{"title":"The finite Balian-Low conjecture","authors":"M. Lammers, Simon Stampe","doi":"10.1109/SAMPTA.2015.7148867","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148867","url":null,"abstract":"We present a conjecture for a finite version of the celebrated Balian-Low Theorem for Gabor systems in L<sup>2</sup>(R). We proceed to prove a special case of the conjecture for C<sup>9</sup>.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127709204","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}
{"title":"Sampling circuits for 1D and 2D sensors for low-power purpose","authors":"L. Fesquet, A. Darwish, G. Sicard","doi":"10.1109/SAMPTA.2015.7148927","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148927","url":null,"abstract":"Sampling is becoming one of the most important topics for the Internet of Things (IoT). Indeed, the amount of data daily produced is so huge that the data processing cost will deeply affect the electricity generation in a near future. The big data is already a reality but a good way to mitigate this incredible data flow is to differently sample the information. This article presents - based on asynchronous analog-to-digital conversion - a way to limit the data flow and the power consumption for a host of sensors. By an adequate sampling technique, such as a level-crossing sampling scheme, a drastic activity and power reduction is feasible. An image sensor using 1-level crossing sampling is given as an illustration.","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":"125688872","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}
{"title":"Error bounds for noisy compressive phase retrieval","authors":"B. Bodmann, Nathaniel Hammen","doi":"10.1109/SAMPTA.2015.7148909","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148909","url":null,"abstract":"This paper provides a random complex measurement matrix and an algorithm for complex phase retrieval of sparse or approximately sparse signals from the noisy magnitudes of the measurements obtained with this matrix. We compute explicit error bounds for the recovery which depend on the noise-to-signal ratio, the sparsity s, the number of measured quantitites m, and the dimension of the signal N. This requires m to be of the order of s ln(N/s). In comparison with sparse recovery from complex linear measurements, our phase retrieval algorithm requires six times the number of measured quantities.","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":"126602058","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}
{"title":"Sampling, amenability and the Kunze-Stein phenomenon","authors":"J. Christensen, G. Ólafsson, S. Casey","doi":"10.1109/SAMPTA.2015.7148852","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148852","url":null,"abstract":"Inspired by recent work on the connection between representation theory and atomic decompositions, we take a look at convolution operators on non-unimodular amenable groups as well as non-compact semi-simple Lie groups. We then discuss this in context of sampling. Furthermore, we look at sampling and optimal sampling sets for some often studied spaces.","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":"115218110","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}
{"title":"Recovery guarantees for TV regularized compressed sensing","authors":"C. Poon","doi":"10.1109/SAMPTA.2015.7148945","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148945","url":null,"abstract":"This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its gradient from an incomplete subset of its Fourier coefficients which have been corrupted with noise. The results show that in order to obtain a reconstruction which is robust to noise and stable to inexact gradient sparsity of order s with high probability, it suffices to draw O(s log N) of the available Fourier coefficients uniformly at random. However, if one draws O(s log N) samples in accordance to a particular distribution which concentrates on the low Fourier frequencies, then the stability bounds which can be guaranteed are optimal up to log factors. The final result of this paper shows that in the one dimensional case where the underlying signal is gradient sparse and its sparsity pattern satisfies a minimum separation condition, then to guarantee exact recovery with high probability, for some M <; N, it suffices to draw O(s log M logs) samples uniformly at random from the Fourier coefficients whose frequencies are no greater than M.","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":"124621270","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}
{"title":"Event-driven sampling of signal with quadratic prediction","authors":"A. Gryboś","doi":"10.1109/SAMPTA.2015.7148897","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148897","url":null,"abstract":"Proposed article concerns the topics of the event-driven signal processing, asynchronous analog-to-digital conversion and application of irregular sampling and frame theory to the algorithms of signal reconstruction. In our work we follow the discussions on the non-uniform derivative sampling (SampTA2013) and we focus on analysing an example of the level-crossing sampling with quadratic (second order) prediction.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"90 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120866650","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}
{"title":"Recovery of third order tensors via convex optimization","authors":"H. Rauhut, Zeljka Stojanac","doi":"10.1109/SAMPTA.2015.7148920","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148920","url":null,"abstract":"We study recovery of low-rank third order tensors from underdetermined linear measurements. This natural extension of low-rank matrix recovery via nuclear norm minimization is challenging since the tensor nuclear norm is in general intractable to compute. To overcome this obstacle we introduce hierarchical closed convex relaxations of the tensor unit nuclear norm ball based on so-called theta bodies - a recent concept from computational algebraic geometry. Our tensor recovery procedure consists in minimization of the resulting new norms subject to the linear constraints. Numerical results on recovery of third order low-rank tensors show the effectiveness of this new approach.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"170 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":"116500495","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}
Jean Simatic, L. Fesquet, Brigitte Bidégaray-Fesquet
{"title":"Correctly sizing FIR filter architecture in the framework of non-uniform sampling","authors":"Jean Simatic, L. Fesquet, Brigitte Bidégaray-Fesquet","doi":"10.1109/SAMPTA.2015.7148894","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148894","url":null,"abstract":"Based on non-uniform sampling techniques and event-driven logic, signal processing is evolving to integrate new demands such as power consumption. As power is mainly connected to the processing activity and data volume, the level-crossing sampling scheme offers a simple way to reduce data volume and consequently processing activity. Nevertheless, these good properties could be constraining for the designers because of the non-predictable sample number that can be involved in the processing. In this paper, we target a FIR filter architecture and show how to correctly size its input shift-register. This paper shows a strategy to choose the shift-register depth but also a way to dynamically adapt the computation to an heterogeneous data flow.","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":"130000100","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}
{"title":"Dynamical sampling with an additive forcing term","authors":"A. Aldroubi, K. Kornelson","doi":"10.1109/SAMPTA.2015.7148928","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148928","url":null,"abstract":"In this paper we discuss a system of dynamical sampling, i.e. sampling a signal x that evolves in time under the action of an evolution operator A. We examine the timespace sampling that allows for reconstruction of x. Here we describe the possible reconstruction systems when the system also contains an unknown constant forcing term σ. We give conditions under which both x and σ can be reconstructed from the spacio-temporal set of sampling.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"18 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":"133396627","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}
{"title":"On a time-frequency approach to translation on finite graphs","authors":"M. Begué","doi":"10.1109/SAMPTA.2015.7148839","DOIUrl":"https://doi.org/10.1109/SAMPTA.2015.7148839","url":null,"abstract":"The authors of [1] have used spectral graph theory to define a Fourier transform on finite graphs. With this definition, one can use elementary properties of classical time-frequency analysis to define time-frequency operations on graphs including convolution, modulation, and translation. Many of these graph operators have properties that match our intuition in Euclidean space. The exception lies with the translation operator. In particular, translation does not form a group, i.e., TiTj ≠ Ti+j. We prove that graphs whose translation operators exhibit semigroup behavior are those whose eigenvectors of the Laplacian form a Hadamard matrix.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"324 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":"124578539","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}