Comment on "Asymptotic Achievability of the Cramér-Rao Bound for Noisy Compressive Sampling"

In [1], we proved the asymptotic achievability of the Cramér-Rao bound in the compressive sensing setting in the linear sparsity regime. In the proof, we used an erroneous closed-form expression of ασ for the genie-aided Cramér-Rao bound σTr(AIAI) −1 from Lemma 3.5, which appears in Eqs. (20) and (29). The proof, however, holds if one avoids replacing σTr(AIAI) −1 by the expression of Lemma 3.5, and hence the claim of the Main Theorem stands true. In Chapter 2 of the Ph. D. dissertation by Behtash Babadi [2], this error was fixed and a more detailed proof in the non-asymptotic regime was presented. A draft of Chapter 2 of [2] is included in this note, verbatim. We would like to refer the interested reader to the full dissertation, which is electronically archived in the ProQuest database [2], and a draft of which can be accessed through the author’s homepage under: http://ece.umd.edu/~behtash/babadi_thesis_2011.pdf.