民國101年國人的十大死因，惡性腫瘤（癌症）連續三十一年蟬聯冠軍，平均每一百人中，就有二十八人死於癌症。X光檢查是診斷初步判斷乳腺癌和肺癌最常用的重要手段，通過X光檢查可以瞭解癌的部位和大小等，是治療過程提供準確資訊的重要方法。目前醫學影像研究的挑戰是如何用X光檢查一般難以發現的早期腫瘤，進行癌症的早期治療，目標是解析度比現有X光醫療影像裝置的2mm降低一個數量級到0.2mm。

在這篇論文中，將討論結合納米薄膜技術與X光技術，研製一種新型非晶矽平面X光影像感測器結構，來取代原先單純的p-i-n光二極體，這可以使影像解析度和面板中的像素大小相同。但是面板的接收器中，光轉換成電流儲存在電容當中到消逝的時間極短(約1.5ms)，同時因為高解析度，所以傳送的圖片資料十分龐大，不論使用USB來傳送或者直接儲存到記憶體，皆需要做資料壓縮。經過計算，資料壓縮的比率必須要低於0.27。

考量到X光醫療影像的特性，以及希望達到最好的壓縮比，並節省壓縮執行的時間，首先將使用小波轉換將X光影像轉換為稀疏的信號，再採用壓縮感測 (compressive sampling) 技術來進行影像壓縮，而壓縮資料的重建部分，則是使用超過探測正交化匹配演算法(Over-Detected Orthogonal Matching Pursuit )的方式。最後在模擬中的數據，顯示出圖片可以在不明顯失真的情況下完整回復X光影像，並且達到0.27的目標壓縮比。

Cancer is a major cause of mortality worldwide in the modern world. It can be detected by X-ray medical imaging, but the resolution of X-ray images are quite poor(about 2mm) at detecting cancer in early phase.

In this thesis, the purpose is to improve resolution by one order of magnitude to 0.2mm in conventional X-ray images, in order to detect cancer earlier for early treatment and cost much less than X-Ray Computed Tomography. The hardware architecture is the high resolution X-Ray detection with In-cell TFT panel array. Because of high resolution, the volume of data is too large. To send out the detector array through USB port or to store into flash memory at the signal reserving time(1.5ms), the compressive techniques is needed.

To minimize the compression ratio and execution time, and consider the characteristic of radiograph. We propose the compressive sampling theory, which can recover certain signals from far fewer samples than traditional methods use. The method of reconstruction is mainly leading by Over-Detected Orthogonal Matching Pursuit algorithm, which is a modified algorithm of the well-known Orthogonal Matching Pursuit (OMP) algorithm. Besides, this system consists of Daubechies wavelet transform and thresholding.

The results show that this method improves the execution time significantly, successfully recover the radiograph of chest and breast. The the requirement of compression ratio (0.27) is achieved.

Abstract i
Contents ii
1 Introduction 1
2 System Background 4
2.1 High-Resolution X-Ray Detector Prototype with In Cell TFT Panel Array . 4
2.2 Goal of Design . . . . . . . . . . . . . . . . . . . 6
2.3 Architecture of System . . . . . . . . . . . . .. . . 8
3 Wavelet transform 11
3.1 Subband Coding . . . . . . . . . . . . . . . . . . . 11
3.2 Properties of Daubechies Wavelets . . . . .. . . . . 12
3.3 Method of Interleaving . . . . . . . . . . . 15
4 Radiograph Compression 18
4.1 Introduction of Compressive Sampling . . . . . . . 18
4.2 Recovery by Orthogonal Matching Pursuit . . . . . . 20
4.3 Over-Detected Orthogonal Matching Pursuit . . . . . 22
4.3.1 Early Termination .. . . . . . . . . . . . . 24
4.3.2 Solution-Candidate Set . . . . . . . . . . . . . . 24
5 Analysis and Simulation 27
5.1 Tests of Scintillator . . . . . . . . . . . . . . . 27
5.2 Thresholding and Sparsity . . . . . . . . . . . . . . 29
5.3 Compressive Sampling . . .. . . . . . . . . . . . . . 30
5.3.1 Probability of Detection . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.3.2 Comparison of Execution Time . . . . . . . . . . . 33
5.4 Radiograph . . . . . . . . . . . . . . . . . . . . . 35
5.4.1 Chest Radiograph . . . . . . . . . . . . . . . . . 36
5.4.2 Breast Radiograph . . . . . . . . . . . . . . . . 39
6 Conclusion 41

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