Low-Complexity DCD-Based Sparse Recovery Algorithms
Low-Complexity DCD-Based Sparse Recovery Algorithms
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DOI：
10.1109/access.2017.2715882
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发表时间：
2017-06
期刊：
影响因子：
3.9
通讯作者：
Y. Zakharov;V. Nascimento;R. C. de Lamare;Fernando Goncalves De Almeida Neto
中科院分区：
文献类型：
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作者：
Y. Zakharov;V. Nascimento;R. C. de Lamare;Fernando Goncalves De Almeida Neto
稀疏恢复技术在许多领域都有应用。这种技术的实时实现最近已成为一个重要的研究领域。在本文中，我们提出了计算效率的技术的基础上二分坐标下降（DCD）迭代稀疏复值信号的恢复。我们首先考虑$\ell_{2}\ell_{1}$优化，它可以将解的先验信息以权向量的形式合并。我们提出了一个基于DCD的算法$\ell_{2}\ell_{1}$优化与固定的$\ell_{1}$正则化，然后有效地将其纳入重新加权迭代使用热启动在每次迭代。然后，我们通过对正则化参数进行采样来利用同伦，并得到一个算法，该算法在每次同伦迭代中，使用固定的正则化参数对当前支持进行$\ell_{2}\ell_{1}$优化，然后通过添加/删除元素来更新支持。我们提出了有效的规则添加和删除的元素。同伦算法的性能进一步提高与重新加权。然后，我们提出了一个算法的$\ell_{2}\ell_{0}$优化，利用同伦的$\ell_{0}$正则化;它交替之间的最小二乘（LS）优化的支持和支持更新，我们还提出了一个有效的规则。当热启动的DCD迭代用于LS优化时，算法复杂度降低，并且由于大多数DCD操作是加法和移位，因此特别适合于实时实现。在信道估计的情况下，所提出的算法进行了研究，并与已知的稀疏恢复技术，如匹配追踪（MP）和YALL1算法。数值算例表明，该方法的均方误差小于YALL1算法，而复杂度与MP算法相当。
Sparse recovery techniques find applications in many areas. Real-time implementation of such techniques has been recently an important area for research. In this paper, we propose computationally efficient techniques based on dichotomous coordinate descent (DCD) iterations for recovery of sparse complex-valued signals. We first consider $\ell _{2} \ell _{1}$ optimization that can incorporate a priori information on the solution in the form of a weight vector. We propose a DCD-based algorithm for $\ell _{2} \ell _{1}$ optimization with a fixed $\ell _{1}$ regularization, and then efficiently incorporate it in reweighting iterations using a warm start at each iteration. We then exploit homotopy by sampling the regularization parameter and arrive at an algorithm that, in each homotopy iteration, performs the $\ell _{2} \ell _{1}$ optimization on the current support with a fixed regularization parameter and then updates the support by adding/removing elements. We propose efficient rules for adding and removing the elements. The performance of the homotopy algorithm is further improved with the reweighting. We then propose an algorithm for $\ell _{2} \ell _{0}$ optimization that exploits homotopy for the $\ell _{0}$ regularization; it alternates between the least-squares (LSs) optimization on the support and the support update, for which we also propose an efficient rule. The algorithm complexity is reduced when DCD iterations with a warm start are used for the LS optimization, and, as most of the DCD operations are additions and bit-shifts, it is especially suited to real-time implementation. The proposed algorithms are investigated in channel estimation scenarios and compared with known sparse recovery techniques, such as the matching pursuit (MP) and YALL1 algorithms. The numerical examples show that the proposed techniques achieve a mean-squared error smaller than that of the YALL1 algorithm and complexity comparable to that of the MP algorithm.