# Prediction of Glioma Grades Using Deep Learning with Wavelet Radionic Features
## 3 Materials and Methods
### Wavelet Transform  
Wavelet transform is an important algorithm used in the analysis of MR images [35]. The wavelet transform was applied by discrete wavelet transform with a total of eight filters with four high pass and four low pass. The discrete wavelet transform works on the principle of sub-band coding. Due to its various features and characteristics, it is a good technique for image processing by using mother wavelets. Wavelet reconstruction is a process in which useful image features are selected that extract an image's radiomic features from each sub-part and then detect the discriminatory aspects of these data in visual analysis. This model creates a geometric localization exchange with narrow high-pass and wide low-pass filters and is widely preferred [36]. In previous studies [37; 38], 2D wavelets were used for filtering images, but in the present work, 3D wavelet transform is used for extracting radiomic features. The fact that brain tumors have thin tissue also reflects positively on the classification results of high-pass filters. Radiomic features can be determined on the original brain tumor image or using the filter option. There are many filters used to achieve radiomic features. These include wavelet and Laplacian of Gauss (LoG) filters, and many filters, including square root, logarithm, square, and exponential filters. In addition to the original image, we also used wavelet-transformed images in extracting texture features. In our 3D wavelet technique (x, y, z), sub-volumes are created on three-dimensional spatial axes, resulting in an eight-piece image volume. The 3D volume is filtered on the x-axis and a high-pass and low-pass image is obtained, H (x, y, z) and L (x, y, z). This process is then repeated on the y-axis and four sub-bands (HL, HH, LL, LH) appear. On the third axis (z), these four volumes are filtered into a total of eight sub-bands. Thus, high-pass filters (HLL, HLH, HHL, HHH) and low-pass filters (LLL, LLH, LHL, LHH) are formed. Often, fine texture is obtained from details (i.e., high-pass filters), while coarse texture is obtained from approximate values (i.e., low-pass filters). The decomposition process is a view called wavelet analysis filterbank, which is performed by wrapping the mother wavelets in a single down-sampling step in each direction [39]. We tried various  
Figure 3: 3D tumor segmentation procedures for Grade II brain tumor in 3D Slicer with the ROI identified (**a**), application of GrowCut (**b**), and 3D visualization of the tumor (**c**).  
filter families for wavelet decomposition including Daubechies, Symlets, Coiflets, Haar. Haar is a square function made up of two coefficients, a mother wavelet with both orthogonality and symmetry properties. The biggest drawback is that it is not smooth [40]. Daubechies wavelets are developed by looking at Haar wavelets. It has a larger number of coefficients, but they are not synchronous [41]. Symmetrical main wavelets such as Symlets, Biorthogonal were developed over time. The common feature of these wavelets is that although they have less verticality, they have high smoothness [42]. The Daubechies Wavelet transform is implemented through a series of decompositions, such as the Haar transform. The only difference is that the filter length is more than two. Therefore, it is more local and smoother [43]. Coiflets wavelets developed based on Daubechies [44]. Although there are many mother wavelets, the dependence of the radiomic prognosis prediction to maternal wavelet in terms of patient survival is still not investigated [45]. Daubechies wavelet filter is used in the study. Feature extraction process was started to determine the wavelet filter, which achieved high accuracy in the classification of Grade II and Grade III tumors.