Necessary and sufficient conditions for noiseless sparse recovery via convex quadratic splines

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2019

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Abstract

The problem of exact recovery of an individual sparse vector using the Basis Pursuit (BP) model is considered. A differentiable Huber loss function (a convex quadratic spline) is used to replace the 1-norm in the BP model. Using the theory of duality and classical results from quadratic perturbation of linear programs, a necessary condition for exact recovery leading to a negative result is given. An easily verifiable sufficient condition is also presented.

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SIAM Journal on Matrix Analysis and Applications

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Society for Industrial and Applied Mathematics Publications

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Published Version (Please cite this version)

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English