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

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Polarization based phase retrieval for time-frequency structured measurements 基于极化的时频结构测量相位反演
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148877
Palina Salanevich, G. Pfander
{"title":"Polarization based phase retrieval for time-frequency structured measurements","authors":"Palina Salanevich, G. Pfander","doi":"10.1109/SAMPTA.2015.7148877","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148877","url":null,"abstract":"We consider phaseless measurements in the case when the measurement frame is a Gabor frame, that is, the frame coefficients are of the form of masked Fourier coefficients where the masks are time shifts of the Gabor window. This makes measurements meaningful for applications, but at the same time preserves the flexibility of the frame-theoretic approach. We are going to present a recovery algorithm which requires a sufficiently small number of measurements; it is based on the idea of polarization, which is proposed by Alexeev, Bandeira, Fickus and Mixon [1], [4].","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"11 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":"116797753","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
Maximally concentrated signals in the special affine fourier transformation domain 在特殊仿射傅里叶变换域中的最大集中信号
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148841
A. Zayed
{"title":"Maximally concentrated signals in the special affine fourier transformation domain","authors":"A. Zayed","doi":"10.1109/SAMPTA.2015.7148841","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148841","url":null,"abstract":"The problem of maximizing the energy of a signal bandlimited to E<sub>1</sub> = [-σ, σ] on an interval T<sub>1</sub> = [-τ, τ] in the time domain, which is called the energy concentration problem, was solved by a group of mathematicians, D. Slepian, H. Landau, and H. Pollak, at Bell Labs in the 1960s. The goal of this article is to solve the energy concentration problem for the n-dimensional special affine Fourier transformation which includes the Fourier transform, the fractional Fourier transform, the Lorentz transform, the Fresnel transform, and the linear canonical transform (LCT) as special cases. The solution in dimensions higher than one is more challenging because the solution depends on the geometry of the two sets E<sub>1</sub> and T<sub>1</sub>. We outline the solution in the cases where E<sub>1</sub> and T<sub>1</sub> are n dimensional hyper-rectangles and discs.","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":"116958188","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
Dictionary-sparse and disjointed recovery 字典稀疏和不连贯的恢复
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148896
Tom Needham
{"title":"Dictionary-sparse and disjointed recovery","authors":"Tom Needham","doi":"10.1109/SAMPTA.2015.7148896","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148896","url":null,"abstract":"We consider recovery of signals whose coefficient vectors with respect to a redundant dictionary are simultaneously sparse and disjointed - such signals are referred to as analysis-sparse and analysis-disjointed. We determine the order of a sufficient number of linear measurements needed to recover such signals via an iterative hard thresholding algorithm. The sufficient number of measurements compares with the sufficient number of measurements from which one may recover a classical sparse and disjointed vector. We then consider approximately analysis-sparse and analysis-disjointed signals and obtain the order of sufficient number of measurements in that scenario as well.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"197 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":"115575654","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
Stable nonuniform sampling with weighted Fourier frames and recovery in arbitrary spaces 具有加权傅里叶帧的稳定非均匀采样及其在任意空间中的恢复
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148860
B. Adcock, M. Gataric, A. Hansen
{"title":"Stable nonuniform sampling with weighted Fourier frames and recovery in arbitrary spaces","authors":"B. Adcock, M. Gataric, A. Hansen","doi":"10.1109/SAMPTA.2015.7148860","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148860","url":null,"abstract":"We present recently devised approach for recovery of compactly supported multivariate functions from nonuniform samples of their Fourier transforms. This is the so-called nonuniform generalized sampling (NUGS), based on a generalized sampling framework which permits an arbitrary choice of the reconstruction space and where nonuniform sampling is modeled via weighted Fourier frames. We establish a sharp sampling density which is sufficient to guarantee stable recovery, without imposing any separation condition on the sampling points. In particular for the stable NUGS recovery, we also provide sufficient sampling bandwidths in the case of one-dimensional wavelet reconstructions and show sufficient linear scaling of the sampling bandwidth and the number of wavelets.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"3 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":"122905570","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
Balayage and pseudo-differential operator frame inequalities Balayage和伪微分算子坐标系不等式
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148956
Enrico Au-Yeung, J. Benedetto
{"title":"Balayage and pseudo-differential operator frame inequalities","authors":"Enrico Au-Yeung, J. Benedetto","doi":"10.1109/SAMPTA.2015.7148956","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148956","url":null,"abstract":"Using his formulation of the potential theoretic notion of balayage and his deep results about this idea, Beurling gave sufficient conditions for Fourier frames in terms of balayage. The analysis makes use of spectral synthesis, due to Wiener and Beurling, as well as properties of strict multiplicity, whose origins go back to Riemann. In this setting and with this technology, with the goal of formulating non-uniform sampling formulas, we show how to construct frames using pseudo-differential operators. This work fits within the context of the short time Fourier transform (STFT) and time-frequency analysis.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"413 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":"125057418","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
On the existence of equivalence class of RIP-compliant matrices 关于rip兼容矩阵等价类的存在性
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148895
P. Sasmal, C. S. Sastry, P. Jampana
{"title":"On the existence of equivalence class of RIP-compliant matrices","authors":"P. Sasmal, C. S. Sastry, P. Jampana","doi":"10.1109/SAMPTA.2015.7148895","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148895","url":null,"abstract":"In Compressed Sensing (CS), the matrices that satisfy the Restricted Isometry Property (RIP) play an important role. But it is known that the RIP properties of a matrix Φ and its `weighted matrix' GΦ (G being a non-singular matrix) vary drastically in terms of RIP constant. In this paper, we consider the opposite question: Given a matrix Φ, can we find a non-singular matrix G such that GΦ has compliance with RIP? We show that, under some conditions, a class of non-singular matrices (G) exists such that GΦ has RIP-compliance with better RIP constant. We also provide a relationship between the Unique Representation Property (URP) and Restricted Isometry Property (RIP), and a direct relationship between RIP and sparsest solution of a linear system of equations.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"81 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":"121610138","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
Deterministic construction of Quasi-Cyclic sparse sensing matrices from one-coincidence sequence 单符合序列拟循环稀疏感知矩阵的确定性构造
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148870
Weijun Zeng, Huali Wang, Guangjie Xu, Lu Gan
{"title":"Deterministic construction of Quasi-Cyclic sparse sensing matrices from one-coincidence sequence","authors":"Weijun Zeng, Huali Wang, Guangjie Xu, Lu Gan","doi":"10.1109/SAMPTA.2015.7148870","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148870","url":null,"abstract":"In this paper, a new class of deterministic sparse matrices derived from Quasi-Cyclic (QC) low-density parity-check (LDPC) codes is presented for compressed sensing (CS). In contrast to random and other deterministic matrices, the proposed matrices are generated based on circulant permutation matrices, which require less memory for storage and low computational cost for sensing. Its size is also quite flexible compared with other existing fixed-sizes deterministic matrices. Furthermore, both the coherence and null space property of proposed matrices are investigated, specially, the upper bounds of signal sparsity k is given for exactly recovering. Finally, we carry out many numerical simulations and show that our sparse matrices outperform Gaussian random matrices under some scenes.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"264 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":"122464394","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
2D sparse sampling algorithm for ND Fredholm equations with applications to NMR relaxometry ND Fredholm方程的二维稀疏采样算法及其在核磁共振弛豫测量中的应用
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148914
Ariel Hafftka, H. Celik, A. Cloninger, W. Czaja, R. Spencer
{"title":"2D sparse sampling algorithm for ND Fredholm equations with applications to NMR relaxometry","authors":"Ariel Hafftka, H. Celik, A. Cloninger, W. Czaja, R. Spencer","doi":"10.1109/SAMPTA.2015.7148914","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148914","url":null,"abstract":"In [1], Cloninger, Czaja, Bai, and Basser developed an algorithm for compressive sampling based data acquisition for the solution of 2D Fredholm equations. We extend the algorithm to N dimensional data, by randomly sampling in 2 dimensions and fully sampling in the remaining N-2 dimensions. This new algorithm has direct applications to 3-dimensional nuclear magnetic resonance relaxometry and related experiments, such as T1-D-T2 or T1-T1,ρ-T2. In these experiments, the first two parameters are time-consuming to acquire, so sparse sampling in the first two parameters can provide significant experimental time savings, while compressive sampling is unnecessary in the third parameter.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"80 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":"134178282","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
Exact reconstruction of a class of nonnegative measures using model sets 利用模型集精确重构一类非负度量
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148957
Basarab Matei
{"title":"Exact reconstruction of a class of nonnegative measures using model sets","authors":"Basarab Matei","doi":"10.1109/SAMPTA.2015.7148957","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148957","url":null,"abstract":"In this paper we are concerned with the reconstruction of a class of measures on the square from the sampling of its Fourier coefficients on some sparse set of points. We show that the exact reconstruction of a weighted Dirac sum measure is still possible when one knows a finite number of non-adaptive linear measurements of the spectrum. Surprisingly, these measurements are defined on a model set, i.e quasicrystal.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"36 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":"131216056","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
Phase retrieval without small-ball probability assumptions: Stability and uniqueness 无小球概率假设的相位检索:稳定性和唯一性
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148923
F. Krahmer, Yi-Kai Liu
{"title":"Phase retrieval without small-ball probability assumptions: Stability and uniqueness","authors":"F. Krahmer, Yi-Kai Liu","doi":"10.1109/SAMPTA.2015.7148923","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148923","url":null,"abstract":"We study stability and uniqueness for the phase retrieval problem. That is, we ask when is a signal x ε R<sup>n</sup> stably and uniquely determined (up to small perturbations), when one performs phaseless measurements of the form y<sub>i</sub> = |a<sup>T</sup><sub>i</sub>x|<sup>2</sup> (for i = 1,..., N), 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. It is well known that for many common choices of D, certain ambiguities can arise that prevent x from being uniquely determined. In this note we show that for any sub-Gaussian distribution D, with no additional assumptions, most vectors x cannot lead to such ambiguities. More precisely, we show stability and uniqueness for all sets of vectors T ⊂ R<sup>n</sup> which are not too peaky, in the sense that at most a constant fraction of their mass is concentrated on any one coordinate. The number of measurements needed to recover x ε T depends on the complexity of T in a natural way, extending previous results of Eldar and Mendelson [12].","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":"126963448","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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