本文選題：欠定盲分離　切入點：壓縮感知　出處：《西安電子科技大學》2015年碩士論文

【摘要】：欠定盲分離指對源信號及信道參數(shù)一無所知的情況下,僅僅根據(jù)傳感器接收到的信號直接將源信號恢復出來。壓縮感知是近年來發(fā)展起來的一門壓縮采樣技術(shù),它能以低于奈奎斯特采樣速度的采樣率對信號進行采樣,并且在接收端對源信號進行近乎完美的恢復。由于壓縮感知稀疏信號重構(gòu)與欠定盲分離中的源信號恢復有相同的數(shù)學模型,因此,壓縮感知稀疏信號重構(gòu)算法被廣泛的用來解決欠定盲分離源信號恢復問題。本文研究的就是基于壓縮感知的欠定盲分離源信號恢復技術(shù)。本文的工作可以概括為如下幾個方面:(1)指出了Pando Georgiev等提出的欠定盲分離可完全重構(gòu)條件所存在的問題,對結(jié)論進行了完善。通過對Pando Georgiev等提出的欠定盲分離可完全重構(gòu)條件與壓縮感知中的NSP準則進行對比,發(fā)現(xiàn)了結(jié)論的不一致性,找出了欠定盲分離可完全重構(gòu)條件存在的問題,對結(jié)論進行了修正。(2)針對貪婪算法中的互補匹配追蹤算法復雜度較高的問題,提出了子空間互補匹配追蹤算法。貪婪算法是一種在源信號充分稀疏的條件下性能較好的算法。貪婪算法中時間復雜度較低的匹配追蹤算法恢復精度較低,而精度較高的互補匹配追蹤算法復雜度又較高。針對此問題,本文在互補匹配追蹤算法的基礎(chǔ)上,結(jié)合子空間搜索的思想,提出了子空間互補匹配追蹤算法。提出的算法在顯著減小算法時間復雜度的基礎(chǔ)上,在一定程度上提高了算法的精度,體現(xiàn)出了良好的性能。(3)針對基于L1范數(shù)的稀疏信號重構(gòu)算法復雜度較高的問題,提出了基于L1范數(shù)的互補匹配追蹤算法�，F(xiàn)有的基于L1范數(shù)的稀疏信號重構(gòu)算法存在的問題是復雜度普遍較高,針對此問題,本文將原始優(yōu)化問題進行了降維處理,利用迭代收斂方法求解問題的最優(yōu)解。通過理論分析和仿真實驗得出,該算法在顯著降低算法復雜度的同時,保持了原有算法的精度。(4)針對平滑L0范數(shù)收斂速度慢以及受步長影響較大的問題,提出了基于修正牛頓法的徑向基函數(shù)算法。該算法將修正牛頓法引入到了徑向基函數(shù)算法當中,克服了原始的徑向基函數(shù)算法恢復精度受步長影響較大的問題,通過仿真得出,改進的算法在顯著降低算法復雜度的同時,也提高了算法的精度。
[Abstract]:Undetermined blind separation refers to recovering the source signal directly from the signal received by the sensor without knowledge of the source signal and channel parameters. Compression sensing is a compression sampling technique developed in recent years. It can sample the signal at a rate lower than Nyquist's. And the source signal is restored almost perfectly at the receiving end. Because the reconstruction of compressed perceptual sparse signal has the same mathematical model as the source signal recovery in under-determined blind separation, so, Compressed sensing sparse signal reconstruction algorithm is widely used to solve the problem of undetermined blind source signal recovery. In this paper, we study a compressed perceptual algorithm for the restoration of underdetermined blind separated source signals. The work of this paper can be summarized as follows. The following are several aspects: 1) We point out the problem of the condition that Pando Georgiev et al can completely reconstruct the undetermined blind separation. The conclusion is improved. By comparing the fully reconfigurable condition of underdetermined blind separation proposed by Pando Georgiev and the NSP criterion in compression perception, the inconsistency of the conclusion is found, and the problems existing in the fully reconfigurable condition of under-determined blind separation are found out. The conclusion is modified to solve the problem of high complexity of complementary matching tracking algorithm in greedy algorithm. A subspace complementary matching tracking algorithm is proposed. Greedy algorithm is a better algorithm with sparse source signal. The algorithm with low time complexity in greedy algorithm has low recovery accuracy. The complexity of complementary matching tracking algorithm with high precision is higher. In order to solve this problem, this paper combines the idea of subspace search based on complementary matching tracking algorithm. A subspace complementary matching tracking algorithm is proposed, which can significantly reduce the time complexity of the algorithm and improve the accuracy of the algorithm to a certain extent. It shows good performance. (3) aiming at the problem of high complexity of sparse signal reconstruction algorithm based on L1 norm, This paper presents a complementary matching tracking algorithm based on L1 norm. The existing sparse signal reconstruction algorithm based on L1 norm has a high complexity. In view of this problem, the original optimization problem is reduced by dimension reduction. The iterative convergence method is used to solve the optimal solution of the problem. The theoretical analysis and simulation results show that the algorithm can significantly reduce the complexity of the algorithm at the same time. In order to solve the problem of slow convergence speed of smooth L0 norm and large influence of step size, the accuracy of the original algorithm is maintained. A radial basis function algorithm based on modified Newton method is proposed. The modified Newton method is introduced into the radial basis function algorithm, which overcomes the problem that the restoration accuracy of the original radial basis function algorithm is greatly affected by step size. The improved algorithm can significantly reduce the complexity of the algorithm, but also improve the accuracy of the algorithm.
【學位授予單位】：西安電子科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN911.7

【參考文獻】

相關(guān)期刊論文 前2條

1 Xiang Wang;Zhitao Huang;Yiyu Zhou;;Underdetermined DOA estimation and blind separation of non-disjoint sources in time-frequency domain based on sparse representation method[J];Journal of Systems Engineering and Electronics;2014年01期

2 安澄全;彭軍偉;;基于混合優(yōu)化的平滑l_0壓縮感知重構(gòu)算法[J];應用科技;2013年05期

，

本文編號：1659751