Classification and Analysis of Parkinson’s Disease Based on Gabor and Wavelet Filters

The flow chart for fMRI Data analytics using Gabor and wavelet filters of PD patients is given in Figure 1.

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Figure 1. Flowchart of data analysis

The data set was collected from the Parkinson's progression markers initiative (PPMI) [11]. The data set comprised 10 healthy patients including 6 males and 4 females, and 10 PD patients, including 5 males and 5 females for resting state fMRI. The scan amounts for a period of 504 seconds with a TR of 2.4 seconds for each patient. The age group of subjects was 40-75 years.

For the analysis of PPMI data set, the following software platforms are used: MATLAB 7.10.0, SPM8, NIFTII for Image View, and REST. There are advantages for these tools:

MATLAB 7.10.0:

1. High-level programming language: Easy to learn and use, with extensive toolboxes and libraries.

2. Rapid prototyping: Quick development and testing of algorithms and models.

3. Large community: Access to a vast user community and resources.

SPM8 (Statistical Parametric Mapping):

1. Advanced image analysis: SPM8 provides a wide range of tools for image processing, statistical analysis, and visualization.

2. Neuroimaging expertise: Developed by neuroimaging experts, ensuring accuracy and relevance.

3. Integration with MATLAB: Seamless integration with MATLAB, leveraging its strengths.

NIfTI (Neuroimaging Informatics Technology Initiative):

1. Standardized format: NIfTI provides a standardized format for neuroimaging data, ensuring compatibility and exchangeability.

2. Easy data sharing: Facilitates collaboration and data sharing among researchers.

3. Wide adoption: Widely adopted in the neuroimaging community, ensuring compatibility with various tools.

REST (RESTing-state fMRI analysis toolkit):

1. Specialized toolkit: REST is specifically designed for resting-state fMRI analysis, providing tailored tools and methods.

2. Efficient analysis: REST offers efficient and automated analysis pipelines for large datasets.

3. Advanced metrics: Calculates advanced metrics, such as functional connectivity and network measures.

The selection of MATLAB 7.10.0, SPM8, NIfTI, and REST was driven by their specialized functionalities and widespread use in neuroimaging research. MATLAB offers a versatile programming environment with extensive libraries for rapid data processing and algorithm development. SPM8, integrated with MATLAB, is a robust tool for statistical and spatial analysis of neuroimaging data, designed by experts to ensure precision and reliability. NIfTI ensures data standardization and compatibility across platforms, enabling seamless sharing and collaboration. REST, tailored for resting-state fMRI analysis, provides efficient pipelines for advanced connectivity and network metrics. Together, these tools form a comprehensive framework for accurate and efficient analysis of the PPMI dataset.

2.1 Features extraction

The following features are used to analyze the PD patients and normal persons:

• Amplitude of Low Frequency Fluctuations (ALFF): The activity of the brain in the rest state is reflected by low frequency oscillations. The ALFF feature is the collective power contained in the low frequency band of 0.01Hz to 0.08 Hz. It helps to perceive the abnormally behaving regions in the rest state of the brain. Physiological significance: ALFF reflects spontaneous neural activity by measuring the amplitude of low-frequency oscillations, which indicates localized brain activity in resting-state conditions.
• Fractional ALFF (fALFF): The ALFF feature depends on the physiological noise. A ratio of the total power in the 0.01Hz to 0.08 Hz frequency band of to the total power in the 0 Hz to 0.25 Hz frequency band is obtained, so as to immunize ALFF from noise. This new measure is called fALFF feature [12]. Physiological significance: fALFF is a normalized measure of ALFF that reduces noise effects, highlighting physiologically relevant low-frequency oscillations and improving sensitivity to brain abnormalities.
• Regional Homogeneity (ReHo): The ReHo feature relates the synchronization in time series of voxels of fMRI and their nearest neighbor’s. The Kendall’s coefficient of concordance (KCC) is determined for the clusters of 27 voxels on the pre-processed fMRI images [13, 14]. Physiological significance: ReHo captures the synchronization of neural activity in adjacent voxels, reflecting localized functional coherence and abnormalities in regional connectivity.
• Functional Connectivity: It identifies the network of brain regions that show spontaneous co-activation. The functional connectivity of a region of interest (ROI) can be evaluated by measuring the time averaged course of ROI and by determining its correlation with time series of various regions. Physiological significance: It identifies coordinated activity across different brain regions, indicating the integration and communication within neural networks, which is crucial for understanding disrupted connectivity in PD patients.

A Gabor filter is used for texture analysis in image processing, an attempt to identify objects from obscure backgrounds. Its impulse response is defined by a 2D- plane sinusoidal wave multiplied by a Gabor envelope function [15].

$\begin{aligned} & g(x, y ; \lambda, \theta, \psi, \sigma, \gamma)=exp \left(-\frac{x^{\prime 2}+\gamma^{\prime 2} y^2}{2 \sigma^2}\right) exp \left(i\left(2 \pi \frac{x^{\prime}}{\lambda}+\psi\right)\right)\end{aligned}$

The real part of impulse response of Gabor filter is used for analysis and is given below:

$x^{\prime}=x \cos \theta+y \sin \theta, y^{\prime}=-x \sin \theta+y \cos \theta$

• σ: The standard deviation of the Gaussian envelope and controls the spatial extent of the filter. Larger values of σ result in a broader filter, capturing more global features, while smaller values focus on finer, localized details. In our study, σ is related to the bandwidth (b) and wavelength (λ) to balance spatial and frequency resolution.
• ψ: The phase offset determines the symmetry of the filter. A phase offset of 0 creates a symmetric filter (cosine-like), while π/2 produces an antisymmetric filter (sine-like). The values are chosen based on the dominant structural features in the region of interest (ROI).
• γ: The aspect ratio defines the ratio of the Gaussian envelope along the x- and y-axes. Smaller values elongate the filter, making it more sensitive to edge-like structures, while values closer to 1 produce circularly symmetric filters. For our analysis, γ=0.5 is selected to account for anisotropic structures.
• λ: The wavelength controls the scale of the sinusoidal wave, determining the frequency sensitivity of the filter. By analyzing the average diameter of the ROI, appropriate scales are selected as {0.8 * average diameter, average diameter, 1.2 * average diameter}.
• θ: The orientation defines the angle of the sinusoidal wave, allowing the detection of features at specific directions. In this study, orientations are set as π/6, π/4, π/3, π/2, 2π/3, and 3π/4 to comprehensively capture patterns in multiple directions.

σ is related to bandwidth (b) and wavelength (λ) of Gabor filters as:

$\frac{\sigma}{\lambda}=\frac{1}{\pi} \sqrt{\frac{\ln 2 \sigma}{2 \lambda}}=\frac{1}{\pi} \sqrt{\frac{\ln 2}{2}} \frac{\left\{2^b+1\right\}\left\{2^b+1\right\}}{\left\{2^b-1\right\}\left\{2^b-1\right\}}$

In analysis, bandwidth (b) =1, aspect ratio (γ) =0.5 and phase shift calculated after analyzing the average diameter of the region of interest as {0.8*average diameter, average diameter, 1.2*average diameter}. The total permutations of wavelength and orientations give us 18 Gabor filters as shown in Figure 2 [16]. These parameters are carefully selected to balance precision, scale, and orientation sensitivity for effective texture analysis in image processing.

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Figure 2. Gabor filter in the frequency domain

The filtered images are normalized within [-1, 1] range [17, 18]. The threshold is calculated by the equitation given below:

Threshold = Mean – 0.5 × Standard Deviation

It is a modified form of Niblack’s method. Niblack’s method uses mean and standard deviation of pixels in a windowed area of image to calculate local threshold and segments a single image, while in the proposed method, mean and standard deviation are computed over many images.

2.2 Wavelet Analysis

Wavelets are primarily used to measure energy of certain frequencies of the signal in different intervals of time. The range of frequencies can be varied as per size of the time interval considered and thus give wavelet analysis resolution in both frequency and time.as shown in Figure 3.

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Figure 3. Wavelet filter decomposition

In this proposed work, the Haar wavelet is used for image decomposition. The Haar wavelet is chosen due to its simplicity, computational efficiency, and effectiveness in capturing local features, such as edges and discontinuities, within the fMRI images. Its step-like function allows for rapid calculations, making it ideal for processing large datasets. Additionally, the Haar wavelet offers good data compression by producing sparse coefficients while retaining significant information, which is essential for efficient feature extraction.

In a 2D image, the transformation is applied successively over rows and columns of the image. In MATLAB, the function ‘wavedec2’ finds the wavelet transform of an image using ‘non-standard decomposition’ for desired levels of decomposition and for specified mother wavelet.

The mother wavelet used is ‘HAAR wavelet’ [19]. Its mother wavelet function ψ(t) can be described as:

$\varphi(t)=\left\{\begin{array}{cl}1 & 0 \leq t<\frac{1}{2} \\ -1 & \frac{1}{2} \leq t<1 \\ 0 & \text { otherwise }\end{array}\right.$

The scaling function ψ(t) is represented as

$\Phi(t)= \begin{cases}1 & 0 \leq t<1 \\ 0 & \text { otherwise }\end{cases}$

In this work, the wavelet coefficients till decomposition of level 4 are obtained. The coefficients thus obtained are used to reconstruct images using MATLAB function ‘wrcoef2’ for level 4 decomposition to calculate the threshold parameters.

Also, reconstruction of an image at level 3 decomposition is done to provide a smoothed feature image, to which the threshold is applied.

2.3 Classification methods

The classifiers used in the study are Naïve Bayes, Logistic Regression, SVM based on Sequential Minimal Optimization (SMO), and Decision Stump. These classifiers were chosen based on their distinct working principles and suitability for the classification task. The models were validated by a 10-fold cross-validation scheme, with the classification operations carried out using the WEKA software. A total of 504 attributes were generated to classify between healthy individuals and PD patients [20, 21].

1. Naïve Bayes Classifier

The Naïve Bayes classifier is based on Bayes’ theorem, assuming that the features are conditionally independent. It calculates the probability of each class given the feature values and selects the class with the highest probability. This model is particularly useful when dealing with large datasets with independent features and works well for problems with categorical data. However, its assumption of feature independence may not always hold in complex datasets.

2. Logistic Regression Classifier

Logistic Regression is a statistical model used for binary classification tasks. It models the probability of a class as a logistic function of the input features. Logistic regression is widely used in scenarios where the relationship between the independent variables and the dependent variable is expected to be linear. It is effective when the classes are linearly separable and is interpretable, making it a good choice for many classification problems in health and social sciences.

3. SVM based on Sequential Minimal Optimization (SMO)

Support Vector Machine (SVM) is a powerful classifier that separates classes using a hyperplane in a high-dimensional space. The Sequential Minimal Optimization (SMO) is an optimization algorithm used for training SVMs. It is particularly efficient for large datasets and works well with both linear and non-linear problems using different kernel functions. SVM is effective when there is a clear margin of separation between classes, and its performance can be improved by choosing appropriate kernels and tuning hyperparameters.

4. Decision Stump Classifier

A Decision Stump is a simple machine learning model that combines the benefits of decision trees and stumps. Here’s how it works:

• Root Node: The dataset is fed into the root node.
• Feature Selection: The algorithm selects the best feature (attribute) to split the data.
• Threshold: A threshold value is chosen for the selected feature.
• Left Child: Samples with values below the threshold go to the left child node.
• Right Child: Samples with values above the threshold go to the right child node.
• Class Label: Each child node is assigned a class label (prediction).

The algorithm iteratively selects the best feature and threshold to split the data. The process continues until a stopping criterion is met (e.g., maximum depth or minimum samples per node). The final prediction is made by combining the class labels from the child nodes. The Decision Stump classifier is suitable for simple datasets or as a weak learner in ensemble models like AdaBoost.

2.4 Computational steps

1. Image Standardization and Elimination of Deviations

The images obtained from PPMI are classified as PD patients or normal individuals. The SPM8 tool is used in image processing to standardize the scans and eliminate any deviations. This step is crucial to ensure that the data are comparable across subjects, thus minimizing potential biases caused by inconsistencies in the imaging data.

2. Slice Timing Correction

The Slice Timing Correction tool is used to correct for acquisition time differences within the same brain scan. This step ensures that the functional data from different slices are synchronized, which is important for maintaining the temporal accuracy of the brain activity measurements.

3. Realignment

The Realign utility corrects for patient movement during the scanning process. This step helps eliminate motion artifacts that could distort the data, thereby enhancing the quality and reliability of the images for subsequent analysis.

4. Co-registration

The Co-register utility aligns the functional image with the anatomical image (mean realigned image). This ensures that functional data are mapped onto the structural brain images accurately, facilitating precise localization of brain activity. Co-registration is necessary for comparing brain regions in a consistent anatomical space.

5. Segmentation

The Segment utility is applied to segment various tissue structures (such as gray matter, white matter, and CSF) from the obtained co-registered image. Segmentation is a critical step that helps isolate specific brain regions for further analysis, improving the accuracy of functional data interpretation.

6. Normalization

The Normalize utility [22] transforms the images into a standard brain template. This step ensures that images from different subjects are aligned in a common space, eliminating anatomical variations. Normalization is essential for comparing the data across subjects in a group study.

7. Smoothing

The Smooth utility is used to smooth the time series of each voxel [22]. This process helps reduce noise and improve the signal-to-noise ratio, making the functional activity more detectable and reliable.

8. Feature Extraction (ALFF, fALFF, ReHo)

ALFF, fALFF, and ReHo feature images are calculated from the preprocessed images using the REST toolbox. These features capture key brain activity characteristics, such as low-frequency oscillations and regional synchronization, which are important for differentiating PD patients from healthy controls.

9. Co-registration to AAL Brain Atlas

The feature images are co-registered to the AAL brain Atlas to ensure that the extracted ROIs correspond appropriately to the regions of interest (ROIs) [23], defined in the anatomical space. This step guarantees meaningful comparisons across subjects and allows for accurate identification of specific brain regions associated with PD.

10. Gabor Filtering

The ROIs in the cerebellum are filtered using 18 Gabor filters. This step enhances the texture of the image by applying a set of frequency- and orientation-sensitive filters. The use of Gabor filtering helps identify spatial features related to brain activity, which can be crucial for distinguishing between PD patients and healthy controls. The images are normalized within the range of -1 to 1 for consistency.

11. Thresholding

The filtered images are thresholded to isolate the most significant brain regions and remove irrelevant or noisy data. The thresholding step ensures that only the most informative features are retained for further analysis, allowing the model to focus on key patterns associated with PD.

12. Shape-Based Parameter Calculation

Shape-based parameters, such as perimeter, equivalent diameter, area, minor axis length, major axis length, eccentricity, and orientation, are calculated using MATLAB functions. These parameters provide quantitative measurements of the shape and size of brain structures, which are essential for distinguishing between PD patients and healthy controls.

13. Wavelet Filtering

The ROIs are filtered using wavelet functions in MATLAB. This step allows for the analysis of the signal across different frequency bands, enhancing the feature extraction process by highlighting important frequency components related to PD. The images are normalized within the range of -1 to 1, and thresholding is applied to the filtered images.

14. Reclassification Using New Set of Parameters

The shape-based parameters calculated in step 12 are reclassified using the same Decision Table and Decision Stump classifiers as in step 6. The process is repeated for the new set of parameters to evaluate the performance of the classification model with the wavelet-enhanced features.

15. Comparison of Results

The results from steps 13 and 14 are compared to assess the effectiveness of wavelet filtering in improving the classification accuracy between PD patients and healthy controls.