## SPARSE SIGNAL RECONSTRUCTION FROM NOISY COMPRESSIVE MEASUREMENTS USING CROSS VALIDATION

Citations: | 16 - 0 self |

### BibTeX

@MISC{Boufounos_sparsesignal,

author = {Petros Boufounos and Marco F. Duarte and Richard G. Baraniuk},

title = {SPARSE SIGNAL RECONSTRUCTION FROM NOISY COMPRESSIVE MEASUREMENTS USING CROSS VALIDATION},

year = {}

}

### OpenURL

### Abstract

Compressive sensing is a new data acquisition technique that aims to measure sparse and compressible signals at close to their intrinsic information rate rather than their Nyquist rate. Recent results in compressive sensing show that a sparse or compressible signal can be reconstructed from very few incoherent measurements. Although the sampling and reconstruction process is robust to measurement noise, all current reconstruction methods assume some knowledge of the noise power or the acquired signal to noise ratio. This knowledge is necessary to set algorithmic parameters and stopping conditions. If these parameters are set incorrectly, then the reconstruction algorithms either do not fully reconstruct the acquired signal (underfitting) or try to explain a significant portion of the noise by distorting the reconstructed signal (overfitting). This paper explores this behavior and examines the use of cross validation to determine the stopping conditions for the optimization algorithms. We demonstrate that by designating a small set of measurements as a validation set it is possible to optimize these algorithms and reduce the reconstruction error. Furthermore we explore the trade-off between using the additional measurements for cross validation instead of reconstruction. Index Terms — Data acquisition, sampling methods, data models, signal reconstruction, parameter estimation. 1.

### Citations

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802 |
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688 |
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Citation Context ...escribed in [2], then a sparse/compressible signal can be recovered exactly/approximately using sparse reconstruction algorithms that determine the sparsest signal bx that explains the measurements y =-=[1, 2, 4]-=-. Specific reconstruction algorithms include linear programming (Basis Pursuit) [9] and Orthogonal Matching Pursuit (OMP) [4]; numerical experiments demonstrate good performance using Matching Pursuit... |

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43 |
Fast reconstruction of piecewise smooth signals from incoherent projections. SPARS05
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Citation Context ...ific reconstruction algorithms include linear programming (Basis Pursuit) [9] and Orthogonal Matching Pursuit (OMP) [4]; numerical experiments demonstrate good performance using Matching Pursuit (MP) =-=[10]-=- for reconstruction even though there are no theoretical guarantees. MP is often preferred to OMP due to its significantly reduced computational complexity. 2.3. Reconstruction from Noisy Measurements... |

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Citation Context ...nts are used; the oracle performance is shown for reference. Additionally, OMP outperform both Homotopy continuation (HT) and Homotopy continuation with debiasing (HT/DB). and reconstruct an estimate =-=[15]-=- can be used to reduce the reconstruction error, which suggests increasing M and decreasing Mcv. On the other hand, increasing Mcv will improve the CV estimate and thus ensure that the CV optimum is c... |