Image fusion has become a commonly utilized technology for boosting the medical information in brain images. Magnetic resonance imaging (MRI) depicts the morphology of the brain tissue, it has great spatial resolution but lacks functional information. Positron emission tomography (PET) displays the brain with great function but low spatial resolution. Hence, a fusion of the two imaging techniques will help the neurologist to accurately identify Alzheimer's disease progression. In this paper, a new fusion method that combines two transformation approaches, triangular intensity-hue-saturation (IHS) and discrete wavelet transform (DWT), is introduced. DWT is applied to the intensity component of the PET image and the smoothed version of the MRI image. Wavelet coefficients are fused using a specific fusion rule for the low and high-frequency bands. Inverse DWT is applied to obtain a new intensity component, and the gray version is subtracted from the new intensity. The fused image is obtained by applying the inverse triangular IHS. For evaluation, quantitative measurement and statistical analysis are determined. The proposed method achieved discrepancy, average gradient, mutual information, and overall fusion performance of 7.0529, 5.3879, 0.6550, and 1.6651 respectively. The final results reveal that the proposed method achieved the highest performance compared with existing methods.