本文選題：塊稀疏信號(hào)重構(gòu) + 未知塊結(jié)構(gòu)��； 參考：《電子科技大學(xué)》2017年碩士論文

【摘要】：稀疏重構(gòu)作為壓縮感知中的一個(gè)重要研究課題,其主要研究?jī)?nèi)容是如何在保證信號(hào)重構(gòu)精度的前提下用低維的測(cè)量量來(lái)恢復(fù)高維稀疏信號(hào)。傳統(tǒng)的稀疏表示理論假定稀疏信號(hào)中的非零元素都是隨機(jī)分布在信號(hào)中,但是在處理實(shí)際問(wèn)題時(shí),稀疏信號(hào)中的非零元素往往具有一定的結(jié)構(gòu)特性,充分利用信號(hào)內(nèi)非零元素之間的結(jié)構(gòu)特性可以建立更準(zhǔn)確的重構(gòu)信號(hào)模型,勢(shì)必會(huì)提高重構(gòu)算法的性能,具有重要的研究意義。本文針對(duì)具有分塊結(jié)構(gòu)的稀疏信號(hào)重構(gòu)問(wèn)題進(jìn)行研究。首先針對(duì)已知塊結(jié)構(gòu)的重構(gòu)問(wèn)題,對(duì)基于貪婪迭代的塊稀疏重構(gòu)算法和稀疏塊自適應(yīng)迭代算法進(jìn)行研究,然后針對(duì)實(shí)際應(yīng)用中常出現(xiàn)的未知塊結(jié)構(gòu)的重構(gòu)問(wèn)題,研究了塊稀疏貝葉斯算法和結(jié)構(gòu)耦合稀疏貝葉斯算法。通過(guò)對(duì)結(jié)構(gòu)耦合稀疏貝葉斯(Pattern Coupled Sparse Bayesian learning,PCSBL)算法的研究分析,發(fā)現(xiàn)PCSBL算法將控制元素稀疏性的超參數(shù)互相關(guān)聯(lián),使用一個(gè)預(yù)先設(shè)置好的參數(shù)來(lái)控制信號(hào)元素受相鄰元素的影響程度。然而,在實(shí)際的塊稀疏信號(hào)中,相鄰超參數(shù)之間的相關(guān)性并非處處相同。本文針對(duì)結(jié)構(gòu)耦合稀疏貝葉斯算法的不足之處進(jìn)行了改進(jìn),提出了能夠?qū)⑿盘?hào)相鄰元素的稀疏度以自適應(yīng)方式聯(lián)系起來(lái)的稀疏塊自適應(yīng)耦合算法。本文提出的新算法用一組能夠自適應(yīng)求解的耦合參數(shù)代替結(jié)構(gòu)耦合稀疏貝葉斯算法中的單一預(yù)定參數(shù)去表示相鄰超參數(shù)之間的相關(guān)性。稀疏塊自適應(yīng)耦合算法將互相獨(dú)立的超參數(shù)經(jīng)過(guò)線性變換得到新的相關(guān)超參數(shù),建立了一個(gè)新的分層高斯先驗(yàn)?zāi)Ｐ�。�?shí)驗(yàn)證明,與目前已有的塊稀疏重構(gòu)算法相比,本文提出的使用自適應(yīng)耦合參數(shù)的稀疏貝葉斯算法能夠獲得更好的塊稀疏重構(gòu)性能。為了防止稀疏塊自適應(yīng)耦合算法存在過(guò)擬合問(wèn)題,本文還對(duì)新算法的分層模型進(jìn)行簡(jiǎn)化,使耦合參數(shù)與超參數(shù)一一對(duì)應(yīng),并提出了一種簡(jiǎn)化的稀疏塊自適應(yīng)耦合算法。簡(jiǎn)化模型和算法不僅能夠降低計(jì)算量,還能夠在一定程度上避免過(guò)擬合問(wèn)題的出現(xiàn)。
[Abstract]:Sparse reconstruction is an important research topic in compression sensing. Its main research content is how to restore high-dimensional sparse signals with low-dimensional measurements while ensuring the precision of signal reconstruction. The traditional sparse representation theory assumes that the non-zero elements in sparse signals are randomly distributed in the signals, but when dealing with practical problems, the non-zero elements in sparse signals often have certain structural characteristics. A more accurate reconstruction signal model can be established by making full use of the structural characteristics of non-zero elements in the signal, which will improve the performance of the reconstruction algorithm and have important research significance. In this paper, the problem of sparse signal reconstruction with block structure is studied. Firstly, for the reconstruction of known block structures, the block sparse reconstruction algorithm based on greedy iteration and the sparse block adaptive iterative algorithm are studied. Block sparse Bayes algorithm and structurally coupled sparse Bayesian algorithm are studied. Through the research and analysis of the structure-coupled sparse Bayesian Bayesian learning PCSBL algorithm, it is found that the PCSBL algorithm correlates the superparameters controlling the sparsity of the elements, and uses a pre-set parameter to control the influence of the signal elements on the adjacent elements. However, in the actual block sparse signal, the correlation between adjacent superparameters is not the same everywhere. In this paper, we improve the structural coupling sparse Bayes algorithm, and propose a sparse block adaptive coupling algorithm which can relate the sparsity of adjacent elements to the adaptive method. In this paper, a set of coupling parameters can be solved adaptively instead of a single predefined parameter in the structural coupled sparse Bayes algorithm to represent the correlation between adjacent superparameters. The sparse block adaptive coupling algorithm obtains a new correlation hyperparameter by linear transformation of independent superparameters and establishes a new hierarchical Gao Si priori model. Experimental results show that the proposed sparse Bayesian algorithm with adaptive coupling parameters can achieve better block sparse reconstruction performance than the existing block sparse reconstruction algorithms. In order to prevent the over-fitting problem of sparse block adaptive coupling algorithm, this paper also simplifies the layered model of the new algorithm to make the coupling parameters correspond to the superparameters one by one, and proposes a simplified sparse block adaptive coupling algorithm. The simplified model and algorithm can not only reduce the computational complexity, but also avoid the problem of over-fitting to a certain extent.
【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】：2017
【分類號(hào)】：TN911.7

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本文編號(hào)：2008094