2022/05/08 by Meng Ding, Xiao Fu, Ding, Meng +3 · 2 citations
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #Medical Image Segmentation Techniques #Remote-Sensing Image Classification #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2205.03798
openalex publication_date 2022/05/08 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28
The block-term tensor decomposition model with multilinear rank-(Lr,Lr,1) terms (or, the "LL1 tensor decomposition" in short) offers a valuable alternative for hyperspectral unmixing (HU) under the linear mixture model. Particularly, the LL1 decomposition ensures the endmember/abundance identifiability in scenarios where such guarantees are not supported by the classic matrix factorization (MF) approaches. However, existing LL1-based HU algorithms use a three-factor parameterization of the tensor (i.e., the hyperspectral image cube), which leads to a number of challenges including high per-iteration complexity, slow convergence, and difficulties in incorporating structural prior information. This work puts forth an LL1 tensor decomposition-based HU algorithm that uses a constrained two-factor re-parameterization of the tensor data. As a consequence, a two-block alternating gradient projection (GP)-based LL1 algorithm is proposed for HU. With carefully designed projection solvers, the GP algorithm enjoys a relatively low per-iteration complexity. Like in MF-based HU, the factors under our parameterization correspond to the endmembers and abundances. Thus, the proposed framework is natural to incorporate physics-motivated priors that arise in HU. The proposed algorithm often attains orders-of-magnitude speedup and substantial HU performance gains compared to the existing three-factor parameterization-based HU algorithms.