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Although promising for studying the microstructure of in vivo tissues, the performance and the potentiality of diffusion tensor magnetic resonance imaging are hampered by the presence of high-level noise in diffusion weighted (DW) images. This paper proposes a novel smoothing approach, called the nonstationarity adaptive filtering, which estimates the intensity of a pixel by averaging intensities in its adaptive homogeneous neighborhood. The latter is determined according to five constraints and spatiodirectional nonstationarity measure maps. The proposed approach is compared with an anisotropic diffusion method used in DW image smoothing. Experimental results on both synthetic and real human DW images show that the proposed method achieves a better compromise between the smoothness of homogeneous regions and the preservation of desirable features such as boundaries, even for highly noisy data, thus leading to homogeneously consistent tensor fields and consequently more coherent fibers.