Robust estimation of noise strength in Magnetic Resonance Images (MRIs) is a task of great importance due to its extensive applications in image post-processing techniques. Many noise estimation algorithms have been proposed in the past to retrieve noise characteristics of the magnitude image. These algorithms rely on either the spatial or transform domain information of the image. In this research article, we propose a noise estimation algorithm that utilizes a hybrid Discrete Wavelet Transform (DWT) and edge information suppression based algorithm to estimate the strength of noise in magnitude MR images. The wavelet coefficients corresponding to spatial domain edges are eliminated using a down-sampled complement of the Sobel edge map. The distribution of average noise energy in spatial and transform domain which follows Parseval's theorem is utilized for calculating the initial noise estimate. Further, the robustness of the proposed algorithm is enhanced using Feedforward Neural Network. The proposed algorithm is observed to be computationally fast and accurate. Results on synthetic and clinical T1- and T2-w brain MRIs following Gaussian or Rician distribution show better performance than the existing benchmark algorithms over a wide range of input noise. © 2021 Elsevier Ltd