中文摘要：

无线传感网络中,由于混合支撑集模型对信号（群）值的公共部分不存在约束,给网络框架提供了额外的自由度。考虑到改进的半迭代硬阈值追踪（Semi-Iterative Hard Thresholding Pursuit,SHTP）算法引入了半迭代的思想,其近似解为n次迭代结果的线性组合,修正了目标函数寻求最优解的搜索方向,避免了锯齿效应,在求解l1范数凸优化问题时具有稳定性和鲁棒性。论文将SHTP算法应用于混合支撑集模型,提出一种基于SHTP算法的联合重构算法来求解分布式压缩感知问题,称为联合半迭代硬阈值追踪算法（joint Semi-Iterative Hard Thresholding Pursuit,joint SHTP）。该算法对信号群进行压缩采样,利用信号间的相关性来求解公共部分,将公共部分的支撑集作为重构特有部分时的初始支撑集,并通过信号内部的相关性求解特有部分,适用于无线传感网络中所有的传感器节点将感知到的数据传输到簇头节点进行的联合重构。仿真结果表明,与其他联合重构算法相比,如联合正交匹配追踪（joint Orthogonal Matching Pursuit,joint OMP）算法、联合子空间追踪（joint Subspace Pursuit,joint SP）算法,无论是无噪声情形还是有噪声的情况下,联合半迭代硬阈值追踪算法将具有较大的信号重构噪声比和较小的平均支撑势误差,可实现信号值的精确重构。

英文摘要：

In wireless sensor networks, the mixed support-set model can provide additional degrees of freedom for network frame since it has no constraint on the common signal components. With respect to the high stability and robustness proper- ty of modified Semi-Iterative Hard Thresholding Pursuit algorithm （SHTP） in which the direction of searching objective function is modified based on semi-iterative idea as a convergent method with polynomial acceleration, and the searching di- rection is non-orthogonal for each iterative step by using the liner combination of the n-th iteration result to gain the approxi- mate solution in ~-norm convex optimization. We propose a joint SHTP reconstruction algorithm by combining SHTP algo- rithm with the mixed support-set model to realize the distributed compressed sensing of the signal groups in a multiple-sen- sor setup where all the sensors transmit the sensing data to the centralized node. The algorithm aims at solving a common sparse signal part utilizing the inter-signal correlation to gain a common support set as the initial values, based on which the individual signal part can be reconstructed using the inner-signal correlation. The simulation results show that, compared with the existed joint reconstruction algorithms, such as joint OMP and joint SP, the joint SHTP algorithm could gain the maximum signal to reconstruction noise ratio and the minimum average support cardinality error. It is indicated that the pro- posed algorithm can achieve the precise reconstruction no matter the network setup is noisy or not.