Abstract Signal recovery through l1-minimization may fail for restricted isometry constant δ 2 s > 2 / 2 , therefore lp-minimization is an alternative method. In this paper, we consider the use of lp-minimization with 0 A x = y . We prove that if A satisfies a restricted isometry property with δ 2 s > 2 / 2 , an upper bound p ¯ = ( 2 + 2 ) ( 1 − δ 2 s ) exists such that any s-sparse signal can be recovered through a nonconvex lp-minimization with any p ≤ p ¯ . To the best of our knowledge, this upper bound p ¯ is a significant improvement compared to the best existing results proposed by Wen et al. (2015) [19], i.e., p ¯ = { 50 31 ( 1 − δ 2 s ) , δ 2 s ∈ [ 2 / 2 , 0.7183 ) , 0.4541 , δ 2 s ∈ [ 0.7183 , 0.7729 ) , 2 ( 1 − δ 2 s ) , δ 2 s ∈ [ 0.7729 , 1 ) . Numerical experiment indicates that lp-minimization with a larger p has better recovery effect than with a smaller p. Our result expands the upper bound of p.

中文翻译：

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压缩感知中 l 最小化的 p 的新上限

摘要 对于受限等距常数 δ 2 s > 2 / 2 ，通过 l1 最小化的信号恢复可能会失败，因此 lp 最小化是一种替代方法。在本文中，我们考虑使用 0 A x = y 的 lp 最小化。我们证明，如果 A 满足 δ 2 s > 2 / 2 的受限等距性质，则存在上界 p¯ = ( 2 + 2 ) ( 1 − δ 2 s ) 使得任何 s 稀疏信号都可以通过具有任何 p ≤ p¯ 的非凸 lp 最小化。据我们所知，与 Wen 等人提出的最佳现有结果相比，这个上限 p 是一个显着的改进。(2015) [19], 即 p¯ = { 50 31 ( 1 − δ 2 s ) , δ 2 s ∈ [ 2 / 2 , 0.7183 ) , 0.4541 , δ 2 s ∈ [ 0.7183 , 2 , 17 7 ] − δ 2 s) , δ 2 s ∈ [0.7729, 1) 。数值实验表明，p较大的lp-minimization比p较小的恢复效果更好。我们的结果扩展了 p 的上限。