Neuroimaging the default mode network (DMN) in resting state has been of significant interest for investigating pathological conditions as resting state data are less affected by the variability in the subject's performance and movement-related artefacts in the electromagnetic field which are often issues in event-related activation experiments. An issue to be considered with resting state data is the very low amplitude of the activation patterns which are not induced by any stimulation or stimulus paradigm. Though, many studies have suggested that amplitude of low frequency fluctuation (ALFF) analysis is suitable for resting state functional magnetic resonance imaging (fMRI) data analysis, the low signal-to-noise-ratio (SNR) of acquired neuroimaging data poses a significant problem in the accurate analysis of the same. In this work, a Gaussian Mixture Model (GMM) method to suppress the noise during data pre-processing before ALFF is applied (GMM-ALFF) is proposed, where the optimum numbers of Gaussian distributions are fitted to the data using the Bayesian information criterion (BIC). The method has been tested with artificial data as well as real resting state fMRI data collected from Alzheimer's disease patients with different levels of added noise. Improvement of as much as 40% for artificial datasets and at least 3% for real datasets (p <0.05) have been observed when applying the proposed GMM approach prior to the analysis with the existing ALFF approach.