非凸压缩感知恢复算法及其在宽带频谱感知中的应用研究
发布时间：2018-11-20 13:18
【摘要】：压缩感知是近10年来信号处理领域非常重要的理论成果之一,自2006年正式提出后,在很短时间内吸引了大量研究者的关注,至今在权威期刊仍然不断涌现出新的理论成果和实际应用范例,研究前景广阔,应用潜力巨大。作为压缩感知三大构成部分之一的恢复算法,一直是该领域的热点和难点,虽然已有很多算法被提出,但如何以尽量少的运算量获得更为稀疏和稳健的解,仍然是一个值得探索的问题。本文选择非凸压缩感知作为研究对象。所谓非凸压缩感知,指的是其优化目标函数呈现非凸特性,比凸松弛目标函数(如L1范数)更加接近LO范数,因而在相同条件下,达到全局最优时,可以得到更稀疏的解,同时,具备更好的抗噪性能。但是非凸压缩感知在获得恢复增益的同时,存在提前收敛的风险,如何设计更好的逼近算法,尽量避免局部最优解的出现,是本文研究的出发点之一。本文对几种典型的非凸压缩感知算法进行了深入分析,并提出了新的恢复算法,使用数值仿真证实了本文工作的正确性与有效性。本文的重要贡献体现在以下几点。(1)为揭示稀疏贝叶斯学习的本质,探究其优异恢复能力的来源,证明了EMSBL(使用EM算法的稀疏贝叶斯学习)中第一类与第二类最大似然之间的本质差异,并揭示了FOCUSS,IRL1与EMSBL之间的内在关系。使用数值仿真展示了EMSBL的局部解特性,并与LO范数的局部解进行比较,证实了前者的局部解数目少于后者,因而具有更好的恢复效果,在均方误差和恢复成功率方面优于现有的其他算法。(2)为了使用成熟算法的简单组合获得优异恢复能力,提出了支撑驱动的恢复算法框架SD_IRLp,该框架将恢复过程分为2步：第1步,假设系统中不存在任何噪声,求取一个相对“稠密”的解,并提取其中满足某个阈值条件的支撑；第2步,将第1步所提取的支撑作为先验信息带入某种算法,迭代至收敛,获得稳定解。通过与现有的7种有竞争力的算法比较,基于TBP+FOCUSS的恢复算法在运算效率和恢复性能上达到了很好的折中。所提出的框架具有很好的扩展性与适应性,可基于多种算法组合实现。(3)为克服传统SLO算法恢复性能上的弱点,设计了一个LO范数迭代重加权逼近框架,以平滑可微的代理函数为核心,通过求解目标函数的牛顿方向,并将其视作CCCP,获得了两种恢复算法,所有见诸文献的代理函数均可带入本文的算法进行稀疏恢复。数值仿真证实,本文所设计的一种新型代理函数在应用于所提出算法时,其性能明显优于SLO,较ISLO也有相当的优势。(4)为了更科学有效地使用各类先验信息,对先验信息的类型与使用方式进行了深入分析,研究了3种先验信息的处理方式：第1种,以概率方式引入,控制迭代权值的处理方式；第2种,在稀疏干扰消除的基础上,研究了使用正交投影思想消除已有支撑对后续恢复的影响,形成一种新的算法OP FOCUSS;第3种,推广了正交投影的思想,在压缩域消除已知幅值和支撑的分量后,再次进行恢复,据此提出无需先验信息辅助的PC FOCUSS算法,使恢复性能获得明显提升。(5)为提升认知无线电系统用户切换效率,提出一种新的分布式的宽带频谱感知系统,该系统在采样前端使用了宽带调制转换MWC,并将来自于相邻感知节点的信息作为先验,最后基于所提出的先验信息辅助MSBL(LA-MSBL)算法予以恢复。数值仿真证实,所提出的频谱感知系统可以有效抵抗干扰与衰落,提高频谱感知精度。最后,在总结全文的基础上,对压缩感知的理论研究与应用前景进行了展望,并给出了一些有待深入研究的开放性问题。
[Abstract]:The compression perception is one of the most important theoretical achievements in the field of signal processing in recent 10 years. Since the formal introduction in 2006, the attention of a large number of researchers has been attracted in a short time, so far, new theoretical achievements and practical application examples have been constantly emerging in the authoritative journal, and the research prospect is wide. The application potential is huge. The recovery algorithm, which is one of the three components of compression-aware, has been a hot and difficult point in this field. Although many algorithms have been put forward, how to obtain a more sparse and robust solution with the least amount of computation is still a problem to be explored. In this paper, the non-convex compression sensing is selected as the research object. The so-called non-convex compression perception refers to the non-convex characteristic of the optimized objective function, and is closer to the LO norm than the convex relaxation target function (such as the L1 norm), so that under the same condition, a more sparse solution can be obtained when the global optimal is achieved, and meanwhile, the method has better anti-noise performance. But the non-convex compression perception is the risk of early convergence, and how to design a better approximation algorithm to avoid the occurrence of local optimal solution is one of the starting points of this paper. In this paper, several typical non-convex compression-aware algorithms are deeply analyzed, and a new recovery algorithm is proposed. The correctness and validity of this paper are verified by numerical simulation. The important contribution of this paper is reflected in the following points. (1) In order to reveal the essence of the sparse Bayesian learning and to explore the source of its excellent recovery capability, the essential difference between the first and the second class in the sparse Bayesian learning of the EMSBL (using the sparse Bayesian learning of the EM algorithm) is proved, and the internal relation between the FOCUSS, the IRL1 and the EMSBL is also revealed. The local solution of the EMSBL is shown by numerical simulation, and compared with the local solution of the LO norm, it is proved that the local solution number of the former is less than the latter, so it has better recovery effect and is superior to the existing other algorithms in both the mean square error and the recovery success rate. (2) In order to obtain the excellent recovery capability with the simple combination of the mature algorithm, a support-driven recovery algorithm framework SD _ IRLp is proposed, which divides the recovery process into two steps: step 1, assuming no noise exists in the system, and obtaining a relative 鈥渄ense鈥，
本文编号：2345022
[Abstract]:The compression perception is one of the most important theoretical achievements in the field of signal processing in recent 10 years. Since the formal introduction in 2006, the attention of a large number of researchers has been attracted in a short time, so far, new theoretical achievements and practical application examples have been constantly emerging in the authoritative journal, and the research prospect is wide. The application potential is huge. The recovery algorithm, which is one of the three components of compression-aware, has been a hot and difficult point in this field. Although many algorithms have been put forward, how to obtain a more sparse and robust solution with the least amount of computation is still a problem to be explored. In this paper, the non-convex compression sensing is selected as the research object. The so-called non-convex compression perception refers to the non-convex characteristic of the optimized objective function, and is closer to the LO norm than the convex relaxation target function (such as the L1 norm), so that under the same condition, a more sparse solution can be obtained when the global optimal is achieved, and meanwhile, the method has better anti-noise performance. But the non-convex compression perception is the risk of early convergence, and how to design a better approximation algorithm to avoid the occurrence of local optimal solution is one of the starting points of this paper. In this paper, several typical non-convex compression-aware algorithms are deeply analyzed, and a new recovery algorithm is proposed. The correctness and validity of this paper are verified by numerical simulation. The important contribution of this paper is reflected in the following points. (1) In order to reveal the essence of the sparse Bayesian learning and to explore the source of its excellent recovery capability, the essential difference between the first and the second class in the sparse Bayesian learning of the EMSBL (using the sparse Bayesian learning of the EM algorithm) is proved, and the internal relation between the FOCUSS, the IRL1 and the EMSBL is also revealed. The local solution of the EMSBL is shown by numerical simulation, and compared with the local solution of the LO norm, it is proved that the local solution number of the former is less than the latter, so it has better recovery effect and is superior to the existing other algorithms in both the mean square error and the recovery success rate. (2) In order to obtain the excellent recovery capability with the simple combination of the mature algorithm, a support-driven recovery algorithm framework SD _ IRLp is proposed, which divides the recovery process into two steps: step 1, assuming no noise exists in the system, and obtaining a relative 鈥渄ense鈥，
本文编号：2345022
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