Endmember Learning with K-Means through SCD Model in Hyperspectral Scene Reconstructions

Abstract

This paper proposes a simple yet effective method for improving the efficiency of sparse coding dictionary learning (DL) with an implication of enhancing the ultimate usefulness of compressive sensing (CS) technology for practical applications, such as in hyperspectral imaging (HSI) scene reconstruction. CS is the technique which allows sparse signals to be decomposed into a sparse representation “a” of a dictionary D u . The goodness of the learnt dictionary has direct impacts on the quality of the end results, e.g., in the HSI scene reconstructions. This paper proposes the construction of a concise and comprehensive dictionary by using the cluster centres of the input dataset, and then a greedy approach is adopted to learn all elements within this dictionary. The proposed method consists of an unsupervised clustering algorithm (K-Means), and it is then coupled with an advanced sparse coding dictionary (SCD) method such as the basis pursuit algorithm (orthogonal matching pursuit, OMP) for the dictionary learning. The effectiveness of the proposed K-Means Sparse Coding Dictionary (KMSCD) is illustrated through the reconstructions of several publicly available HSI scenes. The results have shown that the proposed KMSCD achieves ~40% greater accuracy, 5 times faster convergence and is twice as robust as that of the classic Spare Coding Dictionary (C-SCD) method that adopts random sampling of data for the dictionary learning. Over the five data sets that have been employed in this study, it is seen that the proposed KMSCD is capable of reconstructing these scenes with mean accuracies of approximately 20−500% better than all competing algorithms adopted in this work. Furthermore, the reconstruction efficiency of trace materials in the scene has been assessed: it is shown that the KMSCD is capable of recovering ~12% better than that of the C-SCD. These results suggest that the proposed DL using a simple clustering method for the construction of the dictionary has been shown to enhance the scene reconstruction substantially. When the proposed KMSCD is incorporated with the Fast non-negative orthogonal matching pursuit (FNNOMP) to constrain the maximum number of materials to coexist in a pixel to four, experiments have shown that it achieves approximately ten times better than that constrained by using the widely employed TMM algorithm. This may suggest that the proposed DL method using KMSCD and together with the FNNOMP will be more suitable to be the material allocation module of HSI scene simulators like the CameoSim package.

Keywords

• sparse coding
• dictionary learning
• unmixing
• hyperspectral scene reconstruction
• hyperspectral
• multispectral
• k-means