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基于lp-αl1模型下的部分已知支集信号恢复的研究
Research on Partial Known Support Signal Recovery Based on lp-αl1 Model

DOI: 10.12677/AAM.2024.131040, PP. 392-400

Keywords: 压缩感知，lp-αl1最小化，限制等距性，误差估计
Compressed Sensing, lp-αl1 Minimization, Restricted Isometry Property, Error Estimates

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Abstract:

压缩感知通过少量非自适应的线性测量有效地获取稀疏信号，是一种新型的采样方法。它突破了传统的香农采样定理的局限性，以远低于香农采样率的数据实现原始信号的精确恢复。本文在l1，lq(0＜q＜1），l1-l2，l1-αl2(0≤α≤1)等最小化模型基础下，考虑了新模型lp-αl1(0＜p＜1,0＜α≤1)最小化，对部分已知支集的信号重建提出了一个新的条件，得到了信号在l2有界噪声、DS噪声及高斯噪声情形下的误差逼近。
Compressed sensing is a new sampling method which can obtain sparse signals effectively by a small number of non-adaptive linear measurements. It breaks the limitation of the traditional Xiangnong sampling theory and achieves the exact recovery of theoriginal signal with the data far below the Xiangnong sampling rate. In this paper, based on the l1，lq(0＜q＜1），l1-l2，l1-αl2(0≤α≤1) minimization models, a new model called lp-αl1 minimization and a new condition for signal reconstruction with partial known support is proposed, and the error approximation of the signal in the case of l2 bounded noise and DS noise is obtained.

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