太赫茲輻射由於其許多獨特的特性，近年來在許多研究領域引起了極大的關注。太赫茲可以穿透多種非導電材料和許多種分子，從而在太赫茲波段顯示出它們獨特的光譜特性。此外與X射線不同，太赫茲波的低功率輻射不會對生物組織產生危害。因此太赫茲技術在無損檢測、安檢、光譜學、生物信息學、斷層掃描等諸多研究領域的發展中備受期待。然而太赫茲輻射的產生器和探測器仍然非常昂貴，導致構建具有成本效益的太赫茲成像系統面臨許多挑戰。單像素壓縮感測成像被認為是實現太赫茲成像系統的低成本可靠解決方案。 單像素壓縮感測成像僅使用一個感測器進行採樣。通過在系統中使用不同的空間遮罩，可以同時對待測物的信息進行採樣和壓縮，因此能夠使用低於奈奎斯特定理所要求的採樣率進行訊號採樣與還原。

然而，單像素壓縮感測成像需要額外的重建算法來從採樣信號中恢復原始圖像。這導致高解析度成像應用的計算複雜度爆炸式增長。除此之外，使用於太赫茲輻射的單像素成像系統會面臨許多光學和物理元件的不理想效應。這些不理想效應會導致重建算法性能不佳甚至導致重建失敗。為了減少傳統壓縮感知重建算法中的矩陣維度和計算負擔，本研究在太赫茲單像素成像系統中採用了張量壓縮感知框架。本研究還提出了一種通道等化演算法，通過使用克羅內克乘積分解和基於線性回歸的測量值修改，以消除不理想的太赫茲通道對重建圖像的影響。另一方面，基於投影的原子選擇策略被用於基於張量的重建算法，以進一步提高重建性能。 模擬實驗利用均方誤差(MSE)和結構相似性(SSIM)的性能指標來證明圖像品質在重建性能方面的改進。在本研究中，通道模型和模擬是針對64 × 64的圖像進行的。我們會交互比較不同的通道等化方法和重建演算法，通過MSE、SSIM、與視覺效果來比較不同方法對圖像重建性能的影響。

Terahertz (THz) radiation has attracted great research attention in recent years due to its many exciting properties. Terahertz can penetrate several non-conductive materials and plenty of molecules to show their unique spectral characteristics in the terahertz band. Besides, unlike X-ray, terahertz wave is harmless to biological tissues because of its low-power radiation. Therefore, terahertz is highly anticipated in the development of many research fields, such as nondestructive evaluation, security screening, spectroscopy, bioinformatics, and tomography. However, the source generators and the detectors for terahertz are still extremely expensive, resulting in many challenges in constructing a cost-efficient terahertz imaging system. Single-pixel compressive sensing imaging is regarded as a low-cost reliable solution to implement the terahertz imaging system. Single-pixel imaging technology utilizes only one detector for sampling. By the use of spatial masks in the system, the information of the object can be sampled and compressed at the same time, enabling a lower sampling rate compared to what the Nyquist–Shannon theorem required.

However, single-pixel compressive sensing imaging requires an extra reconstruction algorithm to recover the original image from the sampled signals. This can lead to explosive growth in computational burden for high-resolution imaging applications. In addition, the single-pixel imaging system suffers from several undesirable effects on optical and physical components, e.g., Gaussian beam propagation and modulation depth effect. These non-ideal effects always lead to the poor performance or even failure of the reconstruction algorithm. To reduce the matrix dimension and the computational burden in the traditional compressive sensing reconstruction algorithms, this study adopted the tensor compressive sensing framework, which was originally proposed for image compression and restoration, in the terahertz single-pixel imaging systems. This work also proposes a channel equalization algorithm by introducing the nearest Kronecker product decomposition (NKP) and measurements modification based on off-line linear regression (LR) to eliminate the non-ideal THz channel effects on the reconstructed image. On the other hand, the projection-based atom selection strategy was used in the tensor-based reconstruction algorithm to further improve the reconstruction performance. The simulation experiments utilized the performance metrics of mean square error (MSE) and structural similarity (SSIM) to demonstrate image quality improvement in reconstruction performance. In this study, the channel model and the simulation were carried out for 64 × 64 images. Different channel equalization processes and reconstruction algorithms are compared interactively, and the impact of different methods on image reconstruction performance is compared through MSE, SSIM, and visual impression.

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