I am not sure whether my case would apply to yours. My car starts very rough when the engine is cold but then when the engine is getting warmer, the car runs as normal and the pop sound has gone too. Mentioned that symptom to a mechanic who said that the head gas kit has to be replaced. He said its because of the oil has leaked towards the spark plugs. When the engine stays overnight, the oil has actually run down to the spark plugs.But when the engine gets warm, these oil has burned and then the problem will be gone.
This is just my experience though. I am just an IT guy but his explanation makes a bit sense... And now the issue has fixed.