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cs.IT2011★ 11 cited
Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising
David Donoho, Iain Johnstone, Andrea Montanari
Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such undersampling is important…
math.PR2011★ 39 cited
Fast approach to the Tracy-Widom law at the edge of GOE and GUE
Iain M. Johnstone, Zongming Ma
We study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy-Widom limits. We show that one can achieve…
cs.IT2011★ 14 cited
Compressed Sensing over -balls: Minimax Mean Square Error
David Donoho, Iain Johnstone, Arian Maleki +1
We consider the compressed sensing problem, where the object $x_0 \in \bR^N$ is to be recovered from incomplete measurements ; here the sensing matrix is an $n \t…