely functions which are constant along certain submanifolds of R. Hence, we introduce the notion of generalized ridge functions, which are defined to be functions of the form RN ∋ x → f(x) = g(dist(x, M)), (2) where M is a d-dimensional, smooth submanifold of RN and g ε Cs(R). Note that if M is an (N-1)-dimensional, affine subspace of RN and we consider the signed distance in equation (2), we indeed have the case of a usual ridge function. We will analyze how the methods to approximate usual ridge functions apply to generalized ridge functions and investigate new algorithms for their approximation.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125480622","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}
引用次数: 7
Aperiodic geometry design for DOA estimation using compressive sensing 基于压缩感知的DOA估计非周期几何设计
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148942
S. Z. Asghar, B. Ng
{"title":"Aperiodic geometry design for DOA estimation using compressive sensing","authors":"S. Z. Asghar, B. Ng","doi":"10.1109/SAMPTA.2015.7148942","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148942","url":null,"abstract":"Antenna arrays used in compressive sensing based DOA estimation algorithms are generated randomly to minimize mutual coherence. This scheme suffers from practical limitations. For an antenna array that is sufficiently random, some elements of the array would almost always fall very close to each other, which is not practicable. Rectangular arrays, although very uniform and practicable, suffer from poor performance when used in compressive sensing algorithms that assume spatial sparsity. Aperiodic arrays seem to offer a compromise solution. This paper demonstrates that it is possible to design aperiodic antenna array by using a simple disturbance optimization scheme, that can be applied to multiple aperiodic array geometries. The optimization scheme uses a few parameters to generate an aperiodic geometry. We will also see that the optimized aperiodic array has better performance than several other geometries studied in this paper and performs very close to random array configuration.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"1028 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123128529","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}
引用次数: 1
Weaving properties of Hilbert space frames 希尔伯特空间框架的编织特性
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148861
P. Casazza, Richard G. Lynch
{"title":"Weaving properties of Hilbert space frames","authors":"P. Casazza, Richard G. Lynch","doi":"10.1109/SAMPTA.2015.7148861","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148861","url":null,"abstract":"We will prove some new results in the theory of Weaving Frames. Two frames {φi}iεI and {Ψ<sub>i</sub>}iεI in a Hilbert space H are woven if there are constants 0 <; A ≤ B so that for every subset σ ⊂ I, the family {φ<sub>i</sub>}<sub>iεσ</sub> ∪ {ψ<sub>i</sub>}<sub>iεσc</sub> is a frame for H with frame bounds A, B. We begin by introducing the main results in weaving frames. We then prove some new basic properties. This is followed by showing a fundamental connection between frames and projections, providing intuition on woven frames. Finally, a weaving equivalent of an unconditional basis for weaving Riesz bases is considered.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123414865","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}
引用次数: 58
Eigenvector localization on data-dependent graphs 数据依赖图的特征向量定位
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148963
A. Cloninger, W. Czaja
{"title":"Eigenvector localization on data-dependent graphs","authors":"A. Cloninger, W. Czaja","doi":"10.1109/SAMPTA.2015.7148963","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148963","url":null,"abstract":"We aim to understand and characterize embeddings of datasets with small anomalous clusters using the Laplacian Eigenmaps algorithm. To do this, we characterize the order in which eigenvectors of a disjoint graph Laplacian emerge and the support of those eigenvectors. We then extend this characterization to weakly connected graphs with clusters of differing sizes, utilizing the theory of invariant subspace perturbations and proving some novel results. Finally, we propose a simple segmentation algorithm for anomalous clusters based off our theory.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114991195","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}
引用次数: 3
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