# The Fusion of MRI and CT Medical Images Using Variational Mode Decomposition
## 3 **Scanners**  
Image fusion can be categorized into spatial and transform domain techniques [10]. In spatial domain methods, the fusion takes place between the pixels of the source images directly. The maximum, minimum, average, weighted average and PCA are examples of the spatial domain fusion methods, which are easy to implement and computationally efficient. Direct pixel-based fusion methods use a weighted pixel of input images to form a fused image [11]. The activity level of the pixels determines these weights. In the literature, various machine learning methods such as neural networks and support vector machines (SVM) are also used to select the pixels with the highest activity [12; 13]. In [14], an iterative block-level fusion method is proposed. First, the source images are decomposed into small square blocks, and PCA is computed on those blocks. Next, weights are found using the average of the PCA components. Finally, a maximum average mutual information fusion rule is employed for the final blending of input images. In [15], a pixel-level image fusion method is proposed using PCA. Here, the first PCA components from both the input images are multiplied individually, and those weighted images are added for fusion. However, these methods might exhibit spatial color, information loss, and brightness distortions [16; 17]. Image fusion methods based on the transform domain techniques are receiving much consideration [18]. Pyramid [19], wavelet [20], and multi-resolution singular value decomposition (MSVD) are examples of traditional methods [21] in this category. However, transform domain fusion methods have a few drawbacks [18]. For example, most pyramid methods suffer from blocking artifacts and a loss of source information, even producing artifacts around edges [22]. Wavelets suffer shift sensitivity, poor directionality, an absence of phase information, poor performance at edges and texture regions, and produce artifacts around edges because of the shift-variant nature [22]. Despite the reliable quantification results, MSVD fusion methods might result in poor visual quality [23]. To address the issues mentioned above, other transform domain fusion techniques such as A Trous wavelet transform (ATWT), curvelet transform (CVT), and ridgelet transform are suggested in [24]. These methods provide better results concerning the visual  
Figure 1: Illustration of the classification of different medical brain imaging modalities. aspect, preserving spatial and spectral information. Nevertheless, these techniques suffer from artifacts around the edges in the fused image [25]. In [26], a new pixel-level image fusion approach using convolutional sparsity-based morphological component analysis (CS-MCA) is introduced. This method achieves sparse representation by combining MCA and sparse convolutional representation into the unified optimization method. This approach might suffer from a spatial consistency problem, resulting in the degradation of spatial details [27]. An NSST-based fusion scheme is proposed in [28].This approach used a blend of NSST with weighted local energy (WLE) and a weighted sum of eight- neighborhood-based modified Laplacian (WSEML) to integrate MRI and CT images. However, this method is a non-adaptive approach. A summary of different types of image fusion methods, their advantages and drawbacks are tabulated in Table 1.  
An adaptive transform-domain fusion technique might provide a better solution to the challenges mentioned above. In these fusion approaches, the basis function of the transform technique depends on the source image's characteristics. With the help of adaptive wavelets, the image's crucial features can be highlighted, which helps in the fusion process. Hence, adaptive wavelets turned out to be a preferable representation compared to standard wavelets. Similar works based on VMD decomposition-based techniques can be found in [35; 36].