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Author Wakin, Michael B. ♦ Park, Jae Young ♦ Yap, Han Lun ♦ Rozell, Christopher J.
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Johnson-lindenstrauss Lemma ♦ Block Diagonal Matrix ♦ Main Diagonal Block ♦ Measure Bound ♦ Dense Matrix ♦ Block Diagonal Measurement Matrix ♦ Nonzero Entry ♦ Signal Play ♦ Much Theoretical Analysis ♦ Diagonal Matrix ♦ Concentration Exponent ♦ Main Result State ♦ Subgaussian Random Variable ♦ Energy Distribution ♦ Randomized Compressive Operator ♦ Index Term Compressive Sensing ♦ Measure Inequality
Description Concentration of measure inequalities are at the heart of much theoretical analysis of randomized compressive operators. Though commonly studied for dense matrices, in this paper we derive a concentration of measure bound for block diagonal matrices where the nonzero entries along the main diagonal blocks are i.i.d. subgaussian random variables. Our main result states that the concentration exponent, in the best case, scales as that for a fully dense matrix. We also identify the role that the energy distribution of the signal plays in distinguishing the best case from the worst. We illustrate these phenomena with a series of experiments. Index Terms — Compressive Sensing, concentration of measure, Johnson-Lindenstrauss lemma, block diagonal matrices 1.
in Proc. Int. Conf. Acoustics, Speech, Signal Proc. (ICASSP
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2010-01-01