L1/2正则子在Lq (0 < q < 1)正则子中的代表性: 基于相位图的实验研究

徐宗本; 郭海亮; 王尧; 张海

doi:10.3724/SP.J.1004.2012.01225

L_1/2正则子在L_q (0 < q < 1)正则子中的代表性: 基于相位图的实验研究

doi: 10.3724/SP.J.1004.2012.01225

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出版历程
- 收稿日期: 2011-03-16
- 修回日期: 2011-06-22
- 刊出日期: 2012-07-20

Representative of L_1/2 Regularization among L_q (0 < q ≤ 1) Regularizations: an Experimental Study Based on Phase Diagram

摘要

摘要: 近期, 正则化方法吸引了越来越多的关注. 在L1正则子之后，Lq (0 q 1) 正则子被提出用于更好的求解稀疏性问题. 一个自然的问题是：在所有Lq (0 q 1) 正则子中, 哪一个q是最好的选择？通过采用相位图, 以及一组关于信号恢复与误差校正问题的实验, 我们表明: (i) 随着q减小, Lq正则子得到更稀疏的解; (ii) 当1/2L1/2正则子始终产生最好的稀疏解，且当0 q 1/2时，正则子的性能没有显著的区别. 因此, 我们认为L1/2正则子可被看作是一个Lq (0 q 1) 正则子的代表.
- Lq正则子 /
- 相位图 /
- 信号恢复 /
- 误差校正
Abstract: Recently, regularization methods have attracted in-creasing attention. Lq (0 q 1) regularizations were proposed after L1 regularization for better solution of sparsity problems. A natural question is which is the best choice among Lq regu-larizations with all q in (0, 1)? By taking phase diagram studies with a set of experiments implemented on signal recovery and error correction problems, we show the following: 1) As the value of q decreases, the Lq regularization generates sparser solution. 2) When 1/2 ≤ q 1, the L1/2 regularization always yields the best sparse solution and when 0 q ≤ 1/2, the performance of the regularizatons takes no significant difference. Accordingly, we conclude that the L1/2 regularization can be taken as a rep-resentative of Lq (0 q 1) regularizations.
- Lq regularization /
- phase diagram /
- signal recovery /
- error correction

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[1]

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