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Beyond sparsity: Universally stable compressed sensing when the number of 'free' values is less than the number of observations

Publication ,  Journal Article
Reeves, G
Published in: 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
December 1, 2013

Recent results in compressed sensing have shown that a wide variety of structured signals can be recovered from undersampled and noisy linear observations. In this paper, we show that many of these signal structures can be modeled using an union of affine subspaces, and that the fundamental number of observations needed for stable recovery is given by the number of 'free' values, i.e. the dimension of the largest subspace in the union. One surprising consequence of our results is that the fundamental phase transition for random discrete-continuous signal models can be attained by a universal estimator that does not depend on the distribution. © 2013 IEEE.

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2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013

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Publication Date

December 1, 2013

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17 / 20
 

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Reeves, G. (2013). Beyond sparsity: Universally stable compressed sensing when the number of 'free' values is less than the number of observations. 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, 17–20. https://doi.org/10.1109/CAMSAP.2013.6713996
Reeves, G. “Beyond sparsity: Universally stable compressed sensing when the number of 'free' values is less than the number of observations.” 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, December 1, 2013, 17–20. https://doi.org/10.1109/CAMSAP.2013.6713996.
Reeves G. Beyond sparsity: Universally stable compressed sensing when the number of 'free' values is less than the number of observations. 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013. 2013 Dec 1;17–20.
Reeves, G. “Beyond sparsity: Universally stable compressed sensing when the number of 'free' values is less than the number of observations.” 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, Dec. 2013, pp. 17–20. Scopus, doi:10.1109/CAMSAP.2013.6713996.
Reeves G. Beyond sparsity: Universally stable compressed sensing when the number of 'free' values is less than the number of observations. 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013. 2013 Dec 1;17–20.

Published In

2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013

DOI

Publication Date

December 1, 2013

Start / End Page

17 / 20