近年來，關於太赫茲(TeraHertz)系統的相關研究急遽增長。太赫茲系統的持續改進已經促成在物理、工程、生物和醫學領域上許多新穎和吸引人的應用。然而，太赫茲系統經常受限於過長的資料採集時間以及發射器與接收器成本過高的問題，由於我們必須機械式地移動發射器與接收器來重建完整的太赫茲影像。而陣列式的太赫茲系統的成本與複雜度過高，因此此研究使用單相素太赫茲系統。隨著太赫茲系統使用需求的增加，重建算法的計算複雜度和影像採集速度的要求變得越來越重要。這項研究的目的是使用壓縮感知(Compressive Sensing) 來追求低計算複雜度、高圖像重建性能和降低影像重建的時間。此研究使用了一種熱門的演算法Orthogonal Matching Pursuit via Matrix Inversion Bypass(OMP-MIB)。此演算法的硬體架構是設計給稀疏性為6，64筆的量測訊號。OMP-MIB演算法的綜合結果為解決單像素太赫茲系統的難題提供了良好的理論依據。

In recent years, there has been a dramatic proliferation in research concerning singlepixel
terahertz (THz) system. The continuing improvements in the THz imaging system
have led to various and fascinating applications in the elds of physics, engineering,
biology, and medicine. However, under current technology, we need to move transmitters
and receivers mechanically to reconstruct the complete THz image. Thus, the cost of
transmitters and the receivers and the long acquisition time are the main obstacles for
the growth in the THz system. With the increasing usage of THz system, computational
complexity and speed of image acquisition requirements for reconstruction algorithms
have become more critical. The purpose of this study is to use compressive sensing (CS)
to pursue low computational complexity, high image reconstruction performance, and
low image reconstruction time. This study used orthogonal matching pursuit via matrix
inversion bypass (OMP-MIB) [1] algorithm, one of the popular compressive sensing
algorithms. The architecture is designed for 64 measurement data with sparsity 6. The
synthesis result of the OMP-MIB algorithm provides a good theoretical formulation to
deal with the challenging problem of the single-pixel THz system.

Contents
1 Introduction 1
1.1 Terahertz System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Compressive Sensing System . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Organization of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Terahertz Compressed Sensing Imaging System and Reconstruction
Algorithm 5
2.1 Terahertz Compressive Sensing Imaging System . . . . . . . . . . . . . . 6
2.1.1 Signal-Pixel Imaging System . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Application on Compressive Sensing Terahertz System . . . . . . 9
2.2 Signal Model of Compressive Sensing . . . . . . . . . . . . . . . . . . . . 12
2.3 Reconstruction Algorithms for Compressive Sensing . . . . . . . . . . . . 16
2.3.1 l1-Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Orthogonal Matching Pursuit . . . . . . . . . . . . . . . . . . . . 17
2.3.3 Projection-based Atom Selection Orthogonal Matching Pursuit
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 Orthogonal Matching Pursuit via Matrix Inversion Bypass Algorithm
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Architecture Design 25
3.1 Environment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
ii CONTENTS
3.2 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Initial Set-up Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Iteration Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4.1 Index Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.2 Divider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Timing Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Simulation and FPGA Implementation Results 37
4.1 Simulation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Pre-synthesis Design and Verication . . . . . . . . . . . . . . . . . . . . 41
4.3 Synthesis Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 Conclusion and Future Work 47
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
References 49

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