is there any way to restore ASM logs

Often the bigip would be configured to send logs to a remote syslog server. Restoring is not a possibility I guess. If any logging file /var/log/xxx is deleted, you can touch and create a file and assign proper privileges to make it working and restart syslog-ng service.

Please await your next maintanence window and use the below restore procedure,

Bring back deleted files with lsof
http://www.linux.com/archive/articles/58142 

I haven't tried this one yet, But I am going to test this saturday when I have time with my UAT box.

Let me know if it works.