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Recently, the Alzheimer's disease (AD), a neurological illness has affected roughly 70 percent of the world's estimated 46 million dementia cases. Though there's no treatment for Alzheimer's disease, timely screening as well as correct definition of the illness's course can help patients and families lead better lives. using standardized mental status evaluations, the Alzheimer's disease is presently evaluated. These standardized mental status evaluations are frequently supplemented with pricey neuroimaging images and invasive laboratory investigations, making the process time-consuming and extremely expensive. Despite this, electroencephalography (EEG) had also developed as a noninvasive effective way in the recent decades, for early AD diagnosis, vying with neuroimaging technologies like MRI and PET. Recently, the deep learning has been widely utilized for AD diagnosis. Even though AD diagnosis has improved dramatically, early detection and precise diagnosis remain a major challenge. It is critical to review the existing literature works on AD diagnosis before developing an alternative and successful solution for early AD diagnosis. These studies will help pave the way for future researchers. As a result, a modest and comprehensive analysis in the field of AD diagnosis is carried out in this research work. The most interesting recent research papers (from 2019 to 2022) have been gathered and analyzed in a variety of ways, including different datasets (MRI, EEG, and fMRI) collected for diagnosis, different techniques used for “pre-processing, segmentation, feature extraction, feature selection, and classification (Machine Learning/ Deep Learning)”, as well. In addition, the accuracy, sensitivity, and precision of each work are depicted. Furthermore, the present hurdles in AD detection is discussed, which will serve as a foundation for sustainable researchers.