Flight Instructor reported engine roughness and power loss while in the traffic pattern and returned to the departure airport for a precautionary landing.

Narrative

On initial climb off of Runway XX; we experienced a rapid and noticeable loss of power and engine roughness. Since the power loss was so sudden and so low; I immediately took control of the aircraft from my student. I notified ZZZ Tower immediately that we needed to return to the airport. I started turning off of the published/assigned departure of runway heading before cancelling IFR. Tower suggested the cancellation right after I notified them of the engine roughness; and therefore continued in a tight left pattern for Runway XX. I stayed tight due to the possibility of a full power loss. Once established in the downwind I was well below pattern altitude; approximately 700 feet AGL. I reduced power slightly and the engine roughness went away. The Tower then gave me landing clearance and I made an uneventful landing on Runway XX. I never [requested priority handling] but the Tower asked me if I needed any assistance; to which I declined. Upon further examination of the aircraft post flight; the mechanics were unable to replicate the issue on the ground during a full run-up. To my knowledge; the roughness could have been due to detonation. This was also suggested by one of the mechanics. The roughness on the climb-out lasted about 20-30 seconds.