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## Compression Schemes for Time-Varying Sparse Signals

Citations: | 1 - 1 self |

### Citations

1364 | Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones
- Sturm
- 1999
(Show Context)
Citation Context ...tion path illustrating the selected rows of the dictionary A for t = 1, 2, . . . , 25 s. optimization problem can be solved using readily available convex optimization solvers like CVX [20] or SeDuMi =-=[21]-=-. We underline that the formulation (11) will also optimize the number of rows of Φt. In case a specific compression rate is desired (i.e., N is known a priori), we solve the following equivalent prob... |

1063 |
CVX: Matlab software for disciplined convex programming. [Online]. Available: http://stanford.edu/ ∼ boyd/cvx
- Grant, Boyd
- 2009
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Citation Context ...s. (b) The solution path illustrating the selected rows of the dictionary A for t = 1, 2, . . . , 25 s. optimization problem can be solved using readily available convex optimization solvers like CVX =-=[20]-=- or SeDuMi [21]. We underline that the formulation (11) will also optimize the number of rows of Φt. In case a specific compression rate is desired (i.e., N is known a priori), we solve the following ... |

697 | An Introduction to Compressive Sensing
- Baraniuk, Davenport, et al.
- 2010
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Citation Context ...ints on the state variables). In particular, we are interested in state sequences that are sparse in nature, which have received a lot of attention in the recent past through compressive sensing (CS) =-=[7]-=-. The theory developed under the classical CS framework advocates sensing architectures based on random matrices, which has been proven essential to provide recovery algorithms, reconstruction guarant... |

340 | Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies. - Krause, Singh, et al. - 2008 |

332 | Sparsity and smoothness via the fused lasso
- Tibshirani, Saunders, et al.
- 2005
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Citation Context ... a much broader class of structured signals, including structured sparse signals (or block-sparse signals) [22], smoothness (i.e., sparsity of the coefficients and also sparsity of their differences) =-=[23]-=-, to list a few. Depending on the structure of the state, the g(xt) has to be modified accordingly. More specifically, for structured sparse signals we use a regularizer that accounts for block sparsi... |

329 | Bayesian compressive sensing
- Ji, Xue, et al.
- 2008
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Citation Context ...in [15, Ch. 6], [16] the variance of the distribution from which the (random) sensing matrices are generated is designed such that the average information gain is maximized. The Bayesian CS framework =-=[17]-=- allows to quantify the sparse reconstruction error through the so-called error bars, which again allows to adaptively design the sensing matrices. Both [16] and [17] use experimental design technique... |

114 | Compressed Sensing: Theory and Applications - Eldar, Kutyniok |

101 | Structured compressed sensing: from theory to applications
- Duarte, Eldar
- 2011
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Citation Context ...ructured sensing operators to accommodate practical applications such as sensor networks (e.g., for source localization and field estimation), imaging, and cognitive radio sensing, to list a few. See =-=[8]-=- for a more detailed review on structured CS. We consider the problem of adaptive compressive sensing of time-varying sparse signals with possibly time-varying sparsity patterns and/or order. This pro... |

96 | Sensor Selection via Convex Optimization. - Joshi, Boyd - 2009 |

90 | Kalman filtered compressed sensing,” - Vaswani - 2008 |

54 |
A note on the group Lasso and a sparse group Lasso. arXiv:1001.0736v1 [math.ST],
- Friedman, Hastie, et al.
- 2010
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Citation Context ...which are often studied together with the CS framework. The sparsity prior can be extended to a much broader class of structured signals, including structured sparse signals (or block-sparse signals) =-=[22]-=-, smoothness (i.e., sparsity of the coefficients and also sparsity of their differences) [23], to list a few. Depending on the structure of the state, the g(xt) has to be modified accordingly. More sp... |

36 | Compressed sensing of time-varying signals - Angelosante, Giannakis, et al. - 2009 |

36 |
On Kalman filtering with nonlinear equality constraints.
- Julier, Jr
- 2007
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Citation Context ...,Rvt), where Rvt ∈ RM×M represents the covariance matrix of vt. Alternatively, the evolution of the time-varying sparse sequence (2) can be described using a pseudo-measurement formulation [9], [14], =-=[19]-=-. More specifically, it is assumed that xt evolves according to the following model dynamics: xt = Htxt−1 + ut; (3a) pseudo-measurement: 0 = g(xt) + et, (3b) where Ht is an M × M state-transition matr... |

32 |
Methods for Sparse Signal Recovery Using Kalman Filtering with Embedded Pseudo-Measurement Norms and Quasi-Norms
- Carmi, Gurfil, et al.
(Show Context)
Citation Context ...pressive sensing of time-varying sparse signals with possibly time-varying sparsity patterns and/or order. This problem has been studied in the past leading to various forms of sparsity-aware filters =-=[9]-=-–[12], and are applied to problems like visual surveillance [13] and target localization [14]. We study the design of sensing matrices for such problems; however, the focus will not be on the signal r... |

19 | Adaptive sensing for sparse signal recovery,” in
- Haupt, Castro, et al.
- 2009
(Show Context)
Citation Context ...ing matrices for such problems; however, the focus will not be on the signal recovery itself. Sensing matrix design for sparse recovery has been studied in various forms. For example, in [15, Ch. 6], =-=[16]-=- the variance of the distribution from which the (random) sensing matrices are generated is designed such that the average information gain is maximized. The Bayesian CS framework [17] allows to quant... |

14 | Sensor selection for event detection in wireless sensor networks - Bajovic, Sinopoli, et al. - 2011 |

13 | Sequential compressed sensing
- Malioutov, Sanghavi, et al.
- 2010
(Show Context)
Citation Context ...sive sensing of time-varying sparse signals with possibly time-varying sparsity patterns and/or order. This problem has been studied in the past leading to various forms of sparsity-aware filters [9]–=-=[12]-=-, and are applied to problems like visual surveillance [13] and target localization [14]. We study the design of sensing matrices for such problems; however, the focus will not be on the signal recove... |

12 | Sparsity-promoting sensor selection for non-linear measurement models
- Chepuri, Leus
- 2013
(Show Context)
Citation Context ...on problem is convex in wt. However, the solution of (11) is not yet Boolean, and the approximate Boolean solution has to be recovered. This can be done either by deterministic or randomized rounding =-=[4]-=-. The relaxed 0 5 10 15 20 25 30 0 5 10 15 20 25 30 target track Sensors Selected sensors x-axis coordinates [m], time [s] yax is co o rd in at es [m ], tim e [s] (a) 1 3 5 7 9 11 13 15 17 19 21 23 25... |

6 |
Adaptive rate compressive sensing for background subtraction,”
- Warnell, Reddy, et al.
- 2012
(Show Context)
Citation Context ...ime-varying sparsity patterns and/or order. This problem has been studied in the past leading to various forms of sparsity-aware filters [9]–[12], and are applied to problems like visual surveillance =-=[13]-=- and target localization [14]. We study the design of sensing matrices for such problems; however, the focus will not be on the signal recovery itself. Sensing matrix design for sparse recovery has be... |

4 | Sparsity-promoting adaptive sensor selection for non-linear filtering
- Chepuri, Leus
- 2014
(Show Context)
Citation Context ...s achieved is referred to as sensor selection. Sensor selection is an experimental design problem, and has been studied in the context of inference tasks like estimation, filtering, and detection [1]–=-=[6]-=- (see references therein). In this paper, we extend the sensor selection framework for non-linear filtering developed in [6] to sampling designs for filtering problems involving structured signals (mo... |

3 |
Tracking target signal strengths on a grid using sparsity,” arXiv preprint arXiv:1104.5288
- Farahmand, Giannakis, et al.
- 2011
(Show Context)
Citation Context ... and/or order. This problem has been studied in the past leading to various forms of sparsity-aware filters [9]–[12], and are applied to problems like visual surveillance [13] and target localization =-=[14]-=-. We study the design of sensing matrices for such problems; however, the focus will not be on the signal recovery itself. Sensing matrix design for sparse recovery has been studied in various forms. ... |

1 | Sensor selection for estimation, filtering, and detection
- Chepuri, Leus
- 2014
(Show Context)
Citation Context ...ce is achieved is referred to as sensor selection. Sensor selection is an experimental design problem, and has been studied in the context of inference tasks like estimation, filtering, and detection =-=[1]-=-–[6] (see references therein). In this paper, we extend the sensor selection framework for non-linear filtering developed in [6] to sampling designs for filtering problems involving structured signals... |

1 |
Near-optimal sensor placement for signals lying in a union of subspaces
- Badawy, Ranieri, et al.
- 2014
(Show Context)
Citation Context ...he sensing matrices. Both [16] and [17] use experimental design techniques with performance measures like differential entropy to adaptively learn the sensing matrix starting from a random matrix. In =-=[18]-=-, a greedy algorithm based on a submodular performance measure has been proposed for sensing operator design for a signal lying in the union of subspaces. However, the sensing design schemes discussed... |