本文選題：稀疏貝葉斯學(xué)習(xí) + 結(jié)構(gòu)配對(duì)層次模型　； 參考：《電子科技大學(xué)》2014年碩士論文

【摘要】：本文主要考慮了塊狀稀疏(block-sparse)信號(hào)的恢復(fù)問(wèn)題,利用壓縮感知理論,通過(guò)挖掘信號(hào)的稀疏特性及塊狀聚類結(jié)構(gòu)特性,基于低維的測(cè)量量來(lái)恢復(fù)高維的信號(hào)。這樣的方案可以在保證信號(hào)恢復(fù)精度的同時(shí),有效的降低恢復(fù)信號(hào)所需的測(cè)量量。本文主要考慮的場(chǎng)景是,稀疏信號(hào)的非零系數(shù)是呈塊狀聚類的形式出現(xiàn)的,但是其非零塊的位置和大小是未知的。通過(guò)貝葉斯學(xué)習(xí)的方法,構(gòu)建層次化高斯先驗(yàn)?zāi)Ｐ?來(lái)恢復(fù)塊狀稀疏信號(hào)。本文首先在噪聲方差已知的條件下,采用基于結(jié)構(gòu)配對(duì)的層次化高斯先驗(yàn)?zāi)Ｐ蛠?lái)表征信號(hào)系數(shù)間的統(tǒng)計(jì)相關(guān)性,采用一組超參數(shù)(hyperparameter)來(lái)控制信號(hào)的稀疏性。傳統(tǒng)貝葉斯學(xué)習(xí)方法中,每個(gè)超參數(shù)都單獨(dú)的控制其對(duì)應(yīng)的信號(hào)系數(shù)的性質(zhì)。與傳統(tǒng)的貝葉斯稀疏學(xué)習(xí)方法不同,本文中提出的基于結(jié)構(gòu)配對(duì)的壓縮感知恢復(fù)算法中,每個(gè)信號(hào)稀疏的先驗(yàn)分布,不僅與自身對(duì)應(yīng)的超參數(shù)有關(guān),而且與其相鄰系數(shù)的超參數(shù)有關(guān),這樣的基于結(jié)構(gòu)配對(duì)的參數(shù)化模型,可以將相鄰系數(shù)關(guān)聯(lián)起來(lái),因此,這樣的結(jié)構(gòu)可以有效的促進(jìn)信號(hào)的塊狀聚類特征,挖掘信號(hào)塊狀先驗(yàn)。在這樣的高斯先驗(yàn)?zāi)Ｐ拖?采用期望最大化(expectation-maximization)算法,通過(guò)循環(huán)迭代,恢復(fù)塊狀信號(hào)。同時(shí),本文還考慮了在噪聲方差未知的情況下的信號(hào)恢復(fù),在這種情況下,將信號(hào)看做隱藏參數(shù),并同樣采用期望最大化的方法,依次迭代出估計(jì)信號(hào)及噪聲方差的值,從而實(shí)現(xiàn)對(duì)稀疏信號(hào)的恢復(fù)。文中還進(jìn)一步介紹了一種基于結(jié)構(gòu)配對(duì)的改進(jìn)重加權(quán)優(yōu)化算法,這種算法同樣可以在未知信號(hào)分塊結(jié)構(gòu)和稀疏度的前提下,挖掘信號(hào)內(nèi)在塊狀聚類信息,利用較少的測(cè)量量,有效的恢復(fù)信號(hào)。文章還進(jìn)一步研究了時(shí)變稀疏信號(hào)的恢復(fù),即不再僅僅考慮單一時(shí)隙稀疏信號(hào)恢復(fù),而是考慮多時(shí)隙測(cè)量向量的情況。但是與傳統(tǒng)多測(cè)量向量的情況不同,本文中考慮的多測(cè)量信號(hào)的稀疏結(jié)構(gòu)不再是隨時(shí)間恒定不變的,因?yàn)樵诤芏嗲闆r下,稀疏信號(hào)的非零系數(shù)位置,是隨時(shí)間發(fā)生緩慢變化的,在本文中,我們就研究了這一問(wèn)題模型下的信號(hào)恢復(fù)問(wèn)題,采用的主要方法是將時(shí)變稀疏信號(hào)模型通過(guò)數(shù)學(xué)變換,轉(zhuǎn)化為塊結(jié)構(gòu)未知的塊稀疏信號(hào)的恢復(fù)問(wèn)題進(jìn)行恢復(fù)。仿真結(jié)果表明通過(guò)挖掘信號(hào)的稀疏性以及塊狀特征,利用本文提出的基于結(jié)構(gòu)配對(duì)的層次化高斯模型,可以有效的恢復(fù)塊狀稀疏信號(hào),在噪聲方差已知時(shí),信號(hào)可以以很高的概率完全恢復(fù)。而在存在噪聲,且噪聲方差未知時(shí),也可以對(duì)信號(hào)實(shí)現(xiàn)有效恢復(fù)。對(duì)自然數(shù)據(jù),如圖像、聲音數(shù)據(jù)的仿真也表明,自然界的很多信號(hào)都具有這樣的塊狀稀疏特征,且可以利用本文提出的算法進(jìn)行有效恢復(fù)。另一方面,對(duì)DoA模型中時(shí)變信號(hào)的恢復(fù),同樣表明本文所提出算法對(duì)于時(shí)變信號(hào)的恢復(fù)也具有比較好的效果。
[Abstract]:In this paper, the recovery problem of block-sparsed-block signals is mainly considered. Using the theory of compression perception, the high-dimensional signals are recovered based on low-dimensional measurements by mining the sparse characteristics of the signals and the structural characteristics of block-like clustering. This scheme can effectively reduce the amount of measurement needed to restore the signal while ensuring the accuracy of the signal recovery. The main scenario considered in this paper is that the non-zero coefficients of sparse signals appear in the form of block clustering but the position and size of the non-zero blocks are unknown. A hierarchical Gao Si priori model is constructed to restore block sparse signals by Bayesian learning. In this paper, a hierarchical Gao Si priori model based on structural pairing is used to characterize the statistical correlation between signal coefficients under the condition that the noise variance is known, and a set of hyperparametric parameters are used to control the sparsity of the signal. In the traditional Bayesian learning method, each superparameter controls the properties of the corresponding signal coefficients separately. Different from the traditional Bayesian sparse learning method, the prior distribution of each signal sparse is not only related to its own hyperparameter, but also to the prior distribution of each signal in the proposed algorithm based on structural pairings. Moreover, this parameterized model based on structural pairing can correlate the adjacent coefficients with the superparameters of the adjacent coefficients. Therefore, this structure can effectively promote the block clustering features of signals and mine the block priori of signals. In this Gao Si priori model, the expected maximization algorithm is used to recover the block signal by cyclic iteration. At the same time, this paper also considers the signal recovery when the noise variance is unknown. In this case, the signal is regarded as a hidden parameter, and the expected maximization method is used to iterate out the estimated signal and noise variance in turn. In order to achieve sparse signal recovery. An improved reweighted optimization algorithm based on structural pairing is also introduced in this paper. This algorithm can also mine the inner block clustering information of the signal under the premise of unknown signal block structure and sparse degree, and make use of less measurement quantity. An effective recovery signal. In this paper, the restoration of time-varying sparse signals is further studied, that is, the case of multi-slot measurement vector is not considered only in the case of single slot sparse signal recovery. However, unlike the traditional multi-measurement vector, the sparse structure of the multi-measurement signal considered in this paper is no longer constant with time, because in many cases, the position of the non-zero coefficient of the sparse signal changes slowly with time. In this paper, we study the signal recovery problem under this model. The main method is to transform the time-varying sparse signal model into the block sparse signal recovery problem with unknown block structure by mathematical transformation. The simulation results show that the block sparse signals can be recovered effectively by mining the sparse signals and block features, and using the hierarchical Gao Si model based on structural pairing, when the noise variance is known. The signal can be fully recovered with a high probability. When there is noise and the variance of noise is unknown, the signal can be recovered effectively. The simulation of natural data, such as images and sound data, also shows that many signals in nature have such block sparse features, and can be effectively restored by using the algorithm proposed in this paper. On the other hand, the recovery of time-varying signals in DoA model also shows that the proposed algorithm has a good effect on the recovery of time-varying signals.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7
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本文編號(hào)：1964438