In this paper, we propose a novel sparse recovery method based on the generalized error function. Both the theoretical analysis and the practical algorithms are presented. Numerical experiments are conducted to demonstrate the advantageous performance of the proposed approach over the state-of-the-art sparse recovery methods . Its practical application in magnetic resonance imaging (MRI) reconstruction is studied as well.
In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established for both constrained and unconstrained models. The practical algorithms via both the iteratively reweighted \ell_1 and the difference of convex functions algorithms are presented. Numerical experiments are conducted to illustrate the improvement provided by the proposed approach in various scenarios . Its practical application in magnetic resonance imaging (MRI) reconstruction is studied as well.
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Both the theoretical analysis and the practical algorithms
The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established for both constrained and unconstrained models. The practical algorithms via both the iteratively reweighted \ell_1 and the difference of convex functions algorithms
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demonstrate the advantageous performance of
illustrate the improvement provided by
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over the state-of-the-art sparse recovery methods
in various scenarios