高光譜解混旨在將高光譜影像分解為一組具有代表性的端元光譜及其對應的豐度圖，並滿足非負性與豐度總和為一等具有物理意義的限制條件。此問題在遙測、環境監測及影像分析等領域具有廣泛的應用。然而，真實高光譜資料常常存在遺失或不可靠的觀測值。傳統方法通常先透過插補等前處理方式補齊缺失資料，再進行後續分析。本篇文章不採用缺失值插補，而是直接將取樣遮罩納入具限制條件的遮罩最小平方目標函數中。針對所形成的非凸最佳化問題，我們提出一種交替投影梯度下降法進行求解。在每次迭代中，利用投影算子確保更新後的解始終滿足限制條件。

Hyperspectral unmixing aims to decompose a hyperspectral image into a set of representative endmember spectra and abundance maps, subject to physically meaningful constraints such as nonnegativity and the sum-to-one condition. This problem has important applications in remote sensing, environmental monitoring, and image analysis. However, real hyperspectral data often contain missing or unreliable measurements. Conventional approaches typically perform imputation as a preprocessing step to handle missing data. Instead of imputing these missing values, this work directly incorporates a sampling mask into a constrained masked least-squares objective function. We solve the resulting nonconvex problem using an alternating projected gradient descent method. At each iteration, projection operators are employed to ensure that the solution remains within the feasible set to satisfy the required physical constraints.

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