This　paper　considers　multivariate　deconvolution　density　estimations　under　the　local　Holder　condition　by　wavelet　methods.　A　pointwise　lower　bound　of　the　deconvolution　model　is　first　investigated;　then　we　provide　a　linear　wavelet　estimate　to　obtain　the　optimal　convergence　rate.　The　nonlinear　wavelet　estimator　is　introduced　for　adaptivity,　which　attains　a　nearly　optimal　rate　(optimal　up　to　a　logarithmic　factor).　Because　the　nonlinear　wavelet　estimator　depends　on　an　upper　bound　of　the　smoothness　index　of　unknown　functions,　we　finally　discuss　a　data-driven　version　without　any　assumption　on　the　estimated　functions.