## Kalman filtered compressed sensing

### Cached

### Download Links

- [www.ece.iastate.edu]
- [www.ece.iastate.edu]
- [home.engineering.iastate.edu]
- [www.ece.iastate.edu]
- [home.engineering.iastate.edu]
- [arxiv.org]
- DBLP

### Other Repositories/Bibliography

Venue: | in Proc. IEEE Int. Conf. Image (ICIP), 2008 |

Citations: | 41 - 13 self |

### BibTeX

@INPROCEEDINGS{Vaswani_kalmanfiltered,

author = {Namrata Vaswani},

title = {Kalman filtered compressed sensing},

booktitle = {in Proc. IEEE Int. Conf. Image (ICIP), 2008},

year = {},

pages = {893--896}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear “incoherent ” measurements, in real-time. The signals are sparse in some transform domain referred to as the sparsity basis. For a single spatial signal, the solution is provided by Compressed Sensing (CS). The question that we address is, for a sequence of sparse signals, can we do better than CS, if (a) the sparsity pattern of the signal’s transform coefficients’ vector changes slowly over time, and (b) a simple prior model on the temporal dynamics of its current non-zero elements is available. The overall idea of our solution is to use CS to estimate the support set of the initial signal’s transform vector. At future times, run a reduced order Kalman filter with the currently estimated support and estimate new additions to the support set by applying CS to the Kalman innovations or filtering error (whenever it is “large”). Index Terms/Keywords: compressed sensing, Kalman filtering, compressive sampling, sequential MMSE estimation

### Citations

1719 | Compressed sensing
- Donoho
(Show Context)
Citation Context ...gh intensity variation points [4]), or real-time video reconstruction using the single-pixel camera [5]. The solution to the static version of the above problem is provided by Compressed Sensing (CS) =-=[1, 6, 7]-=-. The noise-free observations case [1] is exact, with high probability (w.h.p.), while the noisy case [7] has a small error w.h.p.. But existing solutions for the dynamic problem [5, 8] treat the enti... |

1471 | Good Features to Track
- Shi, Tomasi
- 1994
(Show Context)
Citation Context ...ude sequentially estimating optical flow of a single deforming object (sparse in Fourier domain) from a set of randomly spaced optical flow measurements (e.g. those at high intensity variation points =-=[4]-=-), or real-time video reconstruction using the single-pixel camera [5]. The solution to the static version of the above problem is provided by Compressed Sensing (CS) [1, 6, 7]. The noise-free observa... |

1301 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Candès, Romberg, et al.
(Show Context)
Citation Context ...nknown and time-varying sparsity patterns) from a limited number of linear “incoherent” measurements, in real-time. The signals are sparse in some transform domain referred to as the “sparsity basis” =-=[1]-=-. A common example of such a problem is dynamic MRI or CT to image deforming human organs or to image brain neural activation patterns (in response to stimuli) using fMRI. The ability to perform real-... |

425 | The Dantzig selector: Statistical estimation when 2817 p is much larger than n
- Candes, Tao
- 2007
(Show Context)
Citation Context ...gh intensity variation points [4]), or real-time video reconstruction using the single-pixel camera [5]. The solution to the static version of the above problem is provided by Compressed Sensing (CS) =-=[1, 6, 7]-=-. The noise-free observations case [1] is exact, with high probability (w.h.p.), while the noisy case [7] has a small error w.h.p.. But existing solutions for the dynamic problem [5, 8] treat the enti... |

220 |
Sparse MRI: The application of compressed sensing for rapid
- Lustig, Donoho, et al.
(Show Context)
Citation Context ... to perform real-time MRI capture and reconstruction can make interventional MR practical [2]. Human organ images are usually piecewise smooth and thus the wavelet transform is a valid sparsity basis =-=[1, 3]-=-. Due to strong temporal dependencies, the sparsity pattern usually changes slowly over time. MRI captures a small (sub-Nyquist) number of Fourier transform coefficients of the image, which are known ... |

171 | Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit. 2007. Available at http://www-stat.stanford.edu/ ~donoho/Reports/2006/StOMP-20060403.pdf
- Donoho, Starck
(Show Context)
Citation Context ...eshold or until the estimated set ∆ is empty or for a fixed number of iterations. A similar idea forms the basis of iterative CS reconstruction techniques such as stagewise Orthogonal Matching Pursuit=-=[13]-=-. Deleting Near-Zero Coefficients. Over time, some coefficients may become zero (or nearly-zero) and remain zero. Alternatively, some coefficients may wrongly get added, due to CS error. In both cases... |

134 | Bayesian compressive sensing
- Ji, Xue, et al.
- 2008
(Show Context)
Citation Context ...will be unobservable. Unless all unobservable modes are stable, the error will blow up. Other recent work that also attempts to use prior knowledge with CS, but to reconstruct only a single signal is =-=[10, 11, 12]-=-. 2. THE MODEL AND PROBLEM FORMULATION Let (zt)m×1 denote the spatial signal of interest at time t and (yt)n×1, with n<m, denote its observation vector at t. The signal, zt, is sparse in a given spars... |

54 | An architecture for compressive imaging
- Wakin, Laska, et al.
- 2006
(Show Context)
Citation Context ...(sparse in Fourier domain) from a set of randomly spaced optical flow measurements (e.g. those at high intensity variation points [4]), or real-time video reconstruction using the single-pixel camera =-=[5]-=-. The solution to the static version of the above problem is provided by Compressed Sensing (CS) [1, 6, 7]. The noise-free observations case [1] is exact, with high probability (w.h.p.), while the noi... |

15 | Particle filters for infinite (or large) dimensional state spaces-part 2 - Vaswani - 2006 |

13 | Compressed sensing image reconstruction via recursive spatially adaptive filtering
- Egiazarian, Foi, et al.
(Show Context)
Citation Context ...will be unobservable. Unless all unobservable modes are stable, the error will blow up. Other recent work that also attempts to use prior knowledge with CS, but to reconstruct only a single signal is =-=[10, 11, 12]-=-. 2. THE MODEL AND PROBLEM FORMULATION Let (zt)m×1 denote the spatial signal of interest at time t and (yt)n×1, with n<m, denote its observation vector at t. The signal, zt, is sparse in a given spars... |

12 | Compressed sensing in dynamic mri - Gamper, Boesiger, et al. - 2008 |

2 |
Exploiting prior knowledge in the recovery of signals from noisy random projections
- Garcia-Frias, Esnaola
- 2007
(Show Context)
Citation Context ...will be unobservable. Unless all unobservable modes are stable, the error will blow up. Other recent work that also attempts to use prior knowledge with CS, but to reconstruct only a single signal is =-=[10, 11, 12]-=-. 2. THE MODEL AND PROBLEM FORMULATION Let (zt)m×1 denote the spatial signal of interest at time t and (yt)n×1, with n<m, denote its observation vector at t. The signal, zt, is sparse in a given spars... |

2 |
Application of mr technology to endovascular interventions in an xmr suite
- Martin, Weber, et al.
- 2002
(Show Context)
Citation Context ...he beating heart or to image brain neural activation patterns (in response to stimuli) using fMRI. The ability to perform real-time MRI capture and reconstruction can make interventional MR practical =-=[2]-=-. Human organ images are usually piecewise smooth and thus the wavelet transform is a valid sparsity basis [1, 3]. Due to strong temporal dependencies, the sparsity pattern usually changes slowly over... |

1 |
Analyzing kalman filtered compressed sensing
- Vaswani
- 2008
(Show Context)
Citation Context ...ssed (explained earlier). Since the suppression is small, the algorithm still works in practice, but the error bound results for the DS cannot be applied. Alternatively, as we explain in ongoing work =-=[13]-=-, one can rewrite ˜yt,f = Aβt + wt where βt � [(xt − ˆxt)T , (xt)T c] is a “sparse-compressible” signal with a “large” nonzero part, (xt)Δ, a “small” or “compressible” nonzero part, (xt − ˆxt)T and th... |