Necessary and sufficient conditions for noiseless sparse recovery via convex quadratic splines
Pınar, Mustafa Ç.
SIAM Journal on Matrix Analysis and Applications
Society for Industrial and Applied Mathematics Publications
194 - 209
Item Usage Stats
MetadataShow full item record
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 $\ell_1$-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.
KeywordsExact recovery of a sparse vector
Huber loss function
Strictly convex quadratic programming
Convex quadratic splines