太赫兹波是近期許多研究人員關注的領域。它具有許多有價值的特性，例如能夠穿透非金屬物質，而不同的物質在太赫兹頻段有著明顯不同的響應。此外，太赫兹對生物組織無害。因此，它可以應用於許多領域，包括電路缺陷檢測、材料分析和醫學成像。
雖然太赫兹具有出色的發展潛力，但實際應用中存在一些障礙。太赫兹源產生器和接收器非常昂貴，因此傳統的像素陣列成像方法並不實用。另一方面，光柵掃描只需要一個接收器，但需要很長時間來捕獲一張太赫兹圖像。許多研究人員改用單像素壓縮感知成像系統來捕獲太赫兹圖像。單像素成像系統僅使用一個探測器和數字微鏡器件，通過在數字微鏡裝置上使用多個遮罩來捕獲物體圖像，然後可以使用壓縮感知來重建圖像。在數字微鏡裝置和壓縮感知的幫助下，單像素壓縮感知成像系統可以在短時間內使用一個探測器測量信號。
然而，壓縮感知需要一個適當的取樣矩陣才能實現高重建質量。基於先前重建結果的兩階段自適應壓縮感知提出了一種新的設計取樣矩陣的方法。它基於先前的重建結果創建了一個取樣矩陣，並成功提高了第二階段的重建質量。然而，對於高分辨率圖像重建，兩階段自適應壓縮感知的計算複雜度非常高，不適合進行硬件實現。
本論文提出了基於近似訊息傳遞信號重建的太赫兹單像素壓縮感知成像系統的兩階段壓縮感知方法。近似消息傳遞是一種低複雜度的凸優化算法，可以提高重建質量。在圖像解析度為64×64、量測次數為 1600 的情況下，所提出的方法的計算成本僅為兩階段自適應壓縮感知算法的一半。圖像質量的均方誤差(MSE)從 0.048 降低到 0.039，對應的結構相似性(SSIM)從 0.420 提高到 0.446。此外，還實現了相應的硬體處理器。使用賽靈思 ZCU102板驗證了硬體的實現結果，所提出的架構的吞吐量可達到每秒 130 幀。

Terahertz wave (THz) is an area of recent interest to many researchers. It has many valuable properties, such as the ability to penetrate non-metallic substances, and different substances have distinct responses in the THz band. In addition, THz is harmless to biological tissue. Therefore, it can be applied to many fields, including circuit defect detection, material analysis, and medical imaging.
Although THz has excellent potential for development, there are some obstacles for practical applications. THz source generators and receivers are so expensive that conventional imaging methods, i.e., pixel arrays are impractical. On the other hand, the raster scan requires only one receiver but takes a lot of time to capture a THz image. Many researchers instead used single-pixel compressive sensing imaging systems for capturing the THz images. The single-pixel imaging system only uses a detector and a digital micromirror device (DMD) to capture an object image by using several masks on the DMD and then compressive sensing (CS) can be used to reconstruct images. With the help of DMD and CS, single-pixel compressive sensing imaging systems can measure signals in a short time with only one detector.
Nevertheless, CS requires an appropriate sampling matrix to achieve high reconstruction quality. Two-stage adaptive compressive sensing proposed a novel way to design a sampling matrix. It created a sampling matrix based on previous reconstruction results and successfully improved the second stage's reconstruction quality. However, the computational complexity of the two-stage adaptive compressive sensing is exceptionally high for high-resolution image reconstruction, making it unsuitable for hardware implementation.
This thesis proposes the two-stage compressive sensing based on the approximate message passing signal reconstruction for terahertz single-pixel compressive sensing imaging systems. Approximate message passing (AMP) is a low-complexity convex optimization algorithm that improves the reconstruction quality. Regarding computational cost under the condition of image resolution N=64×64 measurement M=1600, the proposed method only required half of the computational complexity of the two-stage adaptive compressive sensing algorithm.
The image quality was improved from MSE=0.048 to MSE=0.039 and the corresponding subjective quality was improved from SSIM=0.420 to SSIM=0.446. Furthermore, the corresponding hardware processor was implemented. The hardware implementation result was verified using the Xilinx ZCU102 board, and the throughput of the proposed architecture is up to 130 frames/sec.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Terahertz Waves (THz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Imaging Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Pixel Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Raster Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.3 Single-Pixel Imaging . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Compressive Sensing and Signal Reconstruction Algorithm . . . . . . . . 4
1.4 Adaptive Compressive Sensing . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Terahertz Single-Pixel Imaging System 11
2.1 Terahertz Single-Pixel Imaging System . . . . . . . . . . . . . . . . . . . 11
2.2 Compressive Sensing on THz Single-Pixel Imaging System . . . . . . . . 13
2.3 Two-Stage Adaptive Compressive Sensing Algorithm . . . . . . . . . . . 15
3 Two-Stage Compressive Sensing and Approximate Message Passing Signal Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
3.1 Approximate Message Passing (AMP) . . . . . . . . . . . . . . . . . . . . 21
3.2 AMP in THz System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Proposed Two-Stage Compressive Sensing and Approximate Message Pass ing Signal Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Simulation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Proposed Architecture and Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Hardware Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Hardware Architecture and Timing Schedule . . . . . . . . . . . . . . . . 42
4.2.1 Hardware-Friendly AMP Algorithm . . . . . . . . . . . . . . . . . 42
4.2.2 Top Module of the Proposed Hardware . . . . . . . . . . . . . . . 43
4.2.3 Sub-Modules Design . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.4 Timing Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 Fixed-Point Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Implementation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73
5.1 Xilinx ZCU102 MPSoC Platform . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Implementation and Image Reconstruction Result . . . . . . . . . . . . . 74
5.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6 Conclusion and Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . 81
References . . . . . . . . . . . . . . . . . . . . . . . . . . 83

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