隨著近來科技的發展，研究發現太赫茲波擁有兩種重要的特性，包含良好的穿透能力以及對生物體不會造成傷害的重要性質，所以在目前的研究中，被廣泛的應用在醫學診斷，行李安檢，電路檢測或是藥物檢測等領域中，而這些應用也促進太赫茲成像系統蓬勃發展。

在本論文中，我們利用一維壓縮感知的數學模型對應到太赫茲影像系統模型，由於一維壓縮感知的演算法複雜度高，且要達到高品質的影像還原需要較高的量測成本。因此，本篇論文提出二階段自適應性壓縮感知演算法來減少量測成本，首先使用二階段方法來解決自適應性壓縮感知所需的事前資訊，而自適應性調整量測矩陣則是將量測集中在高能量的部分，藉此提高影像品質與降低量測成本。

模擬結果證明所提出的演算法可以在均方誤差 (MSE) 和結構相似性 (SSIM)方面表現更好。 在計算方面圖像尺寸為32×32，K=200，目標MSE為0.08，將上述參數應用於所提出的演算法和傳統的壓縮感知，提出的兩階段自適應性壓縮感知可以減少 34.3% 的浮點運算（FLOPs）的數量比傳統的壓縮傳感在太赫茲單像素成像系統中。 在計算成本方面圖像尺寸條件為32×32，K=200，總測量次數Mtotal 為 512，應用於提出的算法和傳統的壓縮4感知，提出的兩階段自適應壓縮感知可以降低21.4%的MSE並且比傳統的壓縮傳感提高了 20.8% 的 SSIM。

With the recent development of science and technology, studies have found that terahertz radiation has two important characteristics, including good penetration ability and no cause harm to organisms. Therefore, in the current research, terahertz waves are widely used in medical imaging, baggage screening, circuit detection, or drug detection. these applications also promote the flourishing development of terahertz imaging systems.

In this thesis, we use the one-dimensional compressive sensing model to construct the terahertz single-pixel compressive sensing image system model. To reduce the complexity and measurement cost of the signal reconstruction for compressive sensing, this thesis proposes a two-stage adaptive compressive sensing algorithm to reduce the measurement cost. The two-stage method is used to solve the prior information required for adaptive compressive sensing. The adaptive adjustment of the measurement matrix concentrates the measurement on the high-energy component, thereby improving image quality and reducing measurement costs.

The simulation results prove that the proposed algorithm can perform better in terms of mean square error (MSE) and structural similarity (SSIM). In terms of the computational cost with the condition of image size is 32$\times$32, $K =$ 200, and the target MSE is 0.08, which is applied to the proposed algorithm and traditional compressive sensing, the proposed two-stage adaptive compressive sensing can reduce 34.3$\%$ of the number of the number of floating point operations (FLOPs) than the traditional compressive sensing in the terahertz single-pixel imaging system. In terms of the computational cost with the condition of image size is 32$\times$32, $K =$200, and the total number of measurements $M_{total}$ is 512, which is applied to the proposed algorithm and traditional compressive sensing, the proposed two-stage adaptive compressive sensing can reduce 21.4$\%$ of MSE and improve 20.8 $\%$ of SSIM than traditional compressive sensing.

1 Introduction 1
1.1 Terahertz Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Organization of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Adaptive Compressive Sensing and Terahertz Single-Pixel Imaging
System 7
2.1 Terahertz Single-Pixel Imaging System . . . . . . . . . . . . . . . . . . . 7
2.1.1 Model of Terahertz Single-Pixel Imaging System . . . . . . . . . . 8
2.2 Compressive Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Model of Compressive Sensing . . . . . . . . . . . . . . . . . . . . 11
2.3 Adaptive Compressive Sensing . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Proposed Two-stage Adaptive Compressive Sensing algorithm 19
4 Simulation Result 27
4.1 Experiment Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.1 Measurement in the Second Stage . . . . . . . . . . . . . . . . . . 28
4.1.2 Random Flip Number per Mask . . . . . . . . . . . . . . . . . . . 28
4.1.3 Multi-Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.4 System with Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.5 Number of Floating Point Operations Analysis . . . . . . . . . . . 30
ii CONTENTS
4.2 Performance Metrics of Reconstruction . . . . . . . . . . . . . . . . . . . 30
4.3 Simulation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3.1 Measurement in the Second Stage . . . . . . . . . . . . . . . . . . 34
4.3.2 Random Flip Number per Mask . . . . . . . . . . . . . . . . . . . 41
4.3.3 Multi-Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3.4 System with Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.5 Number of Floating Point Operations Analysis . . . . . . . . . . . 78
5 Conclusion and Future Work

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