Sparse recovery under weak moment assumptions

Guillaume Lecué; Shahar Mendelson

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arXiv · 1401.2188

Sparse recovery under weak moment assumptions

Guillaume Lecué·Shahar Mendelson

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Abstract

We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible estimate -- exhibited by a random gaussian matrix. We also prove that this moment condition is necessary, up to a $\log \log $ factor. Applications to the Compatibility Condition and the Restricted Eigenvalue Condition in the noisy setup and to properties of neighbourly random polytopes are also discussed.

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Guillaume Lecué, Shahar Mendelson. 2014-01-09. Sparse recovery under weak moment assumptions. https://arxiv.org/abs/1401.2188

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