Multiscale Spectral–Spatial Unmixing Network With Boltzmann-Inspired Adaptive Temperature

Hyperspectral unmixing (HU) aims to decompose mixed pixels into endmembers with corresponding abundances. However, while several existing convolutional autoencoder methods usually use fixed convolutional kernels, making it difficult to capture the global context. In addition, due to the huge solution space of unmixing, existing methods usually adopt a consistent sparsity constraint and lack adaptivity. To overcome the above limitations, we propose a multi-scale spectral-spatial unmixing network with Boltzmann-inspired adaptive temperature (MSSTNet). First, the spectral attention block (SEAB) and spatial attention block (SAAB) are designed to capture the dependence between spectral bands and enhance spatial feature extraction, respectively. These are integrated into multi-scale spectral-spatial attention blocks (MSSABs) with varying convolution kernels, which enable the network to focus on local and global image structures at the same time. Moreover, inspired by the Boltzmann distribution, we introduce a temperature matrix T in the softmax activation to regulate the output sparsity, similar to the effect of temperature on the particle energy distribution. The Euclidean distance and cosine distance between adjacent pixels are used to construct the similarity matrix to capture the spectral difference caused by the amplitude change, and then the T matrix is constructed. The softmax layer is divided by the resulting T matrix, so as to impose sparsity constraints of varying strengths on different areas. Evaluations on simulated and real datasets demonstrate the proposed approach's superiority over state-of-the-art methods. The code is publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/RSstudy/MSSTNet</uri>.