本文選題：多任務(wù) + 壓縮感知　； 參考：《國防科學(xué)技術(shù)大學(xué)》2014年博士論文

【摘要】：衛(wèi)星等信號偵收平臺在數(shù)據(jù)存儲、傳輸和處理資源上比較有限,研究如何解決這些問題有一定的意義,而壓縮感知技術(shù)可以針對一般偵收信號的稀疏性特點進(jìn)行有效的數(shù)據(jù)壓縮和重構(gòu),對解決這一問題很有幫助,因此深入研究高效的稀疏信號重構(gòu)算法具有一定的理論和現(xiàn)實意義。本文分別對壓縮信號檢測技術(shù)、多任務(wù)重構(gòu)技術(shù)、多任務(wù)分類重構(gòu)技術(shù)和合成多任務(wù)重構(gòu)技術(shù)這四方面進(jìn)行研究。論文的主要工作和創(chuàng)新點歸納如下:第二章基于NP準(zhǔn)則對隨機(jī)信號的壓縮檢測問題做了研究,給出了檢測概率、虛警概率和檢測門限三者的關(guān)系。分別研究了協(xié)方差為對角矩陣的高斯隨機(jī)信號壓縮檢測問題,具有任意協(xié)協(xié)方差的高斯隨機(jī)信號壓縮檢測問題和非高斯分布的隨機(jī)信號檢測問題。當(dāng)觀測樣點數(shù)太少時,就不能正確的重構(gòu)信號,但是對于壓縮檢測問題,較少的觀測樣點數(shù)就可以達(dá)到理想的檢測概率。第三章針對多個壓縮觀測任務(wù)的原始信號屬于同一類的情況,在貝葉斯框架下,提出了基于Laplace先驗的多任務(wù)壓縮感知算法(Laplace priors based Multitask Compressive Sensing,LMCS),是對單任務(wù)Laplace先驗壓縮感知算法的發(fā)展。分析了同MCS(Multitask Compressive Sensing,MCS)先驗信息共享模型的不同,LMCS的貝葉斯框架比MCS的框架多了一層超先驗信息,使得估計共享參數(shù)具有較大的靈活性,分析表明MCS是LMCS的特例。提出了基于Laplace先驗多任務(wù)壓縮感知的快速算法,把多余的噪聲參數(shù)積分去掉,增強(qiáng)了算法的穩(wěn)定性。證實了在針對一般性稀疏信號的貝葉斯重構(gòu)算法中LMCS算法具有一定的優(yōu)越性。然后針對模塊化稀疏信號提出了一種聯(lián)合重構(gòu)算法,即EMBSBL(Extended Multitask Block Sparse Bayesian Learning,EMBSBL)算法。EMBSBL算法不僅利用信號間的統(tǒng)計相關(guān)性和信號內(nèi)的模塊化信息,而且重構(gòu)時不需要模塊稀疏信號的先驗信息。第四章針對多個壓縮觀測任務(wù)的原始信號屬于不同類的情況,提出了基于MDL(Minmum Description Length,MDL)準(zhǔn)則的多任務(wù)分類重構(gòu)算法。針對這種情況,如果不進(jìn)行分類直接用LMCS或者M(jìn)CS算法進(jìn)行重構(gòu),導(dǎo)致重構(gòu)性能很差。針對一般性稀疏信號進(jìn)行分類重構(gòu),提出了基于MDL準(zhǔn)則的MDL-LMCS和MDL-MCS算法,實驗證實了該算法具有優(yōu)越的分類和重構(gòu)性能。然后針對于結(jié)構(gòu)化稀疏信號,提出了新的分類重構(gòu)算法,即GCEM-Turbo-GAMP-MMV算法,該算法利用狀態(tài)演化特性來確定分類結(jié)果,然后對每類任務(wù)進(jìn)行聯(lián)合重構(gòu),在分類重構(gòu)結(jié)構(gòu)化稀疏信號方面優(yōu)于MDL-LMCS和MDL-MCS算法。第五章針對模塊化稀疏信號提出了一種合成多任務(wù)的壓縮感知算法框架。多任務(wù)合成方法利用了模塊化稀疏信號的特殊結(jié)構(gòu),通過對原始信號中元素和觀測矩陣列的平移,合成多個新的任務(wù),利用最小描述長度準(zhǔn)則確定最佳的合成任務(wù)數(shù),再采用多任務(wù)壓縮感知算法重構(gòu)原始信號,可以得到較好的重構(gòu)性能。在多任務(wù)合成框架下,基于MCS算法和EMBSBL算法發(fā)展了新的合成多任務(wù)重構(gòu)算法,分別簡稱為SMCS(Synthetic MCS,SMCS)算法和SEMBSBL(Synthetic EMBSBL,SEMBSBL)算法。這兩種算法進(jìn)行對比各有優(yōu)缺點,SMCS算法運算時間少,但比后者重構(gòu)精度差;SEMBSBL算法重構(gòu)精度好,但運算量很大,這在處理大數(shù)據(jù)信號時尤為突出。兩種合成多任務(wù)重構(gòu)算法和其它單次重構(gòu)算法對比的優(yōu)點是不需要事先知道模塊化稀疏信號的任何模塊劃分信息,并可以有效提高單次重構(gòu)任務(wù)時的重構(gòu)精度。
[Abstract]:The satellite signal detection platform is limited in data storage, transmission and processing resources. It is of certain significance to study how to solve these problems. And compressed sensing technology can effectively compress and reconstruct the sparse characteristics of the general detection signal. It is very helpful to solve this problem. The sparse signal reconstruction algorithm has some theoretical and practical significance. This paper studies the four aspects of compressed signal detection technology, multi task reconfiguration technology, multi task classification reconstruction technology and synthetic multi task reconstruction technology. The main work and innovation point of this paper are summarized as follows: the second chapter is based on the NP criterion for the compression of random signals. The relationship between detection probability, false alarm probability and detection threshold three is given. The problem of Gauss random signal compression detection with covariance matrix is studied. The problem of Gauss random signal compression detection with arbitrary covariance and random signal detection problem of non Gauss distribution, when the number of observation samples is too few The signal can not be reconstructed correctly, but for the problem of compression detection, fewer observation points can reach the ideal detection probability. In the third chapter, the original signal for multiple compression observation tasks belongs to the same class. In the Bias framework, a multi task compression sensing algorithm based on Laplace prior (Laplace prio) is proposed. RS based Multitask Compressive Sensing, LMCS) is the development of single task Laplace prior compression perception algorithm. The difference of sharing model with MCS (Multitask Compressive Sensing, MCS) prior information is analyzed. The analysis shows that MCS is a special case of LMCS. A fast algorithm based on Laplace prior multitask compression is proposed. The integral of the redundant noise parameters is removed and the stability of the algorithm is enhanced. It is proved that the LMCS algorithm is superior to the Bias reconstruction algorithm for general sparse signal. Then, the modular sparse signal is proposed. A joint reconstruction algorithm, namely, the EMBSBL (Extended Multitask Block Sparse Bayesian Learning, EMBSBL) algorithm.EMBSBL algorithm not only uses the statistical correlation between signals and modularized information within the signal, but also does not need the prior information of the sparse signal of the module. The fourth chapter is aimed at the original signal of multiple compression observation tasks. In the case of different classes, a multi task classification reconstruction algorithm based on the MDL (Minmum Description Length, MDL) criterion is proposed. In this case, the reconstruction performance is poor if the LMCS or MCS algorithm is rebuilt without classification. The classification and reconstruction of the general sparse letter numbers are classified and the MDL-LMCS based on MDL criterion is proposed. And MDL-MCS algorithm, the experiment proves that the algorithm has superior classification and reconfiguration performance. Then, a new classification reconstruction algorithm, called GCEM-Turbo-GAMP-MMV algorithm, is proposed for structured sparse signal. The algorithm uses the state evolution characteristics to determine the classification results, and then reconstructs each class of tasks jointly and structured in the classification reconstruction. The sparse signal is superior to the MDL-LMCS and MDL-MCS algorithms. In the fifth chapter, a multi task compression perceptual algorithm framework is proposed for modularized sparse signal. The multi task synthesis method utilizes the special structure of modularized sparse signal and synthesizes a number of new tasks by translation of elements and observation moments array in the original signal. The minimum description length criterion determines the optimal number of synthetic tasks, and then uses the multi task compression sensing algorithm to reconstruct the original signal, which can get better reconstruction performance. Under the framework of multi task synthesis, a new synthetic multitask reconstruction algorithm is developed based on MCS and EMBSBL algorithms, called SMCS (Synthetic MCS, SMCS) and SEMBSB, respectively. L (Synthetic EMBSBL, SEMBSBL) algorithm. The two algorithms have the advantages and disadvantages of each comparison. The SMCS algorithm has less operation time, but less precision than the latter. The SEMBSBL algorithm has a good reconstruction precision, but the computation is very large. It is particularly prominent in the processing of large data signals. The advantages of the two synthetic multitask reconfiguration algorithms and other single reconfiguration algorithms are compared. It is not necessary to know the modularity information of modular sparse signal beforehand, and it can effectively improve the reconfiguration accuracy of single reconfiguration task.
【學(xué)位授予單位】：國防科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TN911.7

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