On the Achievability of Cramér-Rao Bound In Noisy Compressed Sensing

Details On the Achievability of Cramér-Rao Bound In Noisy Compressed Sensing On the Achievability of Cramér-Rao Bound In Noisy Compressed Sensing

2010-06-13

arxiv.org/abs/1006.2513v2

Computer Science

Information Theory

This paper has been withdrawn by the author due to a crucial error in it, when talking about a mistake in [Akackaya et. al., 2

Scientific paper

Recently, it has been proved in [Babadi et. al., 2009] that in noisy compressed sensing, a joint typical estimator can asymptotically achieve the Cram\'er-Rao lower bound of the problem. To prove this result, [Babadi et. al., 2009] used a lemma, which is provided in [Akackaya et. al., 2008], that comprises the main building block of the proof. This lemma contains a mathematical mistake in its statement and proof which should be corrected. One wonders then whether or not the main results of [Babadi et. al., 2009] are correct. In this correspondence, we will first explain the mistake in the mentioned lemma in [Akackaya et. al., 2008] and will then state a new correct form of it. Then we re-study the main results of [1], and we will show that fortunately they remain valid, that is, the Cram\'er-Rao bound in noisy compressed sensing is achievable and a joint typical estimator can achieve it.

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