If the rough idle goes away after 60 seconds, it's probably not a
clogged air or fuel filter. If you have not changed them recently, it
would not hurt. Anyone can do the air filter in a couple of minutes.
You can do the fuel filter but you have to release the pressure in
the system first - don't do it w/o doing that.

I doubt that it's your DI cassette. The DI is a set of four coils
that provide the high voltage to the spark plugs. The installation
of individual coils is done to allow the engine (ECU) to control spark
to each cylinder individually and to eliminate the secondary ignition
wires.

The DI usually causes run time problems (misses, check engine lights)
when it goes bad. It might change after heating up a little but it
usually gets worse, not better, when you apply heat (run the engine).

If the timing of the problem is very similar each time, I'd guess that
you have a "pollution" valve open and then closing (or vise versa), or
a manifold leak, or perhaps a bad cold start injector (although I
don't think that problem would go on for 60 seconds.).

How does it run otherwise ? How is the "power" when you drive ?