Flight instructor reported on takeoff observing a crop duster fly opposite direction not in communication.

Narrative

Student and I were doing practice landings at 4V4. We had talked about keeping an eye out for crop dusters as we had heard a few on the radio but were all talking about ZZZ. Our steep spiral into a power off 180 had no issues. After a back taxi due to a long landing before and as the takeoff roll started we both scanned the airport environment for hazards and seeing none we started our roll. We rotated and I saw something move in my peripheral vision on the left side of the aircraft and looked to see a crop duster flying less then 100 ft. AGL heading opposite direction (We were departing Runway 26 they must have come from the southwest and turned eastbound to land on an east heading in the grass between the runway and hangers). This aircraft was never talking on the radios and was no where in sight when we started our takeoff roll. We were above them and climbing when I noticed them but still wanted to report the issue.Cause: We scanned for traffic and had our eyes outside. Crop-duster didn't communicate or do anything to make its presences known. Maybe they were closer to the airport but we couldn't see them due to trees and buildings restricting our vision prior to starting our takeoff roll. If the crop-duster had landed into the wind and landed in the direction that other aircraft were landing we could have seen them while at Traffic Pattern Altitude (TPA) and avoided them. Suggestions: Never assess that crop-dusters will land into the wind and triple check for traffic during the roll and climb