**6. Conclusions**

We proposed the local abundance regularizer algorithm for the sparse unmixing problem to improve the accuracy of abundance estimation. By imposing the term to state-of-the-art unmixing algorithms, our algorithm incorporates both spatial and abundance correlation by using the low-rankness of the abundance. We implemented the nuclear norm to the local abundance matrix, which defines the local region not only in the spatial, but also in the abundance dimension. The algorithm was run at certain SNR levels for several simulated data sets, which represent the conditions with and without pure pixels, and for two real data sets. The experimental results indicate that our proposed algorithm performs better than SUnSAL-TV and yields better results than the other state-of-the-art algorithms. Relevant future research will be concerned with exploitation of the low-rankness of abundance for overlapping local regions.

**Acknowledgments:** This work was supported in part by JSPS Grants-in-Aid (24560473), and MIC SCOPE (172310003). The first author acknowledges support from the Indonesia Endowment Fund for Education (LPDP), Ministry of Finance, The Republic of Indonesia.

**Author Contributions:** All the authors significantly contributed to different phases of this manuscript including the preparation, analysis, review and revision. The research plan and mathematical formulation were developed together. Mia Rizkinia implemented the algorithm, prepared the data, and executed the experiments. Masahiro Okuda supervised the research.

**Conflicts of Interest:** The authors declare no conflict of interest.
