string filtering in postgres?

I need to normalize a column for search purposes by stripping all
non-alphanumeric characters:

   UPDATE my-table SET id_stripped = ??? id;

I have been playing with regexp_replace( id, ????,'');

   UPDATE my-table
        SET id_stripped = regexp_replace( id, <various>,'');id;

Without much luck. Can this even be done with regex, or should I just
write a custom sql function?

kt