**1. Introduction**

White matter hyperintensities (WMHs) are commonly observed on T2W or FLAIR brain MR images of elderly people and related to various geriatric disorders including cerebrovascular diseases, cardiovascular diseases, dementia, and psychiatric disorders [1]. According to [2], WMHs are brain lesions that generally show up as brighter areas and can be visualized by T2W and FLAIR MRI sequences. It is also referred to as Leukoaraiosis and is often found in computed tomography (CT) or MRI of older patients. It is a marker of small-vessel vascular disease. In clinical practice, it is indicative of cognitive and emotional dysfunction, particularly in the ageing population. Its initial discovery was observed in the late 1980s by Hachinski and colleagues [2] who described WMH as patchy low attenuation in the periventricular and deep white matter. Since then, detection of WMH has received considerable interest. Although a supervised method may produce better results, it requires human intervention which is very time-consuming and also suffer the issues of intra- and inter-observer variation [3]. Accordingly, segmentation of WMH has been recently directed to semi-unsupervised and automatic methods which rely on computer assisted tools to help diagnosis to avoid human subjective interpretation. Most importantly, such computer assisted diagnosis can be further used to quantify WMH and calculate its volume [3–7]. However, it also comes with two major issues. One is that most works are based on T1 weighted (T1W), T2W and photon density (PD) or FLAIR images to produce spatial statistics to segmen<sup>t</sup> WMH. The other is selection of an appropriate threshold, which ultimately determines the detection results of WMH. Generally, such automatic method is not fully automatic but rather semi-unsupervised because it requires adaptively adjusting threshold values by visual inspection. This paper takes a quite different approach to designing a joint spectral–spatial method that takes advantage of spectral properties provided by MR image sequences to perform subvoxel detection in conjunction with a Gaussian spatial filter to capture spatial contextual information surrounding the WMH detected voxels.

One of the strengths of magnetic resonance imaging (MRI) is its ability in imaging structures of soft tissues. Because an MR image is collected by specifically designed image sequences such as T1W, T2W or PD, it can be considered as a multispectral image [8]. Hyperspectral imaging has recently emerged as an advanced technique in remote sensing to deal with many issues that cannot be resolved by multispectral imaging, specifically, subpixel target detection and mixed pixel classification [9]. Its applications to MRI classification have been also explored in [10–15]. However, it seems that using the concept of hyperspectral imaging techniques for WMH detection in brain MRI has not been investigated. This paper presents a new application of hyperspectral imaging in WMH detection of MR brain images.

To expand capability of multispectral imaging to hyperspectral imaging in data analysis, it suffers from insufficient band dimensionality. To resolve this dilemma, a nonlinear band expansion (NBE) process was previously proposed in [16] which used nonlinear functions to produce a new set of nonlinear band images that can be incorporated into the original images to create a new data set. As more such nonlinearly generated images are included, the resulting multispectral image has become a hyperspectral image. In this case, we can take advantage of the well-known hyperspectral subpixel target detection technique, called constrained energy minimization (CEM) [9,17–19], to detect the lesion of interest [20]. However, the nonlinearly expanded band images by NBE used in [20] can only capture spectral information nonlinearly but not spatial information. As noted above, effectively detecting the boundary of a lesion may also require spatial information due to the shape of the boundary that is closely related to spatial correlation.

This paper develops a novel NBE approach that expands NBE [20] to produce new band images that can capture not only nonlinear spectral information but also spatial information. Since CEM is a pixel-based technique and does not take into account spatial information. In order for CEM to capture spatial information an iterative version of CEM, to be called Iterative CEM (ICEM), is developed for this purpose. Its idea is to apply a Gaussian filter to a CEM-detection map so that the Gaussian-filtered CEM detection map will contain spatial information to be further fed back as a new band image to

create a new image cube. The same process of operating CEM on this new data cube is repeated over again in an iterative manner via feedback loops. To terminate ICEM an automatic stopping rule is also designed, which uses Otsu's method [21] to threshold the Gaussian-filtered CEM detection map obtained at each iteration as a binary image. If the two consecutive binary images agree within an error threshold measured by Dice similarity index (DSI) [22], then ICEM is terminated and the final Otsu's thresholded binary image is the desired lesion detection map.

There are several main contributions derived from NBE-ICEM. One is using NBE to create new band images to make a multispectral image a hyperspectral image. Another is including Gaussian filters to capture spatial information. Thirdly, such Gaussian-filtered spatial information is further fed back to be included in the data cube being processed as new images to account for spatial information of detected WMH lesions. Fourthly, the spatial information included in CEM is increased via repeated feedback loop in an iterative manner. That is, the more feedbacks the more spatial information to be included in the data cube for better boundary detection. Fifthly, Otsu's method is introduced to automatically terminate the iterative process carried out by ICEM. Finally, once the ICEM is terminated, the resulting Otsu's thresholded binary image is the desired final lesion detection result.
