Ditto what Ted replied. You've got to determine what the problem is before "solving" it with random corrections.
Start with Ted's advice. If this faucet's the only one afflicted, then you have a faucet problem. I can't see enough of the faucet from the photo, but it appears that it might be a Delta. If so, it could have debris in the seals or internal passages. It can create a problem like you're describing. Even disassembling the faucet and inspecting/cleaning can be an ineffective remedy, since when the water is shut off, debris in the line can drop back into the line out of sight, and when the line is re-energized, the debris is pushed back up to the faucet and the problem recurs. Fun! Seems the Delta 3614 styles are prone to this malady for some reason. So if you have an obstruction problem, go ahead and remove the parts, but flush the lines out after disassembly to insure any debris is actually removed. Flushing can be a mess, it sometimes help to have a helper operate the valves while you contain the flush water. A large wet-vac with a larger diameter hose helps channel the water.