Nonparametric　Bayesian　techniques　have　been　applied　to　one　dimensional　dictionary　learning　using　beta　process　for　sparse　representation.　However,　in　real　world,　signals　are　often　high　dimensional　tensor　and　have　some　structured　features.　In　this　paper,　we　extend　the　nonparametric　Bayesian　technique　to　structured　tensor　dictionary　learning　under　a　sparse　favouring　beta　process　prior.　The　hierarchical　form　of　tensor　dictionary　learning　model　was　presented,　and　the　inference　process　was　given　via　Gibbs　sampling　analysis　with　analytic　update　equations.　The　tensor　dictionary　is　learned　directly　from　high　dimensional　tensor　data,　so　it　can　make　full　use　of　spatial　structure　information　of　the　original　sample　data.　The　employed　nonparametric　Bayesian　technique　allows　the　noise　variance　to　be　unknown　or　non　stationary,　the　cases　frequently　being　seen　in　many　applications.　Finally,　several　experiments　on　video　reconstruction　and　image　denoising　are　conducted　to　showcase　the　application　of　learned　tensor　dictionaries.　(C)　2016　Elsevier　B.V.　All　rights　reserved.