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Abstract: Recently, it has been proved in Babadi et al. that in noisy compressedsensing, a joint typical estimator can asymptotically achieve the Cramer-Raolower bound of the problem.To prove this result, this paper used a lemma,whichis provided in Akcakaya et al,that comprises the main building block of theproof. This lemma is based on the assumption of Gaussianity of the measurementmatrix and its randomness in the domain of noise. In this correspondence, wegeneralize the results obtained in Babadi et al by dropping the Gaussianityassumption on the measurement matrix. In fact, by considering the measurementmatrix as a deterministic matrix in our analysis, we find a theorem similar tothe main theorem of Babadi et al for a family of randomly generated butdeterministic in the noise domain measurement matrices that satisfy ageneralized condition known as The Concentration of Measures Inequality. Bythis, we finally show that under our generalized assumptions, the Cramer-Raobound of the estimation is achievable by using the typical estimator introducedin Babadi et al.



Autor: Rad Niazadeh, Masoud Babaie-Zadeh, Christian Jutten

Fuente: https://arxiv.org/







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