太赫茲波可以穿透許多非金屬材料，對生物組織是安全的，並且有許多重要物質的能階都在太赫茲波段。因此，太赫茲被視為具有許多重要應用的潛力。例如：物質測試、安全應用、半導體檢測、生物測試等。然而，太赫茲源和太赫茲感測器非常昂貴，以至於大多數研究團隊需要採用光柵掃描(raster scan)或單像素成像(single-pixel imaging)來降低設備成本。本論文適用的太赫茲成像系統是基於單像素成像技術的。因此需要的取樣點數較光柵掃描少，且成像時間更短。但作為代價，單像素成像需要額外的還原算法。而這對於高解析度的應用來說是一個相當大的負擔。

因此，本研究團隊將原本用於壓縮和解壓縮的 GTCS 架構應用於太赫茲單像素成像系統，以在重建過程中減少矩陣維度，並進一步達到減少運算負擔的效果。並且相關成果已發表在IRMMW-THZ 2021 [1]。本文提出的2DCS-PSVD算法的計算量比GTCS-P OMP [1]和Modified GTCS-P低，在32x32及64x64解析度且節省約50%取樣數時(相較於raster scan)的影像品質差不多。以n=32,m=22,I=5,T=6的規格來計算演算法需要的FLOPs的話，2DCS-PSVD只需要Modified GTCS-P 78.90%的FLOPs。最後，本文以Xilinx ZCU102板作為目標的FPGA平台，並實現了2DCS-PSVD的VLSI硬體架構設計。此外，所設計的影體吞吐量高達每秒 1127.27 幀，可為高速半導體檢測或更高解析度的實時成像應用鋪路。

Terahertz (THz) wave can penetrate many non-metallic materials, is safe for biological tissues, and the energy levels of many important substances are in the THz band. Therefore, THz is seen as having the potential for many important applications. For example : substance testing, security applications, inspection of semiconductor, biological testing, etc. Yet, the THz sources and detectors are so expensive that most of the research teams need to adopt raster scan or single-pixel imaging to reduce equipment costs. The target THz imaging system in this thesis is based on single-pixel imaging, which requires fewer samples and the imaging time is shorter. However, single-pixel imaging requires additional reconstruction stage. And this is a considerable burden for high-resolution applications.

Therefore, our research team applied the GTCS framework originally used for compression and decompression on THz single-pixel imaging systems to reduce the matrices dimension while the process of reconstruction and achieve the effect of reducing the computational burden. Besides, our research team presented the associated results in the IRMMW-THz 2021. The thesis further proposes the 2DCS-PSVD algorithm, which has a lower computational burden than the GTCS-P OMP and the modified GTCS-P, and the image quality of these three algorithms are close when saving about half the number of samples required for raster scan at the resolutions of 32 x 32 and 64 x 64. In terms of the computational cost with the condition of n=32, m=22, P=5 and T=6, which is applied on the proposed design, the 2DCS-PSVD only requires 78.90% of the number of FLOPs than the modified GTCS-P. Last but not the least, this thesis implements the proposed 2DCS-PSVD algorithm on the Xilinx ZCU102 board. The throughput of the proposed hardware architecture is up to 1127.27 frames per second, which paves way for high-speed semiconductor inspection or higher-resolution real-time imaging applications.

1 Introduction 1
1.1 Terahertz Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Associated Scanning Methodologies and Single-Pixel Imaging . . . . . . . 3
1.2.1 Pixel Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Raster Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.3 Single-Pixel Imaging . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Model of Compressed Sensing . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Reconstruction Algorithms and Research Motivation . . . . . . . . . . . 6
2 Terahertz Single-Pixel Imaging System 9
2.1 Terahertz Single-Pixel Imaging System . . . . . . . . . . . . . . . . . . . 10
2.2 Compressed Sensing on Terahertz Single-Pixel Imaging System . . . . . . 11
3 Generalized Tensor Compressed Sensing 15
3.1 2D Compressive Sensing on Terahertz Single-Pixel Imaging System . . . 16
3.2 Generalized Tensor Compressive Sensing With Parallelizable Recovery
(GTCS-P) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Generalized Tensor Compressive Sensing With Parallelizable Recovery
via OMP (GTCS-P OMP) . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Modified Generalized Tensor Compressive Sensing With Parallelizable
Recovery (Modified GTCS-P) . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Proposed 2D Compressive Sensing by Power Method for SVD 21
4.1 2D Compressive Sensing by Power Method for SVD Algorithm . . . . . . 21
4.2 Computational Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Proposed Architecture and Specification 41
5.1 Hardware Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Implementation Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3 Architecture Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.4 Fixed-Point Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.5 Implementation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.6 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6 Conclusion and Future work 71
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