By　using　a　kernel　method,　Lepski　and　Willer　establish　adaptive　and　optimal　L-p　risk　estimations　in　the　convolution　structure　density　model　in　2017　and　2019.　They　assume　their　density　functions　to　be　in　a　Nikol＇skii　space.　Motivated　by　their　work,　we　first　use　a　linear　wavelet　estimator　to　obtain　a　point-wise　optimal　estimation　in　the　same　model.　We　allow　our　densities　to　be　in　a　local　and　anisotropic　Holder　space.　Then　a　data　driven　method　is　used　to　obtain　an　adaptive　and　near-optimal　estimation.　Finally,　we　show　the　logarithmic　factor　necessary　to　get　the　adaptivity.