Post-acquisition denoising of magnetic resonance (MR) images is an important step to improve any quantitative measurement of the acquired data. In this paper, assuming a Rician noise model, a new filtering method based on the linear minimum mean square error (LMMSE) estimation is introduced, which employs the self-similarity property of the MR data to restore the noise-less signal. This method takes into account the structural characteristics of images and the Bayesian mean square error (Bmse) of the estimator to address the denoising problem. In general, a twofold data processing approach is developed; first, the noisy MR data is processed using a patch-based L(2)-norm similarity measure to provide the primary set of samples required for the estimation process. Afterwards, the Bmse of the estimator is derived as the optimization function to analyze the pre-selected samples and minimize the error between the estimated and the underlying signal. Compared to the LMMSE method and also its recently proposed SNR-adapted realization (SNLMMSE), the optimized way of choosing the samples together with the automatic adjustment of the filtering parameters lead to a more robust estimation performance with our approach. Experimental results show the competitive performance of the proposed method in comparison with related state-of-the-art methods.