高光譜解混（Hyperspectral unmixing, HSU）是高光譜影像（HSI）分析中的核心任務，旨在將每個像素的光譜分解為一組端元（endmembers）及其對應的豐度係數（abundance）。隨著高光譜資料的規模與複雜度不斷增加，新興的資料處理方式如量子計算因其在加速遙測分析方面的潛力而受到越來越多關注。2022 年諾貝爾物理學獎頒發給量子科學，更進一步突顯了其推動遙測技術發展的前景。然而，即使在最先進的量子計算機中，可用的糾纏量子位元（qubits）數量仍極為有限，這使得在量子硬體上直接處理具有龐大資料量的高光譜影像，在技術上存在可行性疑慮。
為應對這些限制，本研究提出一種雙分支架構，結合經典深度學習與量子計算，執行解混任務。第一分支採用 Transformer 網路，以捕捉非局部的光譜–空間依賴關係並提取長距離上下文特徵。第二分支引入量子卷積神經網（QuantumConvolutional Neural Network, QCNN），利用分層且具對數深度的量子電路架構，高效提取局部特徵。該互補設計結合了 Transformer 在建模全域關係上的能力與 QCNN對細微局部模式的敏感性。為增強魯棒性，研究中引入量子補值電路（QuantumImputation Circuit, QIC），透過學習特徵空間中的內部相關性來恢復缺失或受損的光譜特徵。最終將兩個分支的輸出融合，生成完整的解混結果。實驗結果顯示，所提出的方法在多個標準高光譜數據集上，相較於現有基準方法，在多項定量指標中均取得更優異的表現。

Hyperspectral unmixing (HSU) is a fundamental task in hyperspectral image analysis. This process seeks to analyze every pixel by identifying the pure spectral components it contains and estimating how much each component contributes to the observed mixture. The scale and complexity of hyperspectral data have grown rapidly. Consequently, emerging computational paradigms such as quantum computing are attracting increasing attention for their potential to accelerate remote sensing analytics. Recognition of quantum information science's significance was reaffirmed when it became the focus of the 2022 Nobel Prize in Physics. Despite this progress, the scarcity of entangled qubits continues to limit the computational capacity of current quantum hardware. This limitation raises significant concerns about the feasibility of directly processing hyperspectral images. These images are characterized by massive data volumes and remain challenging for current quantum hardware.
To address these constraints, this work presents a dual-branch architecture that integrates classical deep learning with quantum computation to jointly perform unmixing and missing data imputation. The first branch uses a transformer network to capture non-local spatial–spectral dependencies and extract long-range contextual features. The second branch introduces a quantum convolutional neural network (QCNN) with a hierarchical, logarithmicdepth quantum circuit architecture. This design is tailored for efficient local feature extraction. The complementary structure combines the capability of the transformer in modeling global relationships with the sensitivity of QCNN to fine-grained patterns. To enhance robustness, a quantum imputation circuit (QIC) is incorporated. The QIC restores missing or corrupted spectral components by exploiting internal correlations within the learned feature space. The outputs of both branches are fused to produce the final unmixing result. Experiments on standard hyperspectral datasets demonstrate that the proposed approach performs better than existing methods and baselines on multiple quantitative metrics.

[1] M. J. Montag and H. Stephani, “Hyperspectral unmixing from incomplete and noisy data,” Journal of Imaging, vol. 2, no. 1, p. 7, 2016.
[2] (2022) The Nobel Prize in Physics. [Online]. Accessed: 2025-10-27. [Online]. Available: https://www.nobelprize.org/prizes/physics/2022/summary/
[3] C. Sanavio, S. Tibaldi, E. Tignone, and E. Ercolessi, “Quantum circuit for imputation of missing data,”IEEE Transactions on Quantum Engineering, vol. 5, p. 2500712, 2024.
[4] C.-H. Lin and Y.-Y. Chen, “Hyperqueen: Hyperspectral quantum deep network for image restoration,”IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1–20, 2023.
[5] J. Preskill, “Quantum computing in the nisq era and beyond,” Quantum, vol. 2, p. 79, 2018.
[6] S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, “Noise-induced barren plateaus in variational quantum algorithms,” Nature communications, vol. 12, no. 1, p. 6961, 2021.
[7] S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, “Hybrid quantum-classical algorithms and quantum error mitigation,” Journal of the Physical Society of Japan, vol. 90, no. 3, p. 032001, 2021.
[8] C.-H. Lin and J.-T. Lin, “Prime: Blind multispectral unmixing using virtual quantum prism and convex geometry,” IEEE Transactions on Geoscience and Remote Sensing, vol. 63, p. 5615715, 2025.
[9] C.-H. Lin and S.-S. Young, “Hyperking: Quantum-classical generative adversarial networks for hyperspectral image restoration,” IEEE Transactions on Geoscience and Remote Sensing, vol. 63, p. 5512119, 2025.
[10] W. Gao, J. Yang, Y. Zhang, Y. Akoudad, and J. Chen, “Ssaf-net: A spatial-spectral adaptive fusion network for hyperspectral unmixing with endmember variability,” IEEE Transactions on Geoscience and Remote Sensing, vol. 63, p. Article 5506015, 2025.
[11] P. Ghosh, S. K. Roy, B. Koirala, B. Rasti, and P. Scheunders, “Hyperspectral unmixing using transformer network,” IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1–16, 2022.
[12] M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, “A generative modeling approach for benchmarking and training shallow quantum circuits,” npj Quantum information, vol. 5, no. 1, p. 45, 2019.
[13] J. M. Bioucas-Dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches,” IEEE journal of selected topics in applied earth observations and remote sensing, vol. 5, no. 2, pp. 354–379, 2012.
[14] N. Keshava and J. F. Mustard, “Spectral unmixing,” IEEE signal processing magazine, vol. 19, no. 1, pp.44–57, 2002.
[15] M. H. Hansen and B. Yu, “Model selection and the principle of minimum description length,” Journal of the american statistical association, vol. 96, no. 454, pp. 746–774, 2001.
[16] R. Heylen, D. Burazerovic, and P. Scheunders, “Fully constrained least squares spectral unmixing by simplex projection,” IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 11, pp. 4112–4122, 2011.
[17] C.-H. Lin, C.-Y. Chi, Y.-H. Wang, and T.-H. Chan, “A fast hyperplane-based minimum-volume enclosing simplex algorithm for blind hyperspectral unmixing,” IEEE Transactions on Signal Processing, vol. 64, no. 8, pp. 1946–1961, 2016.
[18] C.-H. Lin and J. M. Bioucas-Dias, “Nonnegative blind source separation for ill-conditioned mixtures via john ellipsoid,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 5, pp. 2209–2223, 2020.
[19] B. Rasti, B. Koirala, P. Scheunders, and P. Ghamisi, “Undip: Hyperspectral unmixing using deep image prior,” IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1–15, 2021.
[20] Y. Yu, Y. Ma, X. Mei, F. Fan, J. Huang, and H. Li, “Multi-stage convolutional autoencoder network for hyperspectral unmixing,” International Journal of Applied Earth Observation and Geoinformation, vol. 113, p. 102981, 2022.