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研究生： 林昭廷
Lin, Jhao-Ting
論文名稱： 基於凸優化與深度解摺疊之超穎衛星系統：從影像超解析與異物偵測，到量子訊號處理與遙測
Meta-Satellite Systems Based on Convex Optimization and Deep Unfolding: From Image Super-Resolution and Anomaly Detection to Quantum Signal Processing and Remote Sensing
指導教授： 林家祥
Lin, Chia-Hsiang
學位類別： 博士
Doctor
系所名稱： 電機資訊學院 - 電腦與通信工程研究所
Institute of Computer & Communication Engineering
論文出版年： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 268
中文關鍵詞： 異物偵測 、盲源分離 、凸優化 、深度解摺疊 、高光譜影像 、影像超解析 、可解釋人工智慧 、超穎材料 、微型衛星 、多光譜影像 、量子計算 、量子深度學習 、水體偵測
外文關鍵詞： anomaly detection, blind source separation, convex optimization, deep unfolding, hyperspectral image, image super-resolution,, interpretable artificial intelligence, metamaterial, miniaturized satellite, multispectral image, quantum computing, quantum deep learning, waterbody detection
ORCID： 0000-0002-9950-0843
相關次數： 點閱：68  下載：8 
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    • 福爾摩沙衛星八號（福八）的取像成果已於2026年2月首次公開，其拍攝之多光譜影像（multispectral image, MSI）達公尺級空間解析度，給予我們清晰的視野。然而，多光譜影像不像高光譜影像（hyperspectral image, HSI）可利用豐富的頻譜資訊進行地表分析、物質辨識，使得我們僅能看到影像表面，卻無法看透影像本質。影像融合（image fusion）是一種經濟的超解析方式，它可從高光譜影像中萃取頻譜細節，並將其融合至多光譜影像中，提升其頻譜解析度。本文提出了凸深度影像融合（convex/deep image fusion, CODE-IF）演算法。透過重新定義深度學習的角色，該演算法利用小數據和簡單深度網路產出之粗略解去實現數學上簡單的凸Q-二次範數（Q-quadratic norm）正則化。不僅避免了深度學習（deep learning, DE）對大數據和複雜的網路架構的依賴，亦克服凸優化（convex optimization, CO）中需手工設計複雜正則化器（regularizer）的挑戰。

    取得高頻譜解析度另一個更直觀的方式，是對影像進行頻譜超解析（spectral super-resolution）。與現有方法多侷限於CAVE等級之頻譜重建（僅涉及31個可見光頻帶）不同，本文提出了哨兵2號至AVIRIS轉換（conversion from Sentinel-2 to AVIRIS, COS2A）演算法，旨在將12個頻帶的多光譜影像重建為涵蓋可見光至近紅外波段、高達172個頻帶的高光譜影像。基於凸深度小數據學習理論，該演算法採用輕量化且可解釋的深度解摺疊（deep unfolding）網路作為正則化。此外，針對哨兵2號衛星多重空間解析度特性所導致的影像模糊問題，本文進一步推導出頻譜--空間對偶（spectral-spatial duality）定理，將高度不適定的頻譜重建問題轉化為已充分研究的空間超解析問題。該演算法有助於提升台灣現有衛星資源的頻譜解析度，為相關政府部門提供關鍵技術支援（如協助中央氣象署進行溫室氣體偵測）。

    鑒於深度解摺疊網路於輕量化硬體開發之優勢，本文進一步將該網路擴展至孿生影像超解析（twin-image super-resolution, TISR）任務。有別於融合異質數據（如多光譜/高光譜影像）的影像強化技術，孿生影像超解析利用兩張具亞像素偏移的同質影像來實現空間超解析。本文提出的凸自相似性解摺疊超解像模式超解析（convex self-similarity unfolding supermode super-resolution, COSUP）演算法，首次將孿生影像超解析問題制定為凸準則，並利用影像自相似性先驗（self-similarity prior）增強影像品質。該演算法具備高度實用性，可應用於福八或是任何具備雙鏡頭配置之架構。

    為求可跳過頻譜超解析步驟，直接對多光譜影像進行分析。本文更開發了全球首個多光譜解混（multispectral unmixing）方法。多光譜解混在數學上對應於極具挑戰性的欠定盲源分離（underdetermined blind source separation）問題，意指方程式數（頻帶數）少於未知數（物質數）。然而，過往研究都無法破解欠定問題，僅考慮頻帶數多於物質數的場景。本文提出了稜鏡啟發的多光譜端元提取（prism-inspired multispectral endmember extraction, PRIME）演算法來首次破解欠定問題。該演算法利用具備強大特徵提取能力的量子深度網路（quantum deep network, QUEEN）構建虛擬稜鏡，藉此實現頻譜維度的分光以產生額外的頻帶資訊。原本難以求解的欠定問題便可轉化為凸幾何可處理的高光譜解混問題，實現了不經頻譜重建即可直接進行物質辨識的突破。

    隨著衛星影像對於民生與軍事上的發展日益重要，本文在應用層面探索了高光譜異物偵測（hyperspectral anomaly detection, HAD）。高光譜異物偵測旨在將異物與背景區分開，然而，由於無法預先獲取異物的光譜特徵，使得該任務在真實環境中極具挑戰性。本文引入超像素分割（superpixel segmentation）技術來增強廣泛使用的協作表示偵測器（collaborative representation detector, CRD）以重建背景，並將其整合至穩健主成分分析（robust principal component analysis, RPCA），提出SuperRPCA演算法。詳細來說，該演算法將協作表示偵測器費時的像素級運算優化為超像素級處理，顯著降低了運算成本。此外，重建的背景被設計為具有低秩特性的凸正則化器，可取代穩健主成分分析中耗時的核範數（nuclear norm）計算，從而以更高的效率實現最先進的性能。

    本文進一步將研究範疇擴展至利用氣象衛星進行內陸水體偵測（inland waterbody detection, IWD）。針對美國國家航空暨太空總署（National Aeronautics and Space Administration, NASA）氣旋全球導航衛星系統（Cyclone Global Navigation Satellite System, CYGNSS）提供的延遲都卜勒映射（delay-Doppler map, DDM）數據，本文提出了IWD-QUEEN演算法，可提供高時間解析度和廣域覆蓋範圍的偵測結果。透過水體/陸地反射差異，並結合高度糾纏的多頭量子深度網路，該演算法在亞馬遜河流域實現了比傳統方法和現有全球水文地圖更精細尺度的檢索。此外，演算法核心優勢在於無需輔助校正參數，展現高度硬體友善與邊緣運算潛力，使其適合部署於台灣獵風者（TRITON）衛星進行實時監測。

    除了針對衛星數據進行智慧化分析，本文最後亦克服了衛星硬體微型化的瓶頸。奈米尺度的超穎光柵（metagrating）雖可取代傳統笨重光學元件（如分光鏡和柱面透鏡）以縮減衛星體積。然而，該元件的結構設計需要在龐大的奈米天線資料庫中尋找最優排列結構，其可能的總排列數高達10^82種。本文透過將蒙地卡羅樹搜尋融入基因演算法，開發出基因樹搜尋（genetic-type tree search, GTTS）演算法，並引入虛擬空間概念以促進快速結構優化。有別於傳統研發流程高度依賴「設計，製作，量測」的反覆試錯，該演算法不僅在設計階段實現秒級之超構光柵自動逆向設計，還確保了高指向性與精確的偏轉角。

    綜觀全文，本文從硬體逆向設計、影像超解析與異物偵測，到量子訊號處理與遙測應用皆有所研究。研究成果不僅在學術上達成最先進性能，更為台灣未來自主研發之衛星系統提供了堅實的技術支援。

    The imaging results of FORMOSAT-8 were first released in February 2026. Its multispectral images (MSIs) reach meter-level spatial resolution, providing a clear vision of the Earth. However, unlike hyperspectral images (HSIs), MSI lacks the rich spectral information required for detailed surface analysis and material identification. This limitation prevents us from analyzing the MSIs. Image fusion (IF) is an economical approach for spatial super-resolution (SR), in which spectral details are extracted from the HSI and fused into the MSI. This dissertation introduces a convex/deep image fusion (CODE-IF) algorithm. By redefining the role of deep learning (DE), this algorithm uses a rough solution generated by a simple deep network with small training data to implement a mathematically concise convex Q-quadratic norm regularizer. This not only avoids the dependency of deep learning on big data and complex network architectures but also overcomes the challenge in convex optimization (CO) posed by the manual design of sophisticated regularizers.

    Another intuitive way to obtain high spectral resolution is spectral SR. Distinct from existing spectral SR methods that mainly focus on CAVE-level (31 visible bands) reconstruction, the dissertation proposes the conversion from Sentinel-2 to AVIRIS (COS2A) algorithm, which aims to reconstruct 12-band MSI into HSI with up to 172 bands, spanning the visible to near-infrared range. Based on convex/deep (CODE) small-data learning theory, the algorithm uses a lightweight and interpretable deep unfolding network as a regularizer. Moreover, to address the image blurring issues caused by the multispatial resolution characteristics of the Sentinel-2 satellite, this dissertation further derives a spectral-spatial duality, which transforms the highly ill-posed spectral reconstruction problem into a well-studied spatial SR problem. The proposed algorithm enhances the spectral resolution of Taiwan's existing satellite resources and provides key technical support to relevant government departments (e.g., assisting the Central Weather Administration in greenhouse gas detection).

    Given the advantages of the deep unfolding technique in lightweight hardware development, the dissertation extends it further to the twin-image SR (TISR) task. Unlike image enhancement techniques that fuse heterogeneous data (e.g., MSI and HSI fusion), TISR leverages two homogeneous images with subpixel shifts to achieve spatial enhancement. The dissertation introduces the convex self-similarity unfolding supermode SR (COSUP) algorithm, which first formulates the TISR problem as a convex criterion and exploits the self-similarity prior to enhance image quality. The proposed algorithm is highly practical and can be applied to FORMOSAT-8 or any satellite with a dual-lens configuration.

    To analyze the MSIs directly without the need for spectral SR, this dissertation also develops the world's first multispectral unmixing (MU) method. Mathematically, MU corresponds to the highly challenging underdetermined blind source separation (UBSS) problem, where the number of equations (spectral bands) is fewer than the number of unknowns (materials). While previous studies could not solve the underdetermined case and only considered scenarios where bands outnumber materials, this dissertation presents the prism-inspired multispectral endmember extraction (PRIME) algorithm to break this barrier. The algorithm uses a quantum deep network (QUEEN) with advanced feature extraction to construct a virtual prism, thereby facilitating light splitting and generating additional virtual spectral bands. This transforms the difficult underdetermined problem into a hyperspectral unmixing problem solvable via convex geometry, achieving a breakthrough in material identification without spectral reconstruction.

    As satellite imagery becomes increasingly vital for civilian and military applications, this dissertation explores hyperspectral anomaly detection (HAD). HAD aims to distinguish anomalies from the background. However, the unavailable prior information about anomalies makes this task challenging in real-world environments. The dissertation introduces superpixel segmentation to enhance the widely used collaborative representation detector (CRD) for background reconstruction, and integrates it into robust principal component analysis (RPCA), proposing the SuperRPCA algorithm. Specifically, the time-consuming pixel-wise computing of CRD is optimized into superpixel-level processing, reducing computational costs. Furthermore, the reconstructed background is designed as a convex regularizer with low-rank properties, which can replace the time-consuming nuclear norm calculation in RPCA to achieve state-of-the-art (SOTA) performance with superior efficiency.

    The research scope is further extended to inland waterbody detection (IWD) using weather satellites. Using delay-Doppler map (DDM) data from the National Aeronautics and Space Administration (NASA) Cyclone Global Navigation Satellite System (CYGNSS), the dissertation proposes the IWD-QUEEN algorithm, which can provide detection with high temporal resolution and extensive spatial coverage. By leveraging differences in waterbody/land reflection and combining it with a highly entangled multihead QUEEN, the algorithm achieves finer-scale retrieval in the Amazon River Basin than conventional methods and existing global hydrological maps. Furthermore, the core advantage of the algorithm is that it does not require auxiliary correction parameters, demonstrating high hardware friendliness and edge-computing potential, making it suitable for deployment on Taiwan's TRITON satellite for real-time monitoring.

    Beyond intelligent analysis of satellite data, this dissertation also overcomes the bottleneck of satellite hardware miniaturization. While nanoscale metagratings can replace traditional bulky optical components (e.g., spectral splitters and cylindrical lenses) to reduce satellite size, the structural design of metagratings require finding the optimal configuration within a vast database of nanoantennas, with a total of up to 10^82 possible arrangements. The dissertation develops a genetic-type tree search (GTTS) algorithm by integrating the Monte Carlo tree search into the genetic algorithm, and introduces the concept of virtual space to facilitate rapid structural optimization. Unlike traditional development workflows that rely heavily on the trial-and-error cycle of ``design, fabrication, and measurement," the proposed algorithm not only achieves automatic inverse design of metagrating in seconds during the design stage but also ensures high directivity and precise deflection angles.

    In summary, this dissertation spans from hardware inverse design and image SR to quantum signal processing and remote sensing applications. The research results not only academically achieve SOTA performance but also provide a robust technical foundation for future miniaturized satellites performing complex environmental observation and Earth-monitoring missions.

    Abstract in Chinese i Abstract in English iv Acknowledgements vii Contents x List of Tables xvii List of Figures xx Symbol xxxii Nomenclature xxxiv 1 Introduction 1 1.1 CODE-Based Small-Data Learning for Image Fusion 1 1.2 Interpretable Neural Network for Spectral Super-Resolution 2 1.3 Interpretable Neural Network for Subpixel-Shift Twin-Image Super-Resolution 3 1.4 Quantum Deep Network for Multispectral Unmixing 3 1.5 Convex Optimization for Hyperspectral Anomaly Detection 4 1.6 Quantum Deep Network for Inland Waterbody Detection 5 1.7 Nonconvex Optimization for Metagrating Design 6 1.8 Organization of the Dissertation 7 2 Super-Resolution Using CODE Small Data Learning Theory 8 2.1 Existing Methods 8 2.2 CODE Small Data Learning Theory 10 2.3 Proposed Method 13 2.3.1 Criterion Design 14 2.3.2 Deep Regularization and Implementation Details 16 2.3.3 Discussion 20 2.4 Experimental Results 21 2.4.1 Experimental Setting 21 2.4.2 Qualitative and Quantitative Analysis 25 2.4.3 Model-Order Selection and Ablation Studies 30 2.4.4 Real-Data Experimental Results 34 3 Sentinel-2 to AVIRIS Reconstruction Using Interpretable Artificial Intelligence With Spectral-Spatial Duality 37 3.1 Existing Methods 37 3.2 Proposed Method 38 3.2.1 Problem Description 38 3.2.2 Problem Formulation 39 3.2.3 Algorithm Design 40 3.2.4 Implementation Details 42 3.3 Experimental Results 48 3.3.1 Experimental Setting 48 3.3.2 Qualitative and Quantitative Analysis 50 3.3.3 Real-Data Experimental Results 56 3.3.4 Discussion 58 4 Twin-Image Super-Resolution Using Interpretable Artificial Intelligence With Self-Similarity Prior 61 4.1 Existing Methods 61 4.2 Proposed Method 63 4.2.1 Problem Formulation 63 4.2.2 COSUP Algorithm for Solving (4.1) 64 4.2.3 Implementation Details 67 4.3 Experimental Results 70 4.3.1 Experimental Setting 70 4.3.2 Qualitative and Quantitative Analysis 72 4.3.3 Analysis of Realistic Subpixel Shifts and Model-Order Selection 75 4.3.4 Real-Data Experimental Results 77 5 Multispectral Unmixing Using Convex Geometry and Virtual Quantum Prism 83 5.1 Existing Methods 83 5.2 Proposed Method 85 5.2.1 Criterion Design 85 5.2.2 Algorithm Design 88 5.2.3 Quantum Prism Design 90 5.3 Experimental Results 95 5.3.1 Experimental Setting and Protocol Design 95 5.3.2 Qualitative and Quantitative Analysis 98 5.3.3 Ablation Study 100 5.3.4 Discussion 102 6 Hyperspectral Anomaly Detection Using Collaborative Superpixel Representation Prior-Aided Robust Principal Component Analysis 105 6.1 Existing Methods 105 6.2 Related Work 107 6.2.1 Robust Principal Component Analysis 107 6.2.2 Collaborative Representation Detector 109 6.2.3 Overview 109 6.3 Collaborative Superpixel Representation Detector 111 6.3.1 Solution for the Case c^{tilde}_i ∈ P_i 114 6.3.2 Solution for the Case c^{tilde}_i /∈ P_i 114 6.4 Robust Principal Component Analysis with Collaborative Superpixel Representation Detector-Based Regularizer 116 6.5 Experimental Results 120 6.5.1 Data Description 120 6.5.2 Experimental Setting 121 6.5.3 Qualitative and Quantitative Analysis 122 6.5.4 Model-Order Selection 126 6.5.5 Interference Testing 127 7 Inland Waterbody Detection Using Delay-Doppler Map and Quantum Multihead Mechanism 131 7.1 Existing Methods 131 7.2 Proposed Method 133 7.2.1 Delay-Doppler Map 135 7.2.2 Delay-Doppler-Map-Aware Transformer 136 7.2.3 Design of IWD-QUEEN 140 7.2.4 Loss Function 142 7.2.5 Design of IWD-Transformer 143 7.2.6 Discussion 144 7.3 Experimental Results 145 7.3.1 Data Description and Experimental Setting 146 7.3.2 Qualitative and Quantitative Analysis 147 7.3.3 Ablation Study 153 7.3.4 Interference Testing 155 7.3.5 Case Studies 155 8 Metagrating Design Using Unsupervised Clustering-Guided Hybrid Tree Search 166 8.1 Existing Methods 166 8.2 Proposed Algorithm 168 8.2.1 Problem Formulation 168 8.2.2 Solver 169 8.2.3 Discussion 174 8.3 Fabrication and Validation of Metagratings via GTTS Algorithm 176 9 Conclusion and Future Works 182 References 185 Appendix A Appendix for Chapter 2 212 A.1 Proof of Property 1 212 A.2 Proof of Property 2 212 A.3 Proof of Property 3 213 A.4 Proof of Lemma 1 213 Appendix B Appendix for Chapter 3 217 B.1 Proof of Theorem 1 217 B.2 Computational Complexity 218 Appendix C Appendix for Chapter 4 220 C.1 A Generalized Definition within the TISR Problem 220 C.2 Training Details of Swin-T within COSUP Algorithm 221 Appendix D Appendix for Chapter 5 223 D.1 Initialization of PRIME Algorithm 223 D.2 Detailed Design of Quantum Prism Network f 224 Appendix E Appendix for Chapter 6 226 E.1 Derivation of Algorithm 6 226 E.1.1 Solution for Line 4 226 E.1.2 Solution for Line 5 226 E.2 Derivation of (6.18) 227 E.3 Derivation of Algorithm 7 227 E.3.1 Solution for Line 5 227 E.3.2 Solution for Line 6 228 Appendix F Appendix for Chapter 8 229 F.1 Proof of Convergence Property of Algorithm 9 229

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