Magnetic resonance images (MRI) reconstructed with parallel MRI (pMRI) techniques generally have spatially varying (non-stationary) noise levels. However, most of the existing MRI denoising methods rely on a stationary noise model and end with suboptimal results when applied to pMRI images. To address this problem, this paper proposes an improved nonlocal maximum likelihood (NLML) estimation method. In the proposed method, a noise map is computed with a robust noise estimator before the ML estimation of the underlying signal. Also, a similarity measure based on local frequency descriptors (LFD) is introduced to find the nonlocal samples for ML estimation. The experiments on simulated and real magnetic resonance (MR) data demonstrate that the proposed technique has superior filtering capabilities in terms of subjective and quantitative assessments when compared with other state-of-the-art methods.