Fastest way to restore a Sql Server database
Database snapshots are probably the right answer for your specific situation, per Nic's comment.

But for future users finding this question, there are definitely ways to improve native SQL database backup and restore times:


Backup your databases with compression: I/O is typically the bottleneck, this shifts some of the work to CPU.
Change your storage configuration: Store backups locally or on higher-performance SAN
Backup your databases to multiple files (stripes): This might depends on your specific storage and network configuration, but I've found 4- and 8-stripe backups and restores in our environment complete 2x-10x faster than single-stripe backups. Certainly worth some testing.
Make sure instant file initialization is enabled: Helps you carve out the space for restoring files very quickly
Reduce the size of the database: Drop old tables, etc. When possible, of course.
Shrink away empty space: All the appropriate warnings and caveats about shrinking apply, of course.
Enable page or row compression: Makes the database files smaller, so less to write upon restore.