## 1 Introduction  
In the fields of research in medical imaging and diagnostic radiology, computer-aided diagnosis (CAD) has had major interest and development during the last two decades [1; 2; 3; 4; 5; 6; 7; 8; 9]. The objective of this technology is to support radiologists using computer systems in their interpretation of brain images and in the diagnosis of brain diseases. The CAD system provides a second opinion, it makes it possible to analyze medical images thanks to its techniques of pattern recognition and machine learning. This alleviates the fatigue of the radiologist and the burden of the workload, due to the overloaded data. As a result, this technology has the ability to improve diagnostic consistency and accuracy in order to decrease the rate of false negatives, including estimating the extent of the disease. Alzheimer's disease (AD) is one of the brain disorders that is extremely difficult to identify. It is linked to structural atrophy, pathological amyloid deposits and metabolic alterations in the brain [10]. This neurodegenerative disease is the cause of 60% to 70% of cases of dementia [11], which generally begins slowly and worsens over time. It gradually deteriorates cognitive and behavioral capacities and the causes of this disease remain unknown [1], with the exception of certain hereditary forms. A CAD system can help to perform an early diagnosis which is crucial for mitigating the effects of AD. In fact, several diagnostic tools and approaches have been developed in order to provide measures that make it possible to detect early changes during subclinical periods, clarify the underlying mechanisms and inform neuro-protective interventions aimed at slowing down the extent of the disease. As a result, the rising costs are reduced for families and society. In addition to this, magnetic resonance imaging (MRI) [12] has been used for a long time to eliminate several sources of brain disorders. This technology provides a detailed description of the anatomy including brain pathology with spatial resolution and soft tissue contrast. It makes it possible to study the structural and chemical correlates of a disease, which improves understanding of the mechanisms involved [13]. In AD, MRI adds a positive predictive value to the diagnosis [5]; solid experiments have shown that changes in brain structure can be detected with structural MRI in elderly subjects with mild cognitive impairment (MCI) [14]. In this context, patients with MCI to be converted to AD are characterized by significant atrophy of the medial temporal lobes, posterior cingula, lateral and parietal temporal cortex compared to control subjects or stationary MCIs. However, the benefits of structural MRI are limited and several problems have arisen as a result. The MRI went from two-dimensional (2D) to three-dimensional (3D) modality, which caused the neuro-radiologist to rapidly increase the data to be analyzed. Added to this, the resolution and the signal-to-noise ratio (SNR) have become higher [15]. In this regard, the problem of developing new CAD tools, such as data fusion techniques, has been widely addressed in recent years in order to reduce the workload, paying particular attention to the study with a non-invasive way of the existing connectivity between anatomical and functional imaging. This process of data fusion in a multimodal environment makes it possible to generate a more informative merged image which helps diagnosis and forecasting, by combining complementary and redundant information coming from the MRI and from functional modalities, such as, computerized tomography (CT), single photon emission tomography (SPECT) and positron emission tomography (PET), which are characterized by different objectives in radiology. As a result, the resulting fusion image is better suited for visual perception and image processing and analysis tasks [16; 17], providing more condensed and relevant information. In addition, instead of storing several multi-source images, a single merged image is taken into account, which reduces memory costs.