**4. Discussion**

This paper is believed to be the first work ever reported in the literature to attempt to use a hyperspectral subpixel detection, NBE-ICEM, to detect WMHs on MRI. As demonstrated in Tables 2 and 3 and Figures 5–10 and Figures 12–14 the synthetic and real image experiments confirm significant improvements using NBE-ICEM over the LST method in WMH detection.

In comparison between CBEP-CEM1 and CBEP-CEM2, we found from Tables 2 and 3 in the synthetic image experiments that, when the noise level is low (0%, 1%, 3%), CBEP-ICEM1 using a smaller Gaussian window performed better than CBEP-ICEM2 using a larger Gaussian window. However, when the noise level is high (5%, 7%, 9%), the conclusion is reversed, i.e., CBEP-ICEM2 performed better than CBEP-ICEM1. It is also interesting to note that CBEP-ICEM1 performed very poorly when noise level reached 7% and above and even worse than LST. Tables 2 and 3 also shown that it was noise not INU that had an impact on lesion detection. On the other hand, CBEP-ICEM2 generally performed well regardless of noise level if DSI value was set to at least or above 0.8 compared to LST whose DSI values did not go beyond 0.8. The synthetic image experiments suggested that CBEP-ICEM2 was a better technique due to its robustness to noise level and ability in WMH detection.

In addition, based on the results of real image experiments from Figures 12–14, there are three interesting findings. Firstly, the number of iterations carried out by CBEP-ICEM is always two for all three Fazekas grades. Secondly, in Figure 12c, CBEP-ICEM2 and LST performed similarly but quite different in Figures 13c and 14c, where the areas of lesions detected by LST were much smaller than CBEP-ICEM2. Thirdly, the iterative images produced in Figures 12b, 13b and 14b by CBEP-ICEM2 showed that including spatial information captured by Gaussian-filtered CEM detection images did improve lesion detection, particularly edge and boundary pixels.

This paper makes several main contributions to WMH lesions detection in MR brain images. First, it develops NBE to resolve two issues arising in WMH detection, insufficient spectral dimensionality and linear non-separability problem. NBE plays a similar role that kernels play in pattern classification such as support vector machine (SVM). Second, it introduces Gaussian filters to be included in CEM to expand capability of CEM in capturing spatial information surrounding CEM-detected WMH lesions. Third, the real-valued CEM-detection abundance fractional maps provide soft decisions for visual inspection. Fourth, Otsu's method is incorporated in ICEM to produce thresholded binary maps as hard decisions that show WMH lesions detection. This resolves the main issue encountered in LST. Fifth, the feedbacks of Gaussian filtered CEM detection abundance fractional maps allow CEM to perform better detection in WMH lesions when spatial information of lesions is crucial, specifically, their boundaries. Finally, an automatic stopping rule is particularly designed to determine how much spatial information is needed for CEM to perform its best in detection of WMH lesions.
