发布求助
文献互助 智能选刊 最新文献

2015 International Conference on Sampling Theory and Applications (SampTA)最新文献

筛选
英文 中文
Bivariate splines in piecewise constant tension 分段恒张力的二元样条曲线
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148901
Kunimitsu Takahashi, M. Kamada
{"title":"Bivariate splines in piecewise constant tension","authors":"Kunimitsu Takahashi, M. Kamada","doi":"10.1109/SAMPTA.2015.7148901","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148901","url":null,"abstract":"An extension of the bivariate cubic spline on the uniform grid is derived in this paper to have different tensions in different square cells of the grid. The resulting function can be interpreted also as a bivariate extension of the univariate spline in piecewise constant tension which was applied to adaptive interpolation of digital images for their magnification and rotation. The bivariate function will hopefully make it possible to magnify and rotate images better and even to deform images into any shapes. A locally supported basis, which is crucial for the practical use of the bivariate functions, has not been constructed at the moment and its construction is left for the next step of study.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"20 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":"114810189","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
On boundedness inequalities of some semi-discrete operators in connection with sampling operators 一类半离散算子与抽样算子的有界性不等式
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148848
A. Kivinukk, Tarmo Metsmagi
{"title":"On boundedness inequalities of some semi-discrete operators in connection with sampling operators","authors":"A. Kivinukk, Tarmo Metsmagi","doi":"10.1109/SAMPTA.2015.7148848","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148848","url":null,"abstract":"The main aim of this paper is to study some boundedness inequalities of certain semi-discrete operators. These operators allow to unify some inequalities for both the Shannon sampling operators and Kantorovich-type operators.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"30 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":"114863766","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: 6
Phase retrieval without small-ball probability assumptions: Recovery guarantees for phaselift 无小球概率假设的相位恢复:相位提升的恢复保证
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148966
F. Krahmer, Yi-Kai Liu
{"title":"Phase retrieval without small-ball probability assumptions: Recovery guarantees for phaselift","authors":"F. Krahmer, Yi-Kai Liu","doi":"10.1109/SAMPTA.2015.7148966","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148966","url":null,"abstract":"We study the problem of recovering an unknown vector x ε R<sup>n</sup> from measurements of the form y<sub>i</sub> = |a<sup>T</sup><sub>i</sub> x|<sup>2</sup> (for i = 1,..., m), where the vectors a<sub>i</sub> ε R<sup>n</sup> are chosen independently at random, with each coordinate a<sub>ij</sub> ε R being chosen independently from a fixed sub-Gaussian distribution D. However, without making additional assumptions on the random variables a<sub>ij</sub> - for example on the behavior of their small ball probabilities - it may happen some vectors x cannot be uniquely recovered. We show that for any sub-Gaussian distribution V, with no additional assumptions, it is still possible to recover most vectors x. More precisely, one can recover those vectors x that are not too peaky in the sense that at most a constant fraction of their mass is concentrated on any one coordinate. The recovery guarantees in this paper are for the PhaseLift algorithm, a tractable convex program based on a matrix formulation of the problem. We prove uniform recovery of all not too peaky vectors from m = 0(n) measurements, in the presence of noise. This extends previous work on PhaseLift by Candès and Li [8].","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"34 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":"124940169","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: 2
On a lower bound for a periodic uncertainty constant 周期不确定常数的下界
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148964
E. Lebedeva
{"title":"On a lower bound for a periodic uncertainty constant","authors":"E. Lebedeva","doi":"10.1109/SAMPTA.2015.7148964","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148964","url":null,"abstract":"An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A formula connecting uncertainty constants for periodic and non-periodic functions is extended to this class.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"27 5 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":"122127159","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: 0
Nonuniform sparse recovery with random convolutions 随机卷积的非均匀稀疏恢复
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148845
David James, H. Rauhut
{"title":"Nonuniform sparse recovery with random convolutions","authors":"David James, H. Rauhut","doi":"10.1109/SAMPTA.2015.7148845","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148845","url":null,"abstract":"We discuss the use of random convolutions for Compressed Sensing applications. In particular, we will show that after convolving an N-dimensional, s-sparse signal with a Rademacher or Steinhaus sequence, it can be recovered via l1-minimization using only m ≳ s log(N/ε) arbitrary chosen samples with probability at least 1 - ε.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"22 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":"122132755","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: 2
A novel geometric multiscale approach to structured dictionary learning on high dimensional data 高维数据结构化字典学习的一种新的几何多尺度方法
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148961
Guangliang Chen
{"title":"A novel geometric multiscale approach to structured dictionary learning on high dimensional data","authors":"Guangliang Chen","doi":"10.1109/SAMPTA.2015.7148961","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148961","url":null,"abstract":"Adaptive dictionary learning has become a hot-topic research field during the past decade. Though several algorithms have been proposed and achieved impressive results, they are all computationally intensive due to the lack of structure in their output dictionaries. In this paper we build upon our previous work and take a geometric approach to develop better, more efficient algorithms that can learn adaptive structured dictionaries. While inheriting many of the advantages in the previous construction, the new algorithm better utilizes the geometry of data and effectively removes translational invariances from the data, thus able to produce smaller, more robust dictionaries. We demonstrate the performance of the new algorithm on two data sets, and conclude the paper by a discussion of future work.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"22 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":"125568177","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: 0
From paley graphs to deterministic sensing matrices with real-valued Gramians 从paley图到具有实值gramn的确定性感知矩阵
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148915
A. Amini, Hamed Bagh-Sheikhi, F. Marvasti
{"title":"From paley graphs to deterministic sensing matrices with real-valued Gramians","authors":"A. Amini, Hamed Bagh-Sheikhi, F. Marvasti","doi":"10.1109/SAMPTA.2015.7148915","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148915","url":null,"abstract":"The performance guarantees in recovery of a sparse vector in a compressed sensing scenario, besides the reconstruction technique, depends on the choice of the sensing matrix. The so-called restricted isometry property (RIP) is one of the well-used tools to determine and compare the performance of various sensing matrices. It is a standard result that random (Gaussian) matrices satisfy RIP with high probability. However, the design of deterministic matrices that satisfy RIP has been a great challenge for many years now. The common design technique is through the coherence value (maximum modulus correlation between the columns). In this paper, based on the Paley graphs, we introduce deterministic matrices of size q+1/2 × q with q a prime power, such that the corresponding Gram matrix is real-valued. We show that the coherence of these matrices are less than twice the Welch bound, which is a lower bound valid for general matrices. It should be mentioned that the introduced matrix differs from the equiangular tight frame (ETF) of size q-1/2 × q arising from the Paley difference set.","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":"129334422","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: 6
Compressibility of symmetric-α-stable processes 对称-α-稳定过程的可压缩性
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148887
J. P. Ward, J. Fageot, M. Unser
{"title":"Compressibility of symmetric-α-stable processes","authors":"J. P. Ward, J. Fageot, M. Unser","doi":"10.1109/SAMPTA.2015.7148887","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148887","url":null,"abstract":"Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. First, we characterize the Besov regularity of SαS processes. Then the n-term approximation rates follow. To capture the local smoothness behavior, we consider sparse processes defined on the circle that are solutions of stochastic differential equations.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"43 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":"123764416","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: 4
Blind compressed sensing using sparsifying transforms 使用稀疏化变换的盲压缩感知
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148944
S. Ravishankar, Y. Bresler
{"title":"Blind compressed sensing using sparsifying transforms","authors":"S. Ravishankar, Y. Bresler","doi":"10.1109/SAMPTA.2015.7148944","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148944","url":null,"abstract":"Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct both the image and the transform from highly undersampled measurements. The proposed block coordinate descent type algorithm involves efficient updates. Importantly, we prove that although the proposed formulation is highly nonconvex, our algorithm converges to the set of critical points of the objective defining the formulation. We illustrate the promise of the proposed framework for magnetic resonance image reconstruction from highly undersampled k-space measurements. As compared to previous methods involving fixed sparsifying transforms, or adaptive synthesis dictionaries, our approach is much faster, while also providing promising image reconstructions.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"99 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":"127346729","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: 8
On random and deterministic compressed sensing and the Restricted Isometry Property in levels 关于随机和确定性压缩感知及层次上的受限等距特性
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148900
Alexander Bastounis, A. Hansen
{"title":"On random and deterministic compressed sensing and the Restricted Isometry Property in levels","authors":"Alexander Bastounis, A. Hansen","doi":"10.1109/SAMPTA.2015.7148900","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148900","url":null,"abstract":"Compressed sensing (CS) is one of the great successes of computational mathematics in the past decade. There are a collection of tools which aim to mathematically describe compressed sensing when the sampling pattern is taken in a random or deterministic way. Unfortunately, there are many practical applications where the well studied concepts of uniform recovery and the Restricted Isometry Property (RIP) can be shown to be insufficient explanations for the success of compressed sensing. This occurs both when the sampling pattern is taken using a deterministic or a non-deterministic method. We shall study this phenomenon and explain why the RIP is absent, and then propose an adaptation which we term `the RIP in levels' which aims to solve the issues surrounding the RIP. The paper ends by conjecturing that the RIP in levels could provide a collection of results for deterministic sampling patterns.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"189 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":"133865485","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: 6
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信