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研究生:黃振凱
研究生(外文):Huang, Chen-Kai
論文名稱:壓縮感知之探討
論文名稱(外文):A Study on the Compressed Sensing
指導教授:郭淑美郭淑美引用關係
指導教授(外文):Guo, Shu-Mei
口試委員:蔡聖鴻謝孫源洪金車龔旭陽
口試委員(外文):Sheng-Hong TsaiSun-Yuang HsiehKing-Chii HungHsu-Yang Kung
口試日期:2017-07-25
學位類別:碩士
校院名稱:國立成功大學
系所名稱:資訊工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:英文
論文頁數:71
中文關鍵詞:壓縮感知重權重L1範數最小化演算法純量符號函式稀疏訊號重建
外文關鍵詞:Compressed sensingReweighted L1-norm minimization methodScalar sign functionSparse signal recovery
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壓縮感知由於能夠將訊號壓縮至遠小於原訊號大小一半,因此成為近年快速發展的高效壓縮技術。考量到訊號在傳送過程中會受雜訊干擾或是由於壓縮所造成的失真,如何提升壓縮感知重建訊號能力一直是近來研究主題。本文提出了針對雜訊干擾系統的改良重權重L1範數最小化演算法之方法。本論文之方法包含純量符號函式基底權重,及針對訊號重建之前置步驟及後置處理。所提出之純量符號函式權重經實驗證明,在壓縮比高情況下重建訊號效能優越,此外所提出之前置後置處理均有效提升重權重L1範數最小化演算法在處理雜訊訊號方面之效能在應用於壓縮感知時能有效降低雜訊之干擾,進而提升重建效能。本論文之方法會與近年其他方法做比較,並證明本論文之方法優於其他比較方法。
Compressed sensing is an efficient compression technique developed rapidly since this technique can compress the length of a signal into less than a half and thus can be applied in many areas. If we consider the noise interference during transmission of a signal or the lossy due to the signal compression, how to improve the performance on signal recovery has been a main research topic on compressed sensing. This thesis proposes a modified reweighted L1-norm minimization method for
the system with noisy interferences. The proposed improved reweighted L1-norm minimization method would include the optimal scalar-sign function-based weighting (in the least squares sense) and both of the pre-processing and post-processing steps for signal recovery. Experimental results have shown that both the proposed scalar-sign function-based weighting method together with the newly proposed pre- and post- processing steps are able to significantly improve the capability of signal recovery for the system with noisy signals. Comparisons between the proposed method and some state-of-the-art different solvers show that the proposed method outperforms the existing ones.
摘要 I
Abstract II
致謝 III
Contents IV
List of Tables VI
List of Figures VII

Chapter 1 Introduction 1
Chapter 2 Background 4
2.1 Compressed sensing 4
2.2 Restricted isometry property and sparse signal recovery 8
2.3 Noise folding phenomenon 10
2.4 Reweighted -norm minimization algorithm 12
Chapter 3 The Proposed Method 16
3.1 Scalar-sign function-based reweighted L_1-norm minimization algorithm 16
3.2 Proposed pre-processing and post-processing steps in compressed sensing 23
Chapter 4 Experimental Results and Discussions 29
4.1 Criteria for evaluating reconstruction results 29
4.2 Comparisons among different weights 30
4.3 Comparisons between the proposed reweighted -norm minimization algorithm with and without the pre-processing and post-processing steps 36
4.4 Experimental setups and introductions to comparative methods 40
4.5 Comparisons of noise-free signal reconstruction 42
4.6 Comparisons of noisy signal reconstruction 53
Chapter 5 Conslusion 66
Reference 67
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