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• W2890140921 abstract "In this paper, we consider the efficient and robust reconstruction of signals and images via $ell_{1}-alpha ell_{2}~(0<alphaleq 1)$ minimization in impulsive noise case. To achieve this goal, we introduce two new models: the $ell_1-alphaell_2$ minimization with $ell_1$ constraint, which is called $ell_1-alphaell_2$-LAD, the $ell_1-alphaell_2$ minimization with Dantzig selector constraint, which is called $ell_1-alphaell_2$-DS. We first show that sparse signals or nearly sparse signals can be exactly or stably recovered via $ell_{1}-alphaell_{2}$ minimization under some conditions based on the restricted $1$-isometry property ($ell_1$-RIP). Second, for $ell_1-alphaell_2$-LAD model, we introduce unconstrained $ell_1-alphaell_2$ minimization model denoting $ell_1-alphaell_2$-PLAD and propose $ell_1-alphaell_2$LA algorithm to solve the $ell_1-alphaell_2$-PLAD. Last, numerical experiments %on success rates of sparse signal recovery demonstrate that when the sensing matrix is ill-conditioned (i.e., the coherence of the matrix is larger than 0.99), the $ell_1-alphaell_2$LA method is better than the existing convex and non-convex compressed sensing solvers for the recovery of sparse signals. And for the magnetic resonance imaging (MRI) reconstruction with impulsive noise, we show that the $ell_1-alphaell_2$LA method has better performance than state-of-the-art methods via numerical experiments." @default.
• W2890140921 created "2018-09-27" @default.
• W2890140921 creator A5019208966 @default.
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• W2890140921 date "2018-09-09" @default.
• W2890140921 modified "2023-09-27" @default.
• W2890140921 title "Efficient and Robust Recovery of Signal and Image in Impulsive Noise via $ell_1-alpha ell_2$ Minimization" @default.
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• W2890140921 hasPublicationYear "2018" @default.
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