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2010
IEEE

Concentration of measure inequalities for compressive Toeplitz matrices with applications to detection and system identification

8 years 9 months ago
Concentration of measure inequalities for compressive Toeplitz matrices with applications to detection and system identification
In this paper, we derive concentration of measure inequalities for compressive Toeplitz matrices (having fewer rows than columns) with entries drawn from an independent and identically distributed (i.i.d.) Gaussian random sequence. These inequalities show that the norm of a vector mapped by a Toeplitz matrix to a lower dimensional space concentrates around its mean with a tail probability bound that decays exponentially in the dimension of the range space divided by a factor that is a function of the sample covariance of the vector. Motivated by the emerging field of Compressive Sensing (CS), we apply these inequalities to problems involving the analysis of high-dimensional systems from convolution-based compressive measurements. We discuss applications such as system identification, namely the estimation of the impulse response of a system, in cases where one can assume that the impulse response is high-dimensional, but sparse. We also consider the problem of detecting a change in the...
Borhan Molazem Sanandaji, Tyrone L. Vincent, Micha
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2010
Where CDC
Authors Borhan Molazem Sanandaji, Tyrone L. Vincent, Michael B. Wakin
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