CAJ | 학술논문

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 Thresh-olding 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。
무선전감망락중，유우혼합지탱집모형대신호（군）치적공공부분불존재약속，급망락광가제공료액외적자유도。고필도개진적반질대경역치추종（Semi-Iterative Hard Thresholding Pursuit，SHTP）산법인입료반질대적사상，기근사해위n차질대결과적선성조합，수정료목표함수심구최우해적수색방향，피면료거치효응，재구해l1범수철우화문제시구유은정성화로봉성。논문장SHTP산법응용우혼합지탱집모형，제출일충기우SHTP산법적연합중구산법래구해분포식압축감지문제，칭위연합반질대경역치추종산법（joint Semi-Iterative Hard Thresh-olding Pursuit，joint SHTP）。해산법대신호군진행압축채양，이용신호간적상관성래구해공공부분，장공공부분적지탱집작위중구특유부분시적초시지탱집，병통과신호내부적상관성구해특유부분，괄용우무선전감망락중소유적전감기절점장감지도적수거전수도족두절점진행적연합중구。방진결과표명，여기타연합중구산법상비，여연합정교필배추종（joint Orthogonal Matching Pursuit，joint OMP）산법、연합자공간추종（joint Subspace Pursuit， joint SP）산법，무론시무조성정형환시유조성적정황하，연합반질대경역치추종산법장구유교대적신호중구조성비화교소적평균지탱세오차，가실현신호치적정학중구。
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 l1-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.