Enhancing Sparsity by Reweighted l1 Minimization
Enhancing Sparsity by Reweighted l1 Minimization
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DOI：
10.1007/s00041-008-9045-x
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发表时间：
2008-12-01
影响因子：
1.2
通讯作者：
Boyd, Stephen P.
中科院分区：
文献类型：
--
作者：
Candes, Emmanuel J.;Wakin, Michael B.;Boyd, Stephen P.
现在众所周知，（1）可以准确地重建稀疏信号，从似乎是高度不完整的线性测量集集，并且（2）可以通过约束L（1）最小化来完成。在本文中，我们研究了一种稀疏信号恢复的新方法，在许多情况下，在许多情况下，最小化的含义是，精确恢复所需的测量要少得多。该算法包括求解一系列加权L（1） - 刻度问题，其中用于下一个迭代的权重是从当前解决方案的值中计算出来的。我们提出了一系列实验，证明了该算法在稀疏信号恢复，统计估计，误差校正和图像处理领域的显着性能和广泛的适用性。有趣的是，当应用我们的方法用于恢复具有过分统计表示的近距离表示信号时，也可以实现上涨转换的对象。直接的结果是通过改进称为压缩感应的技术来获得高效的数据采集协议。
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained l(1) minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms l(1) minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted l(1)-minimization problems where the weights used for the next iteration are computed from the value of the current solution. We present a series of experiments demonstrating the remarkable performance and broad applicability of this algorithm in the areas of sparse signal recovery, statistical estimation, error correction and image processing. Interestingly, superior gains are also achieved when our method is applied to recover signals with assumed near-sparsity in overcomplete representations-not by reweighting the l(1) norm of the coefficient sequence as is common, but by reweighting the l(1) norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by improving on a technique known as Compressive Sensing.