Compressive Sensing by Random Convolution
SIAM Journal on Imaging Sciences
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
Toeplitz compressed sensing matrices with applications to sparse channel estimation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
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This paper considers the problem of estimating a discrete signal from its convolution with a pulse consisting of a sequence of independent and identically distributed Gaussian random variables. We derive lower bounds on the length of a random pulse needed to stably reconstruct a signal supported on [l, n]. We will show that a general signal can be stably recovered from convolution with a pulse of length m ≥ n log5 n, and a sparse signal which can be closely approximated using s ≤ n/log5 n terms can be stably recovered with a pttlse of length n.