貝蘇章臺灣大學:電信工程學研究所梁隆威Liang, Long-WeiLong-WeiLiang2010-07-012018-07-052010-07-012018-07-052008U0001-2107200812372200http://ntur.lib.ntu.edu.tw//handle/246246/188233近年來，人們為了節省儲存空間或方便傳輸而發展出許多壓縮信號的方法，而這些方法通常都是先將信號完整取得，然後以不嚴重失真為原則將其中不必要的部分刪除。對於感測儀器來說(例如:照相機、收音機等)，將所有信號完整接收之後又將其中大部分的資料刪除是ㄧ種浪費的行為，尤其是壓縮率大為提高的今天，ㄧ個信號的主要資訊只集中在一小部份而其他絕大多數部分將被捨棄。 如今我們將介紹一種新的方法，將信號的壓縮與感測在同一時間完成，稱之為『壓縮感測』(Compressive Sensing)。而經過壓縮的感測值可以經由『疊代式基底搜尋演算法』(Greedy Basis Pursuit)將原本的信號重建回來。 當我們擷取ㄧ段信號時，取樣定理指出若要避免混疊效應(aliasing effect)而重建此信號，則取樣頻率必須大於信號最高頻率的兩倍，也就是我們熟知的奈奎斯速率(Nyquist rate)。由於壓縮感測將壓縮及感測結合在一起，所以其取樣頻率將會大幅減小而低於奈奎斯速率，也因此顛覆了取樣定理。In the last few years, people compress signals after acquiring them. In the process of compression, there would be some information discarded from the signal by the compression algorithm. It is a waste that one obtains a signal and then throws parts of them away. If the compression ratio is large, it means one spend unnecessary time on acquiring this signal. Now we introduce a novel method that acquires and compresses a signal simultaneously, called Compressive Sensing. After compressive sensing a signal, one can get a condensed measurement. The minimization of l 1-norm is used to recover the signal from the measurement. Many algorithms can handle this problem, such as Matching Pursuit, Basis Pursuit and so on. Now we apply a faster algorithm to the problem, that is, Greedy Basis Pursuit. By the CS theory, one acquires a signal in a condensed form. Hence this theory beats the Shannon sampling theorem because it samples signals at a rate significantly below the Nyquist rate.Chapter 1 Introduction 1hapter 2 Greedy Basis Pursuit 3.1 Problem statement 3.2 Related work 4.2.1 Matching Pursuit 5.2.2 Basis Pursuit 6.3 Geometry of Basis Pursuit 7.4 Greedy Basis Pursuit Algorithm 8.4.1 Variables Statement 8.4.2 Initialization 9.4.3 Iteration 10.4.4 Computational Details 13.5 Analysis 18.6 Results 20xperiment 1 20xperiment 2 22xperiment 3 23.7 Conclusion 24hapter 3 Compressive Sensing 27.1 Problem statement 28.2 Sparsity and Incoference 31.2.1 Sparsity 31.2.2 Incoherence 34.3 Undersampling and Sparse Signal Recovery 35.3.1 Undersampling 35.3.2 Sparse Signal Recovery 35.4 Restriction on the Measurement Size 38.5 Discussion 40.6 Conclusion 41hapter 4 Experimental Results of Compressive Sensing 43.1 Audio 44.1.1 Space domain 46.1.2 DCT domain 48.2 Image 50.2.1 Binary image 50.2.2 Gray level image 52.3 Conclusion 58hapter 5 Conclusion and Future Work 61.1 Conclusion 61.2 Future Work 63EFERENCE 652897236 bytesapplication/pdfen-US壓縮感測Compressive SensingGreedy Basis Pursuitthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/188233/1/ntu-97-R95942116-1.pdf