**5. Conclusions**

In conclusion, this paper develops a novel approach, called NBE-ICEM, for WMH lesions detection in MR brain images. It is derived from a hyperspectral imaging-based subpixel target detection method (CEM), but is rather different from CEM in two aspects. One is an introduction of NBE into CEM, which expands the original MR images by including nonlinearly correlated band images generated by NBE to make a multispectral MR image into a hyperspectral MR image since CEM is a hyperspectral imaging technique. The other is the development of an iterative version of CEM, ICEM, which can feed back spatial information captured by Gaussian filters in an iterative manner. More specifically, it applies a Gaussian filter to CEM-detection maps to produce Gaussian-filtered CEM-detected abundance fractional maps that can be further fed back iteratively to form a new set of MR image cubes which will be used a new data set to be re-processed by CEM to improve WMH

lesions detection performance. ICEM can be considered as a joint spectral–spatial filter. The more iterations carried out by ICEM, the more spatial information captured. The work on NBE-ICEM presents a potential and promising technique for WMH lesions detection. It is our belief that there would be new applications of NBE-ICEM to MRI ye<sup>t</sup> to explore in the future, specifically, partial volume estimation for specific tissues of interest.

**Acknowledgments:** The work of this paper was supported by grants from Taichung Veterans General Hospital (TCVGH-1047315C, and TCVGH-1057315C), and grants from Ministry of Science and Technology (MOST 104-2221-E-075A-002, and MOST-105-2221-E-075A-001). The work of L. Wang is supported by the Fundamental Research Funds for Central Universities under Grant JB150508 and the 111 Project (B17035). The works of Y. Wang and M. Song are supported by Fundamental Research Funds for Central Universities (3132016028 and 3132016331) and National Nature Science Foundation of China (61601077 and 61301228), respectively. The work of C.-I Chang is supported by the Fundamental Research Funds for Central Universities under Grant 3132016331.

**Author Contributions:** H.-M.C., J.-W.C., and C.-C.C.C. conceived and designed the experiments; L.W., C.Y., and Y.W. performed the experiments; H.C.W., M.S., and B.X. analyzed the data; C.-I.C., H.-M.C., J.-W.C., and C.-C.C.C. contributed reagents/materials/analysis tools; C.-I C. wrote the paper.

**Conflicts of Interest:** All authors have declared no conflict of interest.
