本文選題：壓縮數(shù)據(jù)分離　切入點：擾動　出處：《西南大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著信息時代的來臨,在生產(chǎn)與生活中我們常常會面對各種各樣的復(fù)雜且富有價值的高維數(shù)據(jù),如何有效地挖掘和處理這些高維數(shù)據(jù)一直是學(xué)術(shù)界與工業(yè)界研究的熱點.壓縮感知是一種新穎且有效的高維數(shù)據(jù)處理理論,它利用信號數(shù)據(jù)的稀疏性和可壓縮性,能夠以高概率實現(xiàn)對信號的精確重構(gòu),目前已在壓縮成像,醫(yī)學(xué)成像,模式識別,圖像處理等領(lǐng)域得到了廣泛應(yīng)用.本文基于壓縮感知理論并結(jié)合應(yīng)用背景研究了不同類型的高維數(shù)據(jù)處理,主要內(nèi)容如下:第一章,概述了壓縮感知理論產(chǎn)生的背景與研究意義,并簡要地介紹了壓縮感知的最新研究進展以及實際應(yīng)用成果.第二章,介紹了壓縮感知的三個主要方面:信號的稀疏表示,測量矩陣的設(shè)計和信號的重構(gòu)理論與重構(gòu)算法.第三章,針對多模態(tài)數(shù)據(jù),首先引入了壓縮數(shù)據(jù)分離模型,然后基于冗余緊框架并利用非凸的D-?q-極小化方法研究了擾動數(shù)據(jù)分離問題.當(dāng)冗余緊框架和測量矩陣滿足互相關(guān)性,零空間性質(zhì),限制性等容條件時,建立了稀疏信號的重構(gòu)條件并獲得了局部最優(yōu)解與原始信號的誤差上界.研究表明了D-?q-極小化方法對冗余緊框架下的稀疏信號恢復(fù)是魯棒的和穩(wěn)定的.第四章,采用凸的?2/?1極小化方法和Block D-RIP理論研究了在冗余緊框架下的塊稀疏信號,所獲結(jié)果表明,當(dāng)Block D-RIP常數(shù)δ2k|τ滿足0δ2k|τ0.2時,?2/?1極小化方法能夠魯棒重構(gòu)原始信號,同時改進了已有的重構(gòu)條件和誤差上限.基于離散傅里葉變換(DFT)字典,我們執(zhí)行了一系列仿真實驗充分地證實了理論結(jié)果.第五章,研究了低秩張量修補問題,基于目標(biāo)秩之前的奇異值不會影響張量秩的極小化這一事實,本文提出了奇異值的部分和極小化的低秩張量修補算法(PSSV-LRTC).針對模擬數(shù)據(jù)和真實數(shù)據(jù)執(zhí)行了一系列實驗,結(jié)果表明我們的算法比已有的算法具有更高的精度和收斂率.第六章,總結(jié)了全文的主要工作,并對擾動數(shù)據(jù)分離,塊稀疏壓縮感知以及張量修補中有進一步研究價值的內(nèi)容作了分析與展望.
[Abstract]:With the advent of the information age, we often face a variety of complex and valuable high-dimensional data in production and life. How to effectively mine and process these high-dimensional data has been a hot topic in academia and industry. Compression perception is a novel and effective theory of high-dimensional data processing, which makes use of the sparsity and compressibility of signal data. It is possible to reconstruct the signal accurately with high probability, and it has been used in compression imaging, medical imaging, pattern recognition and so on. Image processing and other fields have been widely used. In this paper, different types of high-dimensional data processing are studied based on compressed sensing theory and combined with application background. The main contents are as follows: chapter one, This paper summarizes the background and significance of the theory of compressed sensing, and briefly introduces the latest research progress and practical application of compressed sensing. Chapter two introduces three main aspects of compressed sensing: sparse representation of signals. The design of measurement matrix and the theory and algorithm of signal reconstruction. Chapter 3, for multi-modal data, the compression data separation model is introduced first, then based on redundant compact frame and using non-convex D-? The q-minimization method is used to study the problem of perturbed data separation. When the redundant compact frame and the measurement matrix satisfy the mutual correlation, the property of zero space and the restricted equal volume condition, The reconstruction condition of sparse signal is established and the error upper bound between the local optimal solution and the original signal is obtained. The q-minimization method is robust and stable for sparse signal recovery under redundant compact frame. Chapter 4th, convex? 2/? 1 minimization method and Block D-RIP theory are used to study block sparse signals under redundant compact frame. The results show that when the Block D-RIP constant 未 2k 蟿 satisfies 0 未 2k 蟿 0.2? 2/? 1 minimization method can reconstruct the original signal robustly, at the same time improve the existing reconstruction condition and error upper limit. Based on the DFT dictionary of discrete Fourier transform, we have carried out a series of simulation experiments to fully verify the theoretical results. Chapter 5th, Based on the fact that the singular value before the target rank does not affect the minimization of Zhang Liang rank, the problem of low rank Zhang Liang repair is studied. In this paper, a partial and minimized low rank Zhang Liang repair algorithm for singular values is proposed. A series of experiments are performed on simulated and real data. The results show that our algorithm has higher accuracy and convergence rate than the existing algorithms. Chapter 6th. The main work of this paper is summarized, and the contents of disturbance data separation, block sparse compression perception and Zhang Liang repair are analyzed and prospected.
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN911.7

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本文編號：1601348