非凸壓縮感知恢復(fù)算法及其在寬帶頻譜感知中的應(yīng)用研究
發(fā)布時間：2018-11-20 13:18
【摘要】：壓縮感知是近10年來信號處理領(lǐng)域非常重要的理論成果之一,自2006年正式提出后,在很短時間內(nèi)吸引了大量研究者的關(guān)注,至今在權(quán)威期刊仍然不斷涌現(xiàn)出新的理論成果和實際應(yīng)用范例,研究前景廣闊,應(yīng)用潛力巨大。作為壓縮感知三大構(gòu)成部分之一的恢復(fù)算法,一直是該領(lǐng)域的熱點和難點,雖然已有很多算法被提出,但如何以盡量少的運算量獲得更為稀疏和穩(wěn)健的解,仍然是一個值得探索的問題。本文選擇非凸壓縮感知作為研究對象。所謂非凸壓縮感知,指的是其優(yōu)化目標函數(shù)呈現(xiàn)非凸特性,比凸松弛目標函數(shù)(如L1范數(shù))更加接近LO范數(shù),因而在相同條件下,達到全局最優(yōu)時,可以得到更稀疏的解,同時,具備更好的抗噪性能。但是非凸壓縮感知在獲得恢復(fù)增益的同時,存在提前收斂的風險,如何設(shè)計更好的逼近算法,盡量避免局部最優(yōu)解的出現(xiàn),是本文研究的出發(fā)點之一。本文對幾種典型的非凸壓縮感知算法進行了深入分析,并提出了新的恢復(fù)算法,使用數(shù)值仿真證實了本文工作的正確性與有效性。本文的重要貢獻體現(xiàn)在以下幾點。(1)為揭示稀疏貝葉斯學習的本質(zhì),探究其優(yōu)異恢復(fù)能力的來源,證明了EMSBL(使用EM算法的稀疏貝葉斯學習)中第一類與第二類最大似然之間的本質(zhì)差異,并揭示了FOCUSS,IRL1與EMSBL之間的內(nèi)在關(guān)系。使用數(shù)值仿真展示了EMSBL的局部解特性,并與LO范數(shù)的局部解進行比較,證實了前者的局部解數(shù)目少于后者,因而具有更好的恢復(fù)效果,在均方誤差和恢復(fù)成功率方面優(yōu)于現(xiàn)有的其他算法。(2)為了使用成熟算法的簡單組合獲得優(yōu)異恢復(fù)能力,提出了支撐驅(qū)動的恢復(fù)算法框架SD_IRLp,該框架將恢復(fù)過程分為2步：第1步,假設(shè)系統(tǒng)中不存在任何噪聲,求取一個相對“稠密”的解,并提取其中滿足某個閾值條件的支撐；第2步,將第1步所提取的支撐作為先驗信息帶入某種算法,迭代至收斂,獲得穩(wěn)定解。通過與現(xiàn)有的7種有競爭力的算法比較,基于TBP+FOCUSS的恢復(fù)算法在運算效率和恢復(fù)性能上達到了很好的折中。所提出的框架具有很好的擴展性與適應(yīng)性,可基于多種算法組合實現(xiàn)。(3)為克服傳統(tǒng)SLO算法恢復(fù)性能上的弱點,設(shè)計了一個LO范數(shù)迭代重加權(quán)逼近框架,以平滑可微的代理函數(shù)為核心,通過求解目標函數(shù)的牛頓方向,并將其視作CCCP,獲得了兩種恢復(fù)算法,所有見諸文獻的代理函數(shù)均可帶入本文的算法進行稀疏恢復(fù)。數(shù)值仿真證實,本文所設(shè)計的一種新型代理函數(shù)在應(yīng)用于所提出算法時,其性能明顯優(yōu)于SLO,較ISLO也有相當?shù)膬?yōu)勢。(4)為了更科學有效地使用各類先驗信息,對先驗信息的類型與使用方式進行了深入分析,研究了3種先驗信息的處理方式：第1種,以概率方式引入,控制迭代權(quán)值的處理方式；第2種,在稀疏干擾消除的基礎(chǔ)上,研究了使用正交投影思想消除已有支撐對后續(xù)恢復(fù)的影響,形成一種新的算法OP FOCUSS;第3種,推廣了正交投影的思想,在壓縮域消除已知幅值和支撐的分量后,再次進行恢復(fù),據(jù)此提出無需先驗信息輔助的PC FOCUSS算法,使恢復(fù)性能獲得明顯提升。(5)為提升認知無線電系統(tǒng)用戶切換效率,提出一種新的分布式的寬帶頻譜感知系統(tǒng),該系統(tǒng)在采樣前端使用了寬帶調(diào)制轉(zhuǎn)換MWC,并將來自于相鄰感知節(jié)點的信息作為先驗,最后基于所提出的先驗信息輔助MSBL(LA-MSBL)算法予以恢復(fù)。數(shù)值仿真證實,所提出的頻譜感知系統(tǒng)可以有效抵抗干擾與衰落,提高頻譜感知精度。最后,在總結(jié)全文的基礎(chǔ)上,對壓縮感知的理論研究與應(yīng)用前景進行了展望,并給出了一些有待深入研究的開放性問題。
[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，
本文編號：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，
本文編號：2345022
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