Recent advancements in deep learning, particularly in medical imaging, have significantly propelled the progress of healthcare systems. However, examining the robustness of medical images against adversarial attacks is crucial due to their real-world applications and profound impact on individuals' health. These attacks can result in misclassifications in disease diagnosis, potentially leading to severe consequences. Numerous studies have explored both the implementation of adversarial attacks on medical images and the development of defense mechanisms against these threats, highlighting the vulnerabilities of deep neural networks to such adversarial activities. In this study, we investigate adversarial attacks on images associated with Alzheimer's disease and propose a defensive method to counteract these attacks. Specifically, we examine adversarial attacks that employ frequency domain transformations on Alzheimer's disease images, along with other well-known adversarial attacks. Our approach utilizes a convolutional neural network (CNN)-based autoencoder architecture in conjunction with the two-dimensional Fourier transform of images for detection purposes. The simulation results demonstrate that our detection and defense mechanism effectively mitigates several adversarial attacks, thereby enhancing the robustness of deep neural networks against such vulnerabilities.