In this paper,we offer a new sparse recovery strategy based on the generalized error *** introduced penalty function involves both the shape and the scale parameters,making it extremely *** both constrained and uncons...
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In this paper,we offer a new sparse recovery strategy based on the generalized error *** introduced penalty function involves both the shape and the scale parameters,making it extremely *** both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are *** practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are *** experiments are carried out to demonstrate the benefits of the suggested approach in a variety of *** practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.
The weighted l(r) - l(1) minimization method with 0 < r <= 1 largely generalizes the classical l(r) minimization method and achieves very good performance in compressive sensing. However, its restricted isometry...
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The weighted l(r) - l(1) minimization method with 0 < r <= 1 largely generalizes the classical l(r) minimization method and achieves very good performance in compressive sensing. However, its restricted isometry property (RIP) and high-order RIP analysis results remain unknown. In this paper, we fill in this gap by adopting newly developed analysis tools. Moreover, through a novel decomposition of the objective function into a difference of two convexfunctions, we propose to solve the weighted l(r) - l(1) minimization problem via the difference of convex functions algorithms (DCA) directly. Numerical experiments show that our DCA based weighted l(r) - l(1) minimization method gives satisfactory results in sparse recovery no matter whether the measurement matrix is coherent or not. For highly coherent measurements, our proposed method even outperforms the state-of-art l(1) - l(2) minimization method. (C) 2022 Elsevier B.V. All rights reserved.
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