Can a broken Postgresql data directory be reconstructed withoutlosing data?

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