tr equivalent to sed command

[夜神 岩男]

I'm trying to move a script from invoking lots of sed and awk to bash 
builtins and I'm stumped on something I'm sure is simple.

Is there a tr equivalent to the following?
sed 's/[^[:alnum:]]//g'

I just can't seem to get tr -d to accept a negative matching set, but 
perhaps that's not possible?

Thanks in advance

-IY