论文标题
信号恢复的块相互连贯性属性条件
The block mutual coherence property condition for signal recovery
论文作者
论文摘要
压缩传感表明，从不完整的线性测量值中可以稳定回收稀疏信号。但是，在实际应用中，某些信号具有附加的结构，其中非零元素在某些块中出现。我们称之为“块 - 宽度信号”等信号。在本文中，研究了$ \ ell_2/\ell_1-α\ ell_2 $最小化方法，用于稳定恢复块 - sparse信号。建立了基于块相互一致性属性和关联误差的上限估计的足够条件，以确保在存在噪声的情况下通过$ \ ell_2/\ ell_1-al_1-α\ ell_2 $最小化方法在存在噪声的情况下稳定恢复块信号。就我们所知，这是通过$ \ ell_2/\ ell_1-α\ ell_2 $最小化方法稳定地重建块 - sparse信号的第一个块相互连贯性。此外，实施的数值实验验证了$ \ ell_2/\ell_1-α\ ell_2 $最小化的性能。
Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the $\ell_2/\ell_1-α\ell_2$ minimization method for the stable recovery of block-sparse signals is investigated. Sufficient conditions based on block mutual coherence property and associating upper bound estimations of error are established to ensure that block-sparse signals can be stably recovered in the presence of noise via the $\ell_2/\ell_1-α\ell_2$ minimization method. For all we know, it is the first block mutual coherence property condition of stably reconstructing block-sparse signals by the $\ell_2/\ell_1-α\ell_2$ minimization method. Additionally, the numerical experiments implemented verify the performance of the $\ell_2/\ell_1-α\ell_2$ minimization.
