太赫茲輻射是一種能穿透多種非導電材料的電磁輻射。此外，太赫茲輻射的光子能量相較於X光較低，因此太赫茲成像常被應用於斷層掃描、物質分析和電路缺陷檢測。然而，由於太赫茲波發射器和接收器的成本昂貴，不適合使用像素陣列的方式進行成像。光柵掃描雖然只需要使用一個接收器，但成像時間過長。單像素成像同時兼顧低成本與短採樣時間，被視為十分有前景的太赫茲成像技術。
單像素成像只使用一個接收器，並利用壓縮感測技術大幅減少量測次數。壓縮感測利用訊號的稀疏性，可以用遠低於採樣定理所需的採樣次數完美重建訊號。雖然大部分的自然訊號不具有稀疏性，但可以通過某些數學轉換將其轉換為稀疏訊號。對於自然圖像而言，通常會使用離散餘弦轉換作為稀疏轉換的方式。
由於太赫茲單像素成像系統的限制，還原的圖像解析度並不能太高，本研究的圖像大小為64×64像素。然而，低解析度圖像在離散餘閒轉換域中並不稀疏，因此以最小化l_0或l_1範數為目標的還原演算法無法達到高還原品質。為了提高還原品質，本研究提出一種基於總變差增廣拉格朗日懲罰函數交替方向演算法(TVAL3)的低複雜度還原演算法，命名為二維總變差增廣拉格朗日懲罰函數法(2D-TVALM)。TVAL3是一種用於解決總變差最小化問題的演算法。由於總變差正則化不依賴訊號的稀疏性，還原品質不會受到稀疏基底的限制。雖然TVAL3的複雜度相對較低，但他通過將二維圖像轉換維一維訊號來解決問題，仍可進一步提高運算速度。因此本研究透過設計採樣矩陣和一些數學近似方法，大幅降低TVAL3的運算複雜度。
模擬結果顯示，所提出的演算法在還原品質的PSNR比TVAL3高約3 dB，且遠高於其他壓縮感測演算法。在運算時間方面，所提出的演算法比TVAL3快約11倍。最後在15張測試圖像中，所提出的演算法在執行200次迭代後的平均PSNR為40.85 dB，平均運算時間為0.0405秒。此外，本研究將2D-TVALM演算法以硬體實現，並使用40奈米製程製作成處理器。該晶片面積為2.06平方毫米，最大操作頻率在核心電壓1.05伏時為230M赫茲，最大吞吐量為每秒500幀。最低能耗點在0.725伏和120M赫茲，此時功率為39.3毫瓦。

Terahertz (THz) radiation is electromagnetic radiation that can penetrate a wide variety of non-conducting materials. Moreover, the photon energy of THz radiation is relatively low compared to X-ray, and it is harmless to the biological tissues. Thus, THz imaging is suitable for tomography, material identification, and circuit failure detection. However, since the THz source generator and detector are extremely expensive, it is impractical to sense objects by using a pixel array. The raster scanning uses only one detector to measure an object profile for a very long time. Nevertheless, there is an efficient sensing method with both low cost and short measurement time called single-pixel imaging. Single-pixel imaging requires only a single detector and applies the technique of compressive sensing (CS) to substantially reduce the number of measurements. CS utilizes the sparsity of signals to perfectly recover the signals with much fewer samples than those required by Nyquist-Shannon sampling theorem. Despite most of the natural signals are not spares, they can be converted into sparse signals by applying some transformation. For natural images, Discrete-Cosine Transform (DCT) is a suitable
transformation to generate sparse signals.
Due to the limitation of the THz single-pixel imaging system, the system merely supports low-resolution image reconstruction with near-video rate on the standard performance computer. In this work, the resolution of the images is 64×64 pixels. However, low-resolution images are not sparse in DCT domain, so the algorithms which aim to minimize the ℓ0-norm or ℓ1-norm of the recovered signal cannot obtain high reconstruction quality. To improve the reconstruction quality, this work proposes a low-complexity two-dimensional total variation augmented Lagrangian method (2D-TVALM) algorithm based on the well-known total variation augmented Lagrangian alternating-direction algorithm (TVAL3). TVAL3 is a low-complexity and high-performance algorithm for solving the TV minimization problem. Since TV regularization does not depend on the sparsity of signals, the reconstruction quality will not be limited by the selected sparsifying basis. Although TVAL3 has relatively low complexity, it solves the problem by converting 2D images into 1D signals, which can be further improved to speed up the computation time. Thus, this work largely reduces the complexity of TVAL3 by designing the sampling matrix and some mathematic approximations.
The simulation results show that the reconstruction quality of the proposed algorithm is about 3 dB higher than TVAL3 in PSNR and the performance is much better than that of the other CS algorithms based on ℓ0-norm or ℓ1-norm minimization. In the computation time, the proposed algorithm is about 11 times faster than TVAL3. Finally, the average PSNR and elapsed time of the proposed algorithm are 40.85 dB and 0.0402 s respectively with 200 iterations in the 15 test patterns. Additionally, this work further implements the 2D-TVALM algorithm in hardware, and the processor is fabricated in 40-nm CMOS. The area of the chip is 2.06 mm2. The maximum operating frequency of the proposed processor is 230 MHz with 1.05 V core voltage and the maximum throughput is 500 frame/s. The minimum energy point is located at 120 MHz clock frequency and 0.725 V core voltage with 39.3 mW power.

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