## 3 CAD Systems of Brain Disorders Based on Multimodal Fusion
### Multimodal Fusion Techniques Proposed in Literature: Description, Advantages and Disadvantages
#### 3.2.2 Frequency Domain Techniques  
In signal processing, the discrete transformations represent in most cases linear transformations of signals between discrete domains, such as between discrete time and discrete frequency. In the case of medical signal processing, it provides a sparse representation of smooth images in pieces. The most used techniques based on this type of transformation are discrete cosine transform (DCT), curvelet transformation (CT) and wavelet transform. * **Discrete Cosine Transform:** The DCT described in many works [241, 242, 243, 244] makes it possible to perform a discrete transformation which provides a division into N \(\times\) N pixel blocks by operating on each block. As a result, it generates N coefficients which are quantified to reduce their magnitude. It reduces complexity by breaking down images into series of waveforms. It can be used for real applications. However, the merged image is not of good quality if the block size is less than \(8\times 8\) or equivalent to the size of the image itself. * **Curvelet Transform:** The CT used in many works [247, 248, 249, 250, 251, 252] is a means of characterizing curved shapes in images. The concept is to segment the complete image into small overlapping tiles, then the ridgelet transformation is performed on each tile. The curvelet transform provides fairly clear edges because the curvelets are very anisotropic. They are also adjustable to properly represent or improve the edges on several scales. However curvelet do not have time invariance. * **Wavelet Transform:** In wavelet-based fusion, used in different studies [253, 254, 255, 256, 257, 258], once the image is decomposed by wavelet transformation, a multi-scale composite representation is constructed by selecting the salient wavelet coefficients. The most applied techniques based on wavelet transform are discrete wavelet transform (DWT), stationary wavelet transform (SWT) and Kekre's Wavelet transform (KWT). * **Stationary wavelet transform:** SWT [250, 259], allowing a discrete transformation, begins by providing from the original image, information relating to the edges of levels 1 and 2. Then, a measurement of spatial frequency is used to merge the two contour images, and in order to obtain a complete contour image. From level 2 of the decomposition, the SWT offers satisfactory results. Its stationary property guarantees temporal invariance, which is obtained by suppressing the process of subsampling, but SWT is more complex in terms of computation and processing, which consume time. Moreover, although it performs better at separate discontinuities, its effectiveness degrades at the edges and textured locals. - **[PERSON]'s wavelet transform:** The KWT [260], which allows a discrete transformation to be carried out, is applicable for images of different sizes. Its results are generally good. In addition, different variations of KWT are simply generable, only by changing the size of the basic Kekre's transformation. However, this type of transformation is not explored enough. Intensive research is; therefore, desired to bring out its weaknesses. - **Hybrid Approach-Based Fusion:** To achieve a merger, some researchers have used hybrid methods which allow two or more methods to be combined in a single scheme. Below some of them are presented. - **Hybrid SWT and curvelet transform:** With the hybrid SWT/CT technique [261] we first decompose the input images by applying the SWT in order to obtain the high
- and low-frequency components. Thereafter, a curvelet transform is applied to merge the low-frequency components. The principle is based on the segmentation of the whole image into small superimposed mosaics, then for each mosaic, we apply the transformation into crest. Components with high frequencies are merged according to the largest coefficients of absolute value. The final fusion image is finally obtained using the inverse SWT transformation.