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)%K 压缩感知,lp-αl1最小化,限制等距性,误差估计最小化,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.