Precise Undersampling Theorems

By David L. Donoho, Jared Tanner. Proceedings of the IEEE, 2010

311 citations recorded by the source corpus.

How researchers see this paper

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Compressed Sensing (2014, unknown): “Para igual matriz pero con n = 1600 fijo, se muestran: las curvas de umbral de 90 % de probabilidad de éxito (azul), de 50 % (verde) y de 10 % (roja), obtenidas mediante simulaciones numéricas (Imagen tomada de [32]).”
Signal representations with minimum ℓ∞-norm (2012, background): “, as in [9], is interesting open research problem.”
A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm (2008, methodology): “The properties of EM-BP are as given below: 1) It is A low-computation approach to sparse recovery, 2) It works well without the prior knowledge of the signal, 3) It overcomes the l1 phase transition given by Donoho and Tanner [11] under the noiseless setup, 4) It is further improved in conjunction ”
Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory (2013, methodology): “This was fruitfully studied in the context of standard linear regression [HKZ11], as well as sparse recovery.”
Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing (2009, unknown): “as ; it also describes what actually happens at finite problem sizes [39].”
Hard Thresholding Pursuit: An Algorithm for Compressive Sensing (2011, unknown): “[9].”