Can a broken Postgresql data directory be reconstructed without losing data?

[A A]

I'm trying to restore a database from a broken data directory that have lost 
many of its files accidentally.

I have tried unsuccessfully to install new instance of the same Postgresql 
version and then copy (with overwrite) the broken datadir to the new one.here 
the remaining datadir that I'm working on :
   |-base
   |---1
   |---16384
   |---17950
   |---19621
   |---pgsql_tmp
   |-global
   |-pg_multixact
   |---members
   |---offsets
   |-pg_notify
   |-pg_stat_tmp
   |-pg_tblspc
   |-pg_xlog
   |---archive_status