Alzheimer’s disease detection in functional images using 2D Gabor wavelet analysis P. Padilla, J.M. Go ´rriz, J. Ramı ´rez, R. Chaves, F. Segovia, I. Alvarez, D. Salas-Gonza ´lez, M. Lo ´pez and C.G. Puntonet Presented is a Gabor wavelet (GW) based analysis of functional brain images by integrating the 2D GW representation of the images for image classification applied to early diagnosis of Alzheimer’s disease. The 2D GW representation of the brain images is processed by means of a principal component analysis (PCA) for feature extrac- tion and support vector machines (SVMs) for image classification. The proposed method yields up to 96% classification accuracy with 100% sensitivity, thus becoming an accurate method for image classification. Comparison between the conventional PCA plus SVM method and the proposed method is also provided. In addition, the proposed method with Gabor wavelets increases the outcomes of other methods based on voxel as features (VAF), PCA, and so on. Introduction: The 2D Gabor wavelet (GW) analysis has been widely applied in face recognition and detection owing to the robustness of GW features against local distortions, variance of illumination, and so on [1, 2]. Taking advantage of its use in face recognition and its proper outcomes, this GW approach can be used in other image studies, such as functional images. The proper study of functional brain images is of great importance in the early detection of brain anomalies and diseases, as they provide valuable clinical information regarding regional cerebral blood flow or metabolic activity in the brain [3–5]. In this Letter, a 2D GW analysis approach is applied to single photon emission computed tomography (SPECT), for early diag- nosis of Alzheimer’s disease (AD). GWs and GW feature representation: GWs were introduced in image processing owing to their biological relevance and computational prop- erties [1]. The 2D GWs are typically defined as follows: w u,v (¯ z)= 1 2p ‖ ¯ k u,v ‖ 2 s 2 exp −‖ ¯ k u,v ‖ 2 ((x) 2 + y 2 ) 2s 2   exp(j ¯ k u,v ¯ z) (1) ¯ K u,v = 2pf u exp(ju v ) (2) f u =  2 √  2 √ u , u = 0, ... , U − 1 (3) u v = v V p, v = 0, ... , V − 1 (4) where f u and u v define the orientation and scale of the GWs, f max is the maximum frequency, and ¯ k u,v define the wave vector. Hence, a set of 2D wavelets can be obtained, for different scales (u) and orientations (v), forming a set of GWs. One of the most interesting properties of the GW set remains in the frequency domain behaviour of each wavelet of the set: the wavelet actuates as a filter that selects a specific area of the 2D frequency grid of an image, rotating around the centre (zero fre- quency) with v, and at a distance from it according to u, as it can be observed in Fig. 1. Fig. 1 Example set of 16 GWs a Real part b Spectral domain behaviour (amplitude) In typical face recognition studies, a 40-GW set (U ¼ 5, V ¼ 8) is applied for the representation of each image [6]. In this work, a 16- GW set (U ¼ 2, V ¼ 8) was demonstrated enough to derive relevant results, as it will be detailed. In this study, considering that each patient’s data is given by a set of transaxial slices (I), the GW set is applied to each slice (I m ) of patient ‘p’, for p ¼ 1...N, where N is the number of patients of the database. The resulting images (G u,v ) are the convolution of the image with all the wavelets of the set. They can be also computed in terms of direct and inverse fast Fourier transform (FFT). G u,v ( ¯ Z)= I m w u,v ( ¯ Z)= IFFT (FFT (I m )∗ FFT (w u,v ( ¯ Z))) (5) The resulting images (G) of each slice are linearly combined to obtain a new set of GW-based images (IG), which are taken as input data for principal component analysis (PCA) application and further analysis. The general scheme applied is shown in Fig. 2. IG m ( ¯ Z)= ∑ u−v j=o G j ( ¯ Z) (6) set of N gabor-image slices for patient IFFT m=1 m=u ν FFT(image n ) FFT(Gabor m ) set of N image slices for one patient set of M=u ν 2D Gabor wavelets slice n of patient Fig. 2 Flowchart for GW representation of each image slice of patient PCA feature extraction and support vector machine (SVM) classification: In our approach the feature space dimension given by all the IGs is reduced by applying the PCA transformation [3]. PCA is a standard technique for extracting the most significant features from a dataset, frequently used to reduce the raw data to a subset of features that contains the largest amount of variance. It is based on a linear trans- formation acting on a zero mean dataset, that diagonalises its covariance matrix. The resulting eigenvectors are a new set of uncorrelated vari- ables, the variance of which is represented by its eigenvalues, where the first n values concentrate the most discriminant values. Previous to PCA, to select the most discriminant features of the GW- based images (IG) for the PCA transformation, the Fisher discriminant ratio (FDR) is applied, which is characterised by its separation ability as shown in [4, 5]: FDR = (m 1 − m 2 ) 2 s 2 1 + s 2 2 (7) where m i and s i 2 denote the ith class mean value and variance of the input feature, respectively. The resulting reduced feature vector obtained from the different GW-based images is finally taken for classification. The classification is achieved through SVMs, which separates a given set of binary labelled training data with a hyperplane that is maximally distant from the two classes (known as the maximal margin hyperplane) [4, 7]. When no linear separation of the training data is possible, SVM can work in combination with kernel techniques so that the hyperplane defining the SVM corresponds to a nonlinear decision boundary [7]. Evaluation experiments: In this study, baseline SPECT data from 97 participants were collected from the ‘Virgen de las Nieves’ hospital in Granada (Spain). The patients were injected with a gamma emitting 99m Tc-ECD radiopharmaceutical and the SPECT raw data was acquired by a three head gamma camera Picker Prism 3000. The images were initially labelled by experienced physicians of the same hospital, within two classes: NORMAL and AD. In total, the database consists of 97 patients: 41 NORMAL and 56 AD. ELECTRONICS LETTERS 15th April 2010 Vol. 46 No. 8 Authorized licensed use limited to: UNIVERSIDAD DE GRANADA. Downloaded on April 23,2010 at 20:58:55 UTC from IEEE Xplore. Restrictions apply.