Hyperspectral unmixing (HSU) aims to separate each pixel into its constituent endmembers and estimate their corresponding abundance fractions. This work presents an algorithm-unrolling-based network for the HSU task, named the 3D Convolutional Sparse Coding Network (3D-CSCNet), built upon a 3D CSC model. Unlike existing unrolling-based networks, our 3D-CSCNet is designed within the powerful autoencoder (AE) framework. Specifically, to solve the 3D CSC problem, we propose a 3D CSC block (3D-CSCB) derived through deep algorithm unrolling. Given a hyperspectral image (HSI), 3D-CSCNet employs the 3D-CSCB to estimate the abundance matrix. The use of 3D CSC enables joint learning of spectral and spatial relationships in the 3D HSI data cube. The estimated abundance matrix is then passed to the AE decoder to reconstruct the HSI, and the decoder weights are extracted as the endmember matrix. Additionally, we propose a projected simplex volume maximization (PSVM) algorithm for endmember estimation, and the resulting endmembers are used to initialize the decoder weights of 3D-CSCNet. Extensive experiments on three real datasets and one simulated dataset with three different signal-to-noise ratio (SNR) levels demonstrate that our 3D-CSCNet outperforms state-of-the-art methods.

翻译：高光谱解混旨在将每个像素分解为其组成端元并估计相应的丰度分数。本研究提出了一种基于算法展开的网络用于高光谱解混任务，称为三维卷积稀疏编码网络，该网络建立在三维卷积稀疏编码模型之上。与现有基于展开的网络不同，我们的三维卷积稀疏编码网络设计于强大的自编码器框架内。具体而言，为解决三维卷积稀疏编码问题，我们通过深度算法展开提出了三维卷积稀疏编码块。给定高光谱图像，三维卷积稀疏编码网络利用该块估计丰度矩阵。采用三维卷积稀疏编码能够联合学习三维高光谱数据立方体中的光谱与空间关系。估计的丰度矩阵随后传递至自编码器解码器以重建高光谱图像，解码器权重被提取为端元矩阵。此外，我们提出了投影单纯形体积最大化算法用于端元估计，所得端元用于初始化三维卷积稀疏编码网络的解码器权重。在三个真实数据集和一个模拟数据集（包含三种不同信噪比水平）上的大量实验表明，我们的三维卷积稀疏编码网络性能优于现有最先进方法。