## 3 Proposed Methodology
### Data Preprocessing
\(\leftarrow\) M_smoothed // Final processed MRI data
```
**Algorithm 2** MRI Dataset Preprocessing

As far as the MRI data preprocessing is concerned, in the very first attempt, image quality enhancement was performed on each MRI, which included correcting for spatial distortions, aligning sequential images, and enhancing contrast to improve the clarity of the brain structures. After this, the skull stripping process [38] removes the non-brain tissues, like the skull and skin, from the MRI images, which are crucial for focusing the analysis on brain tissue. To standardize the intensity of the MRI images to a common scale, an adopted normalization process [38] has been applied that helps in comparing images across different subjects. However, spatial normalization aligns the images to a standard brain template and ensures that anatomical regions are consistently located across different subjects. In the end, a Gaussian filter [38] is applied to reduce noise and improve the signal-to-noise ratio. ### Feature Extraction

Feature extraction is essential because it simplifies and condenses the vast and complex information provided by each modality into a more manageable and informative set of data. MRI scans offer detailed structural images of the brain, highlighting aspects such as brain volume and cortical thickness, while EEG recordings capture the brain's dynamic electrical activity over time. By extracting key features from both MRI and EEG data, the hybrid model can leverage the complementary strengths of structural and functional brain insights. This synergy enhances the model's performance. Moreover, feature extraction reduces the dimensionality of the data, which is crucial for effectively training machine learning algorithms without losing critical information. It helps in avoiding issues like overfitting and makes the computational process more efficient. In essence, feature extraction is a critical step in merging these two diverse data streams, paving the way for a more robust and accurate diagnosis of Parkinson's Disease. #### 3.3.1 EEG Feature Extraction

The Flexible Analytic Wavelet Transform (FAWT) [39] is particularly effective for EEG feature extraction compared to other statistical methods due to its adaptive time-frequency analysis capabilities. Unlike the Fourier Transform, which only provides frequency information, or standard wavelet transforms with fixed time-frequency resolution, FAWT dynamically adjusts its analysis to match the local characteristics of EEG signals. Moreover, FAWT effectively handles non-stationary EEG signals, providing more accurate and meaningful feature extraction compared to methods that assume stationary signals. The range of features extracted, including instantaneous frequency and amplitude, provides a richer set of data for classifiers in machine learning models, potentially enhancing the accuracy of PD diagnosis. In this research, For a particular EEG signal \(X(t)\), where t represents time. The continuous wavelet transform (CWT) of \(X(t)\) is given by the following equation:

\[Wx(a,b)=\int x(t)\psi a,b(t)dt \tag{1}\]

Here, \(\psi_{\text{a,b}}\)(t) is the wavelet function, a is the scale factor, and b is the translation factor. The wavelet function \(\psi_{\text{a,b}}\)(t) is defined as follows:

\[\psi a,b(t)=\frac{1}{\sqrt{a}}\psi\binom{t-b}{a} \tag{2}\]

\(\psi\)(t) is the mother wavelet, a prototype for generating other wavelets. The adaptation of FAWT to the standard wavelet transform gives better signal characteristics. It performs this by allowing the wavelet function to change its shape (i.e., become more flexible) according to the signal's local features. Mathematically, this adaptability can be incorporated by introducing a parameter \(\theta\)(t) that modifies the wavelet function based on the signal's local properties.