臺灣博碩士論文加值系統

在成像科學領域中，一般性的測量是難以決定相位，例如X射線成像，檢測器可以接收的標準光波，只能是利用傅立葉強度的測量。標準的相位回復問題是從傅立葉強度的測量數據中回復相位資訊，試著重建未知的訊號(或影像)。進行測量與重建時，Albert Fannjiang提出:藉由引進隨機製造的遮罩，可以高度地保持可能解的唯一性，達到全域相位係數的解。在這篇論文中，我們提供一些實驗，說明傳統演算法無法成功重建的情況，對於解決影像相位重建問題，我們的貢獻有
1.利用組合式的演算法，改善傳統演算法的還原(重建影像)效能。
2.提出的組合式演算法當中，以nisvpTV2演算法組合的還原效能再優於其它演算法組合。

In many areas of imaging science, it is difficult to determine the phase of general measurements. For example, in the X-ray imaging, the detector can only measure the Fourier magnitude of the received optical wave. The classical phase retrieval is the problem of retrieving Fourier phase information from Fourier magnitude data. One tries to recover the unknown signal (or image) from measurements. Albert Fannjiang introduced randomly fabricated mask for the reconstruction of Fourier phase retrieval. The main purpose of the mask is to achieve the highly probable uniqueness of solutions up to a global phase factor. In this paper, we provide a number of experiments to explain the situation where traditional algorithms couldn’t successfully reconstruct unknown signals. In order to solve the Fourier phase retrieval, our contributions are the following:
1. We use combinations of algorithms to improve the performance of the traditional methods.
2. Among the proposed combinations of algorithms, the performance of nisvpTV2 algorithm combination is the best among the other combinations of algorithms.

誌謝辭.......... i
中文摘要.......... ii
SUMMARY.......... iii
目錄.......... iv
圖目次.......... vi
表目次.......... viii
符號說明.......... x
壹、Introduction 1
貳、Alternating projection algorithms and alternating direction methods 3
一、Projection algorithms and constrained minimization.......... 3
二、Alternating direction methods.......... 8
參、Phase retrieval algorithms combination 10
肆、Denoising algorithms 12
一、Total variation.......... 12
二、Median filter.......... 14
伍、Initialization algorithms 16
一、Nisvp algorithm.......... 16
二、NisvpTV2 algorithm.......... 17
陸、Experiment 19
一、Phase retrieval algorithms combination.......... 22
(一) Experiment 1.......... 22
(二) Experiment 2.......... 26
(三) Experiment 3.......... 30
二、NisvpTV2 algorithm combination.......... 34
(一) Experiment 4.......... 35
(二) Experiment 5.......... 38
(三) Experiment 6.......... 43
三、Other experiments.......... 47
(一) Experiment 7.......... 48
(二) Experiment 8.......... 51
(三) Experiment 9.......... 54
柒、Conclusion 57
參考文獻 58

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