Endmember extraction and abundance estimation algorithm based on double-compressed sampling

Abstract

Based on double-compressed sampling, a hyperspectral spectral unmixing algorithm (SU_DCS) is proposed, which could directly complete the endmember extraction and abundance estimation. On the basis of the linear mixed model (LMM), we designed spatial and spectral sampling matrices, obtained spatial and spectral measurement data, and constructed a joint unmixing model containing endmember and abundance information. By using operator separation and Lagrangian multiplier algorithm, the endmember matrix, abundance matrix and remixing image can be quickly obtained by matrix operation. The parameters of the unmixing algorithm, including regularization parameter, convergence threshold and spatial sampling rate, are determined using synthetic simulated hyperspectral data. The proposed algorithm is applied to two kinds of real hyperspectral data, with or without ground truth, in order to verify the effectiveness and reliability of the algorithm. Firstly, we provide the performance of the algorithm on real datasets without ground truth. Compared with algorithm VCA_FCLS and algorithm CPPCA_VCA_FCLS, the endmember spectral curve extracted by the proposed SU_DCS is almost consistent with that obtained by VCA_FCLS, and is more smooth than that of obtained by CPPCA_VCA_FCLS. Additionally, the abundance estimation map estimated by the SU_DCS has consistency with the results obtained by VCA_FCLS. Moreover, the proposed SU_DCS has higher peak signal-to-noise ratio (PSNR) for remixing images with higher computational efficiency. Secondly, we provide the performance of the proposed algorithm on four real datasets with ground truth, including dataset Cuprite, dataset Samson, dataset Jasper and dataset Urban. We provide the results of endmember extraction and abundance estimation from the compressed data under different sampling rate conditions. The extracted endmember maintains good consistency with the true spectral curves, and the estimated abundance map can also maintain good spatial consistency with the ground truth. The comparison results with other four comparative algorithms also indicate that the proposed algorithm can obtain relatively accurate endmembers and abundance information from compressed data, the reliability and validity of the proposed algorithm have been proved. In summary, the main innovation of the proposed algorithm is that it can extract endmembers and estimate abundance with high accuracy from a small amount of measurement data.