發(fā)布時(shí)間：2018-07-26 19:39

【摘要】：隨著大數(shù)據(jù)時(shí)代的到來,人們對于高維數(shù)據(jù)處理技術(shù)的需求快速增長,有力推動(dòng)了稀疏信號處理領(lǐng)域和壓縮感知領(lǐng)域的研究進(jìn)展,尤其是高效稀疏重構(gòu)算法的開發(fā)。本文順應(yīng)這種需求,對傳統(tǒng)的?0范數(shù)優(yōu)化算法和近幾年來受到越來越多重視的(廣義)近似消息傳遞算法進(jìn)行了研究,針對近似消息傳遞類型的算法對于非零均值小方差的高斯字典矩陣容易發(fā)散的問題,提出了三種改進(jìn)的廣義近似消息傳遞算法。其中,為了提出第二種改進(jìn)的廣義近似消息傳遞算法,前置提出了兩種新型?0范數(shù)優(yōu)化匹配追蹤算法。第三種改進(jìn)的廣義近似消息傳遞算法則引入了利用稀疏向量各分量的邊緣后驗(yàn)概率變化尋找非零元素下標(biāo)的新型追蹤過程,該追蹤過程區(qū)別于匹配追蹤所使用的殘差與字典矩陣列計(jì)算相關(guān)的方式。本文主要?jiǎng)?chuàng)新點(diǎn)包括四個(gè)部分:1.提出了匹配追蹤的廣義近似消息傳遞算法,該方法通過標(biāo)準(zhǔn)的匹配追蹤過程序貫地找出稀疏向量的非零位置,使用固定支撐集的廣義近似消息傳遞算法估計(jì)非零位置的幅度。這種方法可以顯著提高廣義近似消息傳遞算法的穩(wěn)健性。隨后從構(gòu)造樹結(jié)構(gòu)因子圖的角度分析了該算法的收斂性。2.為了克服正交匹配追蹤過程不能去除支撐集中找錯(cuò)的非零元素位置這個(gè)缺點(diǎn),本文提出了兩種隨機(jī)擾亂和更新支撐集元素的新型匹配追蹤算法,分別稱為隨機(jī)分裂支撐集正交匹配追蹤和隨機(jī)正則化匹配追蹤,后者是對前者的改進(jìn)。隨后從理論上證明了隨機(jī)正則化匹配追蹤算法的收斂性,給出了收斂條件。3.根據(jù)前面兩部分工作,將隨機(jī)正則化匹配追蹤算法與固定支撐集的廣義近似消息傳遞算法結(jié)合起來,得到了隨機(jī)正則化匹配追蹤的廣義近似消息傳遞算法。隨后使用replica方法從理論上分析了固定支撐集的廣義近似消息傳遞算法的收斂性和收斂條件。4.利用Bernoulli-Gaussian先驗(yàn)分布的廣義近似消息傳遞算法在迭代過程中所估計(jì)的稀疏向量各個(gè)元素的邊緣后驗(yàn)概率變化來找出支撐集,可以解釋為一種追蹤過程,再使用固定支撐集的廣義近似消息傳遞算法進(jìn)一步估計(jì)支撐集上的幅度。對于上述算法,本文使用了仿真數(shù)據(jù)和真實(shí)世界的數(shù)據(jù)作為算法的輸入,考察和驗(yàn)證了這些算法的特性。實(shí)驗(yàn)結(jié)果表明,對于壓縮感知問題,上述算法在更一般的字典矩陣條件下也能很好地恢復(fù)稀疏向量。
[Abstract]:With the arrival of big data era, the demand for high-dimensional data processing technology has increased rapidly, which has promoted the research progress of sparse signal processing and compression sensing, especially the development of efficient sparse reconstruction algorithm. In this paper, the traditional 0-norm optimization algorithm and the (generalized) approximate messaging algorithm, which have been paid more and more attention in recent years, are studied. Aiming at the problem that the approximate message passing type algorithm is easy to diverge for the Gao Si dictionary matrix with non-zero mean and small variance, three improved generalized approximate message passing algorithms are proposed. In order to propose a second improved generalized approximate messaging algorithm, two new matching and tracking algorithms with 0-norm optimization are proposed. The third improved generalized approximate messaging algorithm introduces a new tracking process which uses the edge posteriori probability change of each component of sparse vector to find non-zero element subscript. The tracking process is different from the way in which the residual errors used in matching tracing are related to the calculation of dictionary matrix columns. The main innovation of this paper includes four parts: 1. A generalized approximate message passing algorithm for matching tracing is proposed. By using the standard matching tracing program, the nonzero position of the sparse vector is found consistently, and the amplitude of the non-zero position is estimated by using the generalized approximate message passing algorithm with fixed support set. This method can significantly improve the robustness of generalized approximate messaging algorithm. Then the convergence of the algorithm is analyzed from the point of constructing the tree structure factor graph. In order to overcome the shortcoming that the orthogonal matching tracing process can not remove the position of non-zero elements in the support set, two new matching tracking algorithms are proposed to randomly disrupt and update the support set elements. They are called random split support set orthogonal matching tracing and random regularized matching tracing respectively. The latter is an improvement on the former. Then the convergence of the stochastic regularized matching tracking algorithm is proved theoretically, and the convergence condition is given. According to the previous two parts, the random regularization matching tracking algorithm is combined with the fixed support set generalized approximate message passing algorithm, and the generalized approximate message passing algorithm of random regularized matching tracking is obtained. Then the convergence and convergence conditions of the generalized approximate messaging algorithm with fixed support set are analyzed theoretically by using replica method. The generalized approximate message passing algorithm with Bernoulli-Gaussian prior distribution can be interpreted as a tracing process by using the edge posteriori probability variation of each element of the sparse vector estimated in the iterative process. Then the generalized approximate messaging algorithm of fixed support set is used to estimate the amplitude of the support set. For the above algorithms, the simulation data and the real world data are used as the input of the algorithms, and the characteristics of these algorithms are investigated and verified. The experimental results show that the proposed algorithm can recover the sparse vector well under the condition of more general dictionary matrix for the compressed perception problem.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TN911.7

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