相較於僅擁有三個頻帶的傳統RGB 影像，高光譜影像（hyperspectral image, HSI）涵蓋從可見光到不可見光的數百個光譜，其豐富的頻譜資訊使得我們能夠透過分析高光譜影像的頻譜特徵來進行物質辨識，並且已經應用至許多關鍵領域，如衛星遙測。發展台灣自主的微型衛星在近年來已成為我國最重要計畫之一，福衛八號衛星作為「第三期國家太空科技發展長程計畫」第一個高解析度光學遙測衛星即將於2025 年十月發射，足見自主研發重量輕、成本低及高效能衛星為我國太空計畫之首要目標。有鑑於高光譜影像的物質辨別能力，使得學者能夠僅憑從太空拍攝之衛星影像便能了解地表之物質組成及變化，因此發展一顆能夠拍攝高光譜影像的微型衛星能夠為環境監測以及救災防害帶來非常大的幫助。

然而，高光譜影像紀錄了數以百計的頻帶，導致其檔案大小比RGB 影像大非常多，使得高光譜影像之儲存與傳輸成為一項重大挑戰。傳統的解決方法是透過壓縮感知技術來取得高度壓縮過後的檔案。現有的高光譜壓縮感知方法在硬體上大多會包含分光鏡（spectral splitter, SS）、數位微鏡元件（digital micromirror device, DMD）以及柱面透鏡（cylindrical lens, CL）。其中，用於實現隨機投影之數位微鏡元件是一個笨重的元件，不利於應用於微型衛星之開發。於此同時，近期發展出的多功能超穎材料（multifunctional metamaterial）僅憑一個奈米級的超平面（metasurface）便能達成分光鏡和柱面透鏡的分光及聚光功能。基於此概念，本論文開發了全加法高光譜壓縮感知（all-addition hyperspectral compressed sensing）技術，在壓縮編碼端僅使用加法算子以配合多功能超穎材料特性進而符合微型衛星之發展。然而，由於本方法在編碼端極度簡化，導致解碼過程面臨極大的挑戰。為解決此問題，本文基於影像的自相似性設計了一凸優化（convex optimization）準則，此自相似性準則已被寫為凸函數的形式，並透過實驗證明在極低的採樣率下，仍然能夠有效解碼出高光譜影像。此外，本文亦建立一套基於約翰橢球（John ellipsoid, JE）之分析框架，確保演算法在極低的數據純度（data purity）情況下，依舊能夠完整還原高光譜影像。

有鑑於前述提及之高光譜影像的物質辨別能力能夠探測地表的物質組成及變化，使得高光譜衛星影像能夠為環境監測以及救災防害提供更精準的評估，例如高光譜異物偵測可應用於軍事偵測或稀有礦物偵測。因此近年來高光譜衛星影像之變遷偵測因其對於地表監測及精準農業之能力逐漸受到重視，尤其是基於凸優化或是深度學習（deep learning）之高光譜變遷偵測方法。其中，深度學習通常需要大量數據集來學習影像特徵，特別是在高光譜影像中，數據取得不易，且人工標記過程耗費大量時間與資源。而凸優化準則通常需要數學形式複雜的正則化項以有效且適應性的解決不適應高光譜影像反問題。因此，本文基於衛星反演成像的小數據凸深度學習技術（convex deep, CODE）（該技術榮獲國家科學及技術委員會所頒發之未來科技獎）結合凸優化準則及圖神經網路（graph neural network, GNN），提出一種適用於極低標註率的半監督式（semi-supervised）高光譜變遷偵測演算法。此凸深度學習高光譜變遷偵測（CODE-HCD）演算法利用了高光譜影像之特性設計了一凸Q-二次範數正則項，其具有非常簡單的數學結構，因此能實現演算法的高速運算。在極低標註率的情景下，所提出之凸深度學習高光譜變遷偵測在真實高光譜數據集上優於基準高光譜變遷偵測方法，證實此方法之有效性。

近年來，量子計算作為一個備受矚目的領域迅速崛起，引起了研究界的廣泛關注。量子糾纏的相關研究更於2022 年獲得諾貝爾物理學獎。基於參數化量子電路設計的量子深度網路（quantum deep network, QUEEN）在近期也被開發用於解決不同問題，並在多個領域中展現出卓越的表現，例如藥物反應預測、健康檢測以及影像分類等。因此除了上述將凸優化與深度學習結合的方式以外，本文認為在傳統深度學習的方法中導入理論上全新的量子資訊也能夠強化最後的變遷偵測結果。作為先驅性的研究，本文將量子深度學習網路引入圖神經網路高光譜變遷偵測網路以提升其性能。相較於傳統的卷積神經網路（convolutional neural network, CNN）或圖神經網路萃取影像中的仿射特徵，量子深度學習網路汲取么正特徵，為最後的分類提供理論上不同的額外資訊。在所提出的量子深度學習驅動圖神經網絡（QUEEN-empowered GNN, QUEEN-G）中，圖特徵學習模組利用雙時相高光譜影像在超像素（superpixel）層級的圖結構，而量子特徵學習模組則在像素層級學習量子特徵，作為圖特徵學習模組的補充，保留了在超像素中未能保留的像素層級的詳細空間資訊。在最終的分類階段，設計了一個量子分類器來與傳統的全連接分類器協同工作，進一步提升變遷偵測的準確性。實驗結果證明，所提出的QUEEN-G 演算法在真實高光譜數據集上表現優異，且量子計算所提供的么正特徵能有效增強變遷偵測性能。

Compared to traditional RGB images with only three spectral bands, hyperspectral images (HSIs) contain hundreds of spectral bands ranging from visible to invisible wavelength. The rich spectral information enables substance identifiability by analyzing the spectral curves, also known as spectral signatures, of HSIs and has been widely applied in critical fields such as satellite remote sensing. Developing domestically manufactured miniaturized satellite has become one of Taiwan's most significant projects in recent years. FORMOSAT-8, the first high-resolution optical remote sensing satellite under the “Third Phase of the National Space Science and Technology Development Long-term Plan,” is scheduled for launch in October 2025. This highlights the primary objective of Taiwan's space program, which is the independent development of lightweight, cost-effective, and high-performance satellites. Given the substance identifiability of HSIs, researchers can analyze satellite images captured from space to understand the composition and changes of substances on the Earth's surface. Consequently, developing a miniaturized satellite capable of capturing HSIs could greatly benefit environmental monitoring and disaster prevention efforts.

However, HSIs record hundreds of spectral bands, resulting in significantly larger file sizes compared to RGB images. This poses a major challenge for the storage and transmission of hyperspectral data. Traditional approaches address this issue through compressed sensing techniques to achieve highly compressed files. Existing hyperspectral compressed sensing (HCS) methods typically rely on hardware components such as spectral splitter (SS), digital micromirror device (DMD) array, and cylindrical lens (CL). Among these, the DMD, used for implementing random projections, is a bulky component that is unsuitable for miniaturized satellite development. Recently developed multifunctional metamaterials have shown the ability to achieve spectral splitting and focusing using a single nanoscale metasurface, replacing the need for SS and CL. Based on this concept, this dissertation proposes an alladdition HCS method, which utilizes only deterministic addition operators at the encoding stage to align with the characteristics of multifunctional metamaterials, thereby meeting the requirements of miniaturized satellite development. However, due to the extreme simplification of the encoding process, the decoding stage presents significant challenges. To address this, a convex optimization (CO) criterion was designed based on the self-similarity characteristic of HSIs. This self-similarity criterion is formulated as a convex function, and experimental results validate that even at extremely low sampling rates, the proposed decoding approach can accurately reconstruct HSIs. Additionally, this dissertation establishes a convex analysis framework based on the John ellipsoid (JE) to ensure the algorithm's ability to accurately recover HSIs under conditions of extremely low data purity.

Given the aforementioned substance identifiability of HSIs, which enable the detection of substance composition and changes, hyperspectral satellite remote sensing images can provide more accurate predictions for land monitoring and disaster prevention. For example, hyperspectral anomaly detection can be applied to military surveillance or rare mineral detection. Hyperspectral change detection (HCD) has gained increasing attention in recent years due to its contributions to surface monitoring and precision agriculture, particularly methods relying on CO or deep learning (DL). However, DL-based methods typically require big data to learn image patterns, which are difficult to obtain in the hyperspectral domain, and the manual annotation process is highly labor-intensive and expensive. On the other hand, CO criteria often require complex mathematical formulations for regularization terms to effectively address the ill-posed nature of hyperspectral inverse problems. To address these challenges, this dissertation proposes a HCD algorithm based on the convex deep (CODE) theory for satellite inverse imaging, a technique that has been recognized with the FutureTech Award by the National Science and Technology Council (NSTC), Taiwan. By integrating CO criterion with a graph neural network (GNN), the proposed convex deep HCD (CODEHCD) algorithm enables semi-supervised HCD for scenarios with extremely a low labeling rate. The proposed CODE-HCD algorithm combines a convex Q-quadratic norm regularizer tailored to the characteristics of HSIs. This regularizer is constructed with a highly simple mathematical structure, facilitating the algorithm’s high computational efficiency. Under the scenario of an extremely low labeling rate, the proposed CODE-HCD algorithm demonstrates superior performance over state-of-the-art benchmark HCD methods on real hyperspectral datasets, verifying its effectiveness.

In recent years, quantum computing has rapidly emerged as a prominent field, garnering widespread attention from the research community. Studies on quantum entanglement were further recognized with the 2022 Nobel Prize in Physics. Quantum deep networks (QUEENs), designed based on parameterized quantum circuits, have recently been developed to address diverse problems such as drug response prediction, health detection, and image classification. Therefore, in addition to the previously discussed combination of CO and DL, this dissertation proposes that introducing theoretically novel quantum information into traditional DL methods can further enhance the final change detection results. As a pioneering effort, this dissertation introduces QUEENs into GNN-based HCD frameworks to improve change detection accuracy. Unlike traditional convolutional neural networks (CNNs) or GNNs that extract affine-computing features, QUEENs capture unitary-computing features, providing additional and theoretically novel information for final classification. In the proposed QUEEN-empowered GNN (QUEEN-G), the graph feature learning module leverages the graph structure of bitemporal HSIs at the superpixel level, while the quantum feature learning module extracts quantum features at the pixel level, which serves as a complement to the graph feature learning module by preserving detailed pixel-level spatial information that may be lost at the superpixel level. For the final classification stage, a quantum classifier is designed to collaborate with a traditional fully connected classifier for enhancing the detection performance. Experiments on real hyperspectral datasets demonstrate that the proposed QUEEN-G significantly outperforms existing HCD methods, validating that the introduction of quantum unitary features enhances classification accuracy.

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