In　this　paper,　the　anisotropic　diffusion　for　image　denoising　is　considered.　A　new　method　to　construct　diffusion　tensors　is　proposed.　The　tensors　obtained　by　our　approach　depend　on　four　directional　derivatives　of　the　intensity　of　an　image,　and　hence　they　are　adaptively　determined　by　local　image　structure.　It　is　shown　that　the　proposed　diffusion　filter　is　isotropic　in　the　interior　of　a　region,　whereas　it　is　anisotropic　at　edges.　This　property　of　tensors　allows　us　to　efficiently　remove　noise　in　an　image,　particularly　noise　at　edges.　Several　numerical　experiments　are　conducted　on　both　synthetic　and　real　images.　(C)　2012　Elsevier　Inc.　All　rights　reserved.