A new sufficient condition for sparse vector recovery via ℓ1 − ℓ2 local minimization
Ning Bi, Jun Tan, Wai-Shing Tang
Abstract
In this paper, we provide a necessary condition and a sufficient condition such that any [Formula: see text]-sparse vector [Formula: see text] can be recovered from [Formula: see text] via [Formula: see text] local minimization. Moreover, we further verify that the sufficient condition is naturally valid when the restricted isometry constant of the measurement matrix [Formula: see text] satisfies [Formula: see text]. Compared with the existing [Formula: see text] local recoverability condition [Formula: see text], this result shows that [Formula: see text] local recoverability contains more measurement matrices.
Topics & Concepts
Restricted isometry propertyMathematicsMinificationConstant (computer programming)Matrix (chemical analysis)Isometry (Riemannian geometry)CombinatoricsSparse approximationApplied mathematicsPure mathematicsAlgorithmCompressed sensingComputer scienceMathematical optimizationProgramming languageMaterials scienceComposite materialSparse and Compressive Sensing TechniquesRandom Matrices and ApplicationsMicrowave Imaging and Scattering Analysis