本論文的研究重點為基於學習之影像和信號還原技術。第一部份為基於深度學習的影像還原技術，目的是為低品質不清晰的影像回復成高品質的清晰影像並還原細節，現今深度學習為基礎的影像還原技術 (deep learning based image restoration) ，已被證實有著優於傳統人為定義特徵(hand-crafted features)的方法，在電腦視覺問題上達到非常卓越的效能，在本論文中，我們首先將基於深度學習做為基石，探討如何在設計深度學習網路架構上有效地利用先驗知識 (prior information)提升影像還原技術效能。首先，在人臉影像的超解析度技術上，雖然現今使用基於深度學習的架構在視覺上可達到不錯的回復效果，但所回復的人臉影像往往和實際的人臉影像並不相似，造成身分辨識的問題，尤其是在輸入影像在非常低的解析度的情況下。因此，本論文透過在學習過程中使用對比學習 (Contrastive Learning) 嵌入身分資訊，除了在視覺上有著良好的回復品質外，也保留原來人臉影像的身分資訊。
此外，本論文也將影像還原技術應用在太赫茲 (THz)電腦斷層掃描 成像上。由於太赫茲波固有的衍射行為和強水吸收特性會導致各種雜訊以及如深度資訊等物體資訊丟失，現有的研究雖然致力於解決這個問題，但這些方法仍然受到太赫茲光束的衍射限制。為了解決這個問題，本論文從頻域中提取豐富的頻譜振幅和頻譜相位資訊作為先驗知識，利通過設計深度學習網路從兩者不同特性的信號中，學習出有用的特徵資訊作為輔助並引導回復太赫茲影像，而無需任何額外的計算成本或設備，這有利於提高太赫茲成像結果。


論文的第二部分為基於圖信號學習之影像和信號還原技術。雖然現今深度學習的方法在各種電腦視覺應用中均取得了卓越的性能，但深度模型中的參數純粹是從資料中學習而來，時至今日還是無法解釋用數學解釋。且當訓練資料和測試資料特性不同時，效果會有顯著的下降。因此本論文導入了圖信號處理技術，首先運用圖形信號是平滑特性的先驗知識 並進一步在圖拓譜的建圖中引入邊的副權重特性，同時將正和副的相似性信息納入經典的最大事後機率計算中並運用在分類問題上。現有的深度學習的還原方法，並不借助任何顯式變換模型，而單純從具有代表性的大數據中直接學習結果不同，本論文將圖信號處理和深度學習做結合應用在影像去噪上，利用圖信號先驗建構了一個新的圖神經網絡（GNN），並採用了事先定義好的可解析的圖濾波器 (analytical graph filter)，其無需大量訓練資料，並且我們僅通過用CNN學習如何優化並建構適當圖拓撲以達到端到端的學習架構，並解決在實際的應用上當訓練和測試資料在不相同的特性下效果下降的問題。最後，本論文拓展至影像去噪和對比度強化的問題上，我們提出了一種混合圖學習/分析濾波器算法，將上述的圖信號先驗知識做延伸，分別在數學中的空間平滑度和分段平滑度表示影像的量度和對比度，並讓CNN學習如何優化並建構這兩種不同特性的圖拓撲，並使用正邊緣來對抗噪聲和上述提到的負邊緣來強調對比度。

This dissertation focuses on the development and evaluation of image and signal restoration using learning techniques. The first part is concerned with deep learning-based image restoration techniques, particularly aiming to recover high-resolution (HR) details from low-resolution (LR) face images for identity recognition and to restore corrupted terahertz images for tomography reconstruction. To this end, we adopt deep learning as the backbone of data-driven learning and utilize prior information to devise effective deep neural networks for the two different image restoration tasks. First, we propose a generative adversarial network (GAN) based face hallucination scheme to recover high-resolution details of LR face images to boost the performance of identity recognition. Specifically, we propose an identity-preserving face hallucination GAN that learns to recover HR face image details while retaining the identity information of the original LR face image by embedding the face's identity information into the learning process based on contrastive learning. Second, we propose a novel physics-guided deep restoration network for terahertz (THz) tomographic imaging, an emerging field with great application potentials in industrial inspection, security screening, chemical inspection and non-destructive evaluation. THz imaging, however, suffers from its inherent diffraction behavior, strong water absorption properties, and low noise tolerance, which lead to undesired blurs and distortions of reconstructed THz images. The performances of existing restoration methods are highly constrained by the diffraction-limited THz signals. To address the problem, we propose a multi-view Subspace-Attention-guided Restoration Network (SARNet) that fuses multi-view and multi-spectral features of THz images for effective image restoration and 3D tomographic reconstruction. To this end, SARNet uses multi-scale branches to extract intra-view spatio-spectral amplitude and phase features and fuse them via shared subspace projection and self-attention guidance.


The second part of the dissertation deals with image and signal restoration based on graph signal learning. Although modern deep learning methods have achieved excellent performances in various computer vision applications, deep learning models are usually learned purely from data and cannot be explained mathematically. Moreover, the performance of a deep learning model can be significantly degraded when there exists a domain gap between the model's training data and testing data. Therefore, this dissertation introduces graph signal processing (GSP) techniques, which use graph signal priors such as smoothness and sparsity priors, to achieve effective image and signal restoration. To this end, we introduce negative-edge weights in the graph topology construction for a classification problem, and incorporate the positive and negative similarity information into the classical maximum a posteriori (MAP) formulation at the same time to solve the problem. Unlike existing deep learning-based restoration methods, which do not resort to any explicit transform model but learns mainly from data, this dissertation combines graph signal processing with deep learning for image denoising. Specifically, our method constructs a graph neural network (GNN) based on graph signal priors and utilizes analytical graph filters which so not require learning. Our method optimizes the restoration performance in an end-to-end manner only via learning of an appropriate graph topology, rather than learning the filters, at each layer. In this way, it achieves effective image denoising even when the training and testing data have different characteristics. Finally, we further address the problem of joint image denoising and contrast enhancement. We propose a hybrid graph learning/analytic filtering algorithm that extends the above graph signal priors to represent the illumination and reflectance components of an image to promote the spatial smoothness and piecewise smoothness of the image, respectively. Our approach allows GNNs to learn how to optimize and construct graph topologies based on these two smoothness priors, and use positive edges to combat against noise and negative edges to highlight contrast, respectively.

Abstract I
Abstract (Chinese) IV
Acknowledgements VI
Contents VII
1 Overview of Dissertation . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Contributions of Dissertation . . . . . . . . . . . . . . . . . .4
1.3 Dissertation Organization . . . . . . . . . . . . . . . . . . . .6
2 Part I: Image restoration based on Deep Learning . . . . . . . . . 7
3 Identity-Preserving Face Hallucination . . .. . . . . . . . . . . 9
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . .12
3.3 Overview of the Proposed Method . . . . . . . . . . . . . . . . 14
3.4 Identity-Preserving Face Hallucination . . . . . . . . . . . . .15
3.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . .20
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Terahertz Tomographic Imaging . . . . . . . . . . . . . . . . . . 34
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . .39
4.3 Physics-Guided THz Imaging . . . . . . . . . . . . . . . . . . .41
4.4 Overview of the Proposed Method . . . . . . . . . . . . . . . . 46
4.5 Terahertz Tomographic Imaging . . . . . . . . . . . . . . . . . 48
4.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . .56
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5 Part II: Graph Learning-Based Image and Signal Restoration . . . .66
6 Graph Classifier Learning with Negative Edge Weights . . . . . . 68
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .68
6.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3 Graph Smoothness . . . . . . . . . . . . . . . . . . . . . . . 73
6.4 Generalized Smoothness . .. . . . . . . . . . . . . . . . . . . 79
6.5 Graph Construction . . . . . . . . . . . . . . . . . . . . . . 83
6.6 Finding A Perturbation Matrix . . . . . . . . . . . . . . . . . 86
6.7 Algorithm Development . . . . . . . . . . . . . . . . . . . . . 90
6.8 Experimental Results . . . . . . . . . . . . . . . .. . . . . . 92
6.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7 Image Denoising Based on Analytical Graph Filters . . . . . . . 101
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.3 Overview of the Proposed Method . . . . . . . . . . . . . . . .105
7.4 Analytical Graph Filters . . . . . . . . . . . . . . . . . . . 105
7.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . 110
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
8 Graph-based Joint Denoising and Constrast Enhancement . . . . . .114
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.3 Overview of the Proposed Method . . . . . . . . . . . . . . . .120
8.4 Dual Graph Filters . . . . . . . . . . . . . . . . . . . . . . 121
8.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . 126
8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .129
9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .130
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

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