Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively studied. Many reconstruction algorithms have been proposed and shown good reconstruction performance. However, when dealing with large-scale sparse signal reconstruction problem, the storage requirement will be high, and many algorithms also suffer from high computational cost. In this paper, we propose a novel diffusion adaptation framework for CS reconstruction, where the reconstruction is performed in a distributed network. The data of measurement matrix are partitioned into small parts and are stored in each node, which assigns the storage load in a decentralized manner. The local information interaction provides the reconstruction ability. Then, a simple and efficient gradient-descend based diffusion algorithm has been proposed to collaboratively recover the sparse signal over network. The convergence of the proposed algorithm is analyzed. To further increase the convergence speed, a mini-batch based diffusion algorithm is also proposed. Simulation results show that the proposed algorithms can achieve good reconstruction accuracy as well as fast convergence speed.

中文翻译：

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压缩感知重建的扩散适应框架

压缩感知（CS）由于其低采样率和高恢复精度近年来备受关注。作为一个重要的过程，从少量测量数据重建稀疏信号已经得到深入研究。已经提出了许多重建算法并显示出良好的重建性能。但是，在处理大规模稀疏信号重构问题时，存储要求会很高，而且很多算法也存在计算成本高的问题。在本文中，我们提出了一种用于 CS 重建的新型扩散适应框架，其中重建是在分布式网络中进行的。测量矩阵的数据被分成小部分存储在每个节点中，以分散的方式分配存储负载。本地信息交互提供重构能力。然后，提出了一种简单有效的基于梯度下降的扩散算法来协同恢复网络上的稀疏信号。分析了所提出算法的收敛性。为了进一步提高收敛速度，还提出了一种基于小批量的扩散算法。仿真结果表明，所提算法能够达到较好的重建精度和较快的收敛速度。