首页|$L_{p}/L_{q}$ Minimization Method and Stable Recovery of Approximately Block $ k $-Sparse Signals
$L_{p}/L_{q}$ Minimization Method and Stable Recovery of Approximately Block $ k $-Sparse Signals
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Selecting an appropriate optimization method to promote sparsity is of great significance for sparse recovery. In this paper, a novel scale-invariant $L_{p}/L_{q}$ minimization method which employs the ratio of $\ell_{p}$ ($p\in(0,1]$) and $\ell_{q}$ ($q p$) (quasi-) norms is proposed. Based on the prior block support information, mild condition in the frame of block restricted isometry property is established to ensure the stable and robust recovery of approximately block $ k $-sparse signals in different noise settings. Numerical studies support the recoverability of the proposed method and suggest that the new method yields better performance of block-sparse signal recovery compared with the existing results.
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