Shannon Theoretic Limits on Noisy Compressive Sampling

Mehmet Akçakaya; Vahid Tarokh

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arXiv · 0711.0366

Shannon Theoretic Limits on Noisy Compressive Sampling

Mehmet Akçakaya·Vahid Tarokh

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Abstract

In this paper, we study the number of measurements required to recover a sparse signal in ${\mathbb C}^M$ with $L$ non-zero coefficients from compressed samples in the presence of noise. For a number of different recovery criteria, we prove that $O(L)$ (an asymptotically linear multiple of $L$) measurements are necessary and sufficient if $L$ grows linearly as a function of $M$. This improves on the existing literature that is mostly focused on variants of a specific recovery algorithm based on convex programming, for which $O(L\log(M-L))$ measurements are required. We also show that $O(L\log(M-L))$ measurements are required in the sublinear regime ($L = o(M)$).

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Mehmet Akçakaya, Vahid Tarokh. 2007-11-02. Shannon Theoretic Limits on Noisy Compressive Sampling. https://arxiv.org/abs/0711.0366

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