Liu Jing, Huang Kaiyu, Zhang Guoxian
School of Electronics and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
Sensors (Basel). 2017 Apr 20;17(4):907. doi: 10.3390/s17040907.
We consider the joint sparsity Model 1 (JSM-1) in a decentralized scenario, where a number of sensors are connected through a network and there is no fusion center. A novel algorithm, named distributed compact sensing matrix pursuit (DCSMP), is proposed to exploit the computational and communication capabilities of the sensor nodes. In contrast to the conventional distributed compressed sensing algorithms adopting a random sensing matrix, the proposed algorithm focuses on the deterministic sensing matrices built directly on the real acquisition systems. The proposed DCSMP algorithm can be divided into two independent parts, the common and innovation support set estimation processes. The goal of the common support set estimation process is to obtain an estimated common support set by fusing the candidate support set information from an individual node and its neighboring nodes. In the following innovation support set estimation process, the measurement vector is projected into a subspace that is perpendicular to the subspace spanned by the columns indexed by the estimated common support set, to remove the impact of the estimated common support set. We can then search the innovation support set using an orthogonal matching pursuit (OMP) algorithm based on the projected measurement vector and projected sensing matrix. In the proposed DCSMP algorithm, the process of estimating the common component/support set is decoupled with that of estimating the innovation component/support set. Thus, the inaccurately estimated common support set will have no impact on estimating the innovation support set. It is proven that under the condition the estimated common support set contains the true common support set, the proposed algorithm can find the true innovation set correctly. Moreover, since the innovation support set estimation process is independent of the common support set estimation process, there is no requirement for the cardinality of both sets; thus, the proposed DCSMP algorithm is capable of tackling the unknown sparsity problem successfully.
我们考虑在分散场景下的联合稀疏模型1（JSM - 1），其中多个传感器通过网络连接且不存在融合中心。提出了一种名为分布式紧凑传感矩阵追踪（DCSMP）的新算法，以利用传感器节点的计算和通信能力。与采用随机传感矩阵的传统分布式压缩传感算法不同，该算法专注于直接基于实际采集系统构建的确定性传感矩阵。所提出的DCSMP算法可分为两个独立部分，即公共和创新支持集估计过程。公共支持集估计过程的目标是通过融合来自单个节点及其相邻节点的候选支持集信息来获得估计的公共支持集。在接下来的创新支持集估计过程中，将测量向量投影到与由估计的公共支持集索引的列所跨越的子空间垂直的子空间中，以消除估计的公共支持集的影响。然后，我们可以基于投影后的测量向量和投影后的传感矩阵，使用正交匹配追踪（OMP）算法搜索创新支持集。在所提出的DCSMP算法中，估计公共分量/支持集的过程与估计创新分量/支持集的过程解耦。因此，估计不准确的公共支持集不会对估计创新支持集产生影响。证明了在所估计的公共支持集包含真实公共支持集的条件下，所提出的算法能够正确找到真实的创新集。此外，由于创新支持集估计过程独立于公共支持集估计过程，因此对两个集合的基数没有要求；因此，所提出的DCSMP算法能够成功解决未知稀疏性问题。
