The aim of this work is to develop a Computer-Aided-Brain-Diagnosis (CABD) system that can determine if a brain scan shows signs of Alzheimer's disease. The method utilizes Magnetic Resonance Imaging (MRI) for classification with several feature extraction techniques. MRI is a non-invasive procedure, widely adopted in hospitals to examine cognitive abnormalities. Images are acquired using the T2 imaging sequence. The paradigm consists of a series of quantitative techniques: filtering, feature extraction, Student's t-test based feature selection, and k-Nearest Neighbor (KNN) based classification. Additionally, a comparative analysis is done by implementing other feature extraction procedures that are described in the literature. Our findings suggest that the Shearlet Transform (ST) feature extraction technique offers improved results for Alzheimer's diagnosis as compared to alternative methods. The proposed CABD tool with the ST + KNN technique provided accuracy of 94.54%, precision of 88.33%, sensitivity of 96.30% and specificity of 93.64%. Furthermore, this tool also offered an accuracy, precision, sensitivity and specificity of 98.48%, 100%, 96.97% and 100%, respectively, with the benchmark MRI database.