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On the effective measure of dimension in total variation minimization 总变差最小化中尺寸的有效度量
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148960
R. Giryes, Y. Plan, R. Vershynin
{"title":"On the effective measure of dimension in total variation minimization","authors":"R. Giryes, Y. Plan, R. Vershynin","doi":"10.1109/SAMPTA.2015.7148960","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148960","url":null,"abstract":"Total variation (TV) is a widely used technique in many signal and image processing applications. One of the famous TV based algorithms is TV denoising that performs well with piecewise constant images. The same prior has been used also in the context of compressed sensing for recovering a signal from a small number of measurements. Recently, it has been shown that the number of measurements needed for such a recovery is proportional to the size of the edges in the sampled image and not the number of connected components in the image. In this work we show that this is not a coincidence and that the number of connected components in a piecewise constant image cannot serve alone as a measure for the complexity of the image. Our result is not limited only to images but holds also for higher dimensional signals. We believe that the results in this work provide a better insight into the TV prior.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"108 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":"114835925","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
Energy allocation for parameter estimation in block CS-based distributed MIMO systems 基于块cs的分布式MIMO系统参数估计的能量分配
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148946
A. Abtahi, M. Modarres-Hashemi, F. Marvasti, F. Tabataba
{"title":"Energy allocation for parameter estimation in block CS-based distributed MIMO systems","authors":"A. Abtahi, M. Modarres-Hashemi, F. Marvasti, F. Tabataba","doi":"10.1109/SAMPTA.2015.7148946","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148946","url":null,"abstract":"Exploiting Compressive Sensing (CS) in MIMO radars, we can remove the need of the high rate A/D converters and send much less samples to the fusion center. In distributed MIMO radars, the received signal can be modeled as a block sparse signal in a basis. Thus, block CS methods can be used instead of classical CS ones to achieve more accurate target parameter estimation. In this paper a new method of energy allocation to the transmitters is proposed to improve the performance of the block CS-based distributed MIMO radars. This method is based on the minimization of an upper bound of the sensing matrix block-coherence. Simulation results show a significant increase in the accuracy of multiple targets parameter estimation.","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":"114374008","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: 5
Low rank matrix recovery from few orthonormal basis measurements 从少量标准正交基测量中恢复低秩矩阵
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148921
R. Kueng
{"title":"Low rank matrix recovery from few orthonormal basis measurements","authors":"R. Kueng","doi":"10.1109/SAMPTA.2015.7148921","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148921","url":null,"abstract":"Recent insights concerning the PhaseLift algorithm for retrieving phases have furthered our understanding of low rank matrix recovery from rank-one projective measurements. Motivated by the structure of certain quantum mechanical experiments, we introduce a particular class of such rank-one measurements: orthonormal basis measurements. One such measurement corresponds to choosing an orthonormal basis and treating all the rank-one projectors onto different basis elements as a series of consecutive measurement matrices. We elaborate on performing low-rank matrix recovery from few, sufficiently random orthonormal basis measurements and sketch applications of such a procedure in quantum physics. We conclude this article by presenting numerical experiments testing such an approach.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"97 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":"128381429","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: 19
Wavelet frames generated by bandpass prolate functions 用带通扩展函数生成小波帧
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148863
J. Hogan, J. Lakey
{"title":"Wavelet frames generated by bandpass prolate functions","authors":"J. Hogan, J. Lakey","doi":"10.1109/SAMPTA.2015.7148863","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148863","url":null,"abstract":"We refer to eigenfunctions of the kernel corresponding to truncation in a time interval followed by truncation in a frequency band as bandpass prelates (BPPs). We prove frame bounds for certain families of shifts of bandpass prolates, and we numerically construct dual frames for finite dimensional analogues. In the continuous case, the corresponding families produce wavelet frames for the space of square-integrable functions.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"55 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":"132078754","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
Universal embeddings for kernel machine classification 核机分类的通用嵌入
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148902
P. Boufounos, H. Mansour
{"title":"Universal embeddings for kernel machine classification","authors":"P. Boufounos, H. Mansour","doi":"10.1109/SAMPTA.2015.7148902","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148902","url":null,"abstract":"Visual inference over a transmission channel is increasingly becoming an important problem in a variety of applications. In such applications, low latency and bit-rate consumption are often critical performance metrics, making data compression necessary. In this paper, we examine feature compression for support vector machine (SVM)-based inference using quantized randomized embeddings. We demonstrate that embedding the features is equivalent to using the SVM kernel trick with a mapping to a lower dimensional space. Furthermore, we show that universal embeddings-a recently proposed quantized embedding design-approximate a radial basis function (RBF) kernel, commonly used for kernel-based inference. Our experimental results demonstrate that quantized embeddings achieve 50% rate reduction, while maintaining the same inference performance. Moreover, universal embeddings achieve a further reduction in bit-rate over conventional quantized embedding methods, validating the theoretical predictions.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"27 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":"130601547","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
Unconditional convergence constants of Hilbert space frame expansions Hilbert空间框架展开的无条件收敛常数
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148913
P. Casazza, Richard G. Lynch, J. Tremain
{"title":"Unconditional convergence constants of Hilbert space frame expansions","authors":"P. Casazza, Richard G. Lynch, J. Tremain","doi":"10.1109/SAMPTA.2015.7148913","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148913","url":null,"abstract":"We will prove some new, fundamental results in frame theory by computing the unconditional constant (for all definitions of unconditional) for the frame expansion of a vector in a Hilbert space and see that it is √B/A, where A, B are the frame bounds of the frame. It follows that tight frames have unconditional constant one. We then generalize this to a classification of such frames by showing that for Bessel sequences whose frame operator can be diagonalized, the frame expansions have unconditional constant one if and only if the Bessel sequence is an orthogonal sum of tight frames. We then prove similar results for cross frame expansions but here the results are no longer a classification. We also give examples to show that our results are best possible. These results should have been done 20 years ago but somehow we overlooked this topic.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"39 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":"127896333","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 the strong divergence of Hilbert transform approximations from sampled data 抽样数据希尔伯特变换近似的强散度
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148883
H. Boche, V. Pohl
{"title":"On the strong divergence of Hilbert transform approximations from sampled data","authors":"H. Boche, V. Pohl","doi":"10.1109/SAMPTA.2015.7148883","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148883","url":null,"abstract":"It is known that every linear method which determines the Hilbert transform from the samples of the function diverges (weakly). This paper presents strong evidence that all such methods even diverge strongly. It is shown that the common approximation method derived from the conjugate Fej'er means diverges strongly, and that all reasonable approximation methods with a finite search horizon diverge strongly. Moreover, the paper discusses the relation between strong divergence and the existence of adaptive approximation methods.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"48 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":"126702502","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
Steiner equiangular tight frames redux 斯坦纳等角紧框架还原
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148910
M. Fickus, D. Mixon, Jesse Peterson, J. Jasper
{"title":"Steiner equiangular tight frames redux","authors":"M. Fickus, D. Mixon, Jesse Peterson, J. Jasper","doi":"10.1109/SAMPTA.2015.7148910","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148910","url":null,"abstract":"An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. ETFs arise in numerous applications, including compressed sensing. They also seem to be rare: despite over a decade of active research by the community, only a few construction methods have been discovered. One known method constructs ETFs from combinatorial designs known as balanced incomplete block designs. In this short paper, we provide an updated, more explicit perspective of that construction, laying the groundwork for upcoming results about such frames.","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":"114206852","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
Signal model specification testing via kernel reconstruction methods 基于核重构方法的信号模型规格测试
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148939
M. Pawlak
{"title":"Signal model specification testing via kernel reconstruction methods","authors":"M. Pawlak","doi":"10.1109/SAMPTA.2015.7148939","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148939","url":null,"abstract":"Given noisy samples of a signal, the problem of testing whether the signal belongs to a given parametric class of signals is considered. We examine the nonparametric situation as for a well-defined null hypothesis signal model we admit broad alternative signal classes that cannot be parametrized. For such a setup, we introduce testing procedures relying on nonparametric kernel-type sampling reconstruction algorithms properly adjusted for noisy data. The proposed testing procedure utilizes the L2 - distance between the kernel estimate and signals from the parametric target class. The central limit theorem of the test statistic is derived yielding a consistent testing method. Hence, we obtain the testing algorithm with the desirable level of the probability of false alarm and the power tending to one.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"78 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120916885","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
Adaptive estimation and compensation of the time delay in a periodic non-uniform sampling scheme 周期非均匀采样延时的自适应估计与补偿
2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI: 10.1109/SAMPTA.2015.7148936
Jean-Adrien Vernhes, M. Chabert, B. Lacaze, G. Lesthievent, R. Baudin, M. Boucheret
{"title":"Adaptive estimation and compensation of the time delay in a periodic non-uniform sampling scheme","authors":"Jean-Adrien Vernhes, M. Chabert, B. Lacaze, G. Lesthievent, R. Baudin, M. Boucheret","doi":"10.1109/SAMPTA.2015.7148936","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148936","url":null,"abstract":"High sampling rate Analog-to-Digital Converters (ADCs) can be obtained by time-interleaving low rate (and thus low cost) ADCs into so-called Time-Interleaved ADCs (TI-ADCs). Nevertheless increasing the sampling frequency involves an increasing sensibility of the system to desynchronization between the different ADCs that leads to time-skew errors, impacting the system with non linear distortions. The estimation and compensation of these errors are considered as one of the main challenge to deal with in TI-ADCs. Some methods have been previously proposed, mainly in the field of circuits and systems, to estimate the time-skew error but they mainly involve hardware correction and they lack of flexibility, using an inflexible uniform sampling reference. In this paper, we propose to model the output of L interleaved and desynchronized ADCs with a sampling scheme called Periodic Non-uniform Sampling of order L (PNSL). This scheme has been initially proposed as an alternative to uniform sampling for aliasing cancellation, particularly in the case of bandpass signals. We use its properties here to develop a flexible on-line digital estimation and compensation method of the time delays between the desynchronized channels. The estimated delay is exploited in the PNSL reconstruction formula leading to an accurate reconstruction without hardware correction and without any need to adapt the sampling operation. Our method can be used in a simple Built-In Self-Test (BIST) strategy with the use of learning sequences and our model appears more flexible and less electronically expensive, following the principles of “Dirty Radio Frequency” paradigm: designing imperfect analog circuits with subsequently digital corrections of these imperfections.","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":"132825360","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
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