Question: In the four lowest gears (i.e the 28 cog end) when in both the big and small ring, loud noises can be heard coming from what appears to be near the front derailleur. I've uploaded a video of the noise here: 

If I shift up from the 4th smallest gear then the noise goes away. I've checked to make show the chain isn't rubbing on the derailleur cage, and it doesn't look like it is. I've attached a picture of what it looks like when in the small ring and the 3rd lowest gear in the back. I even tried to set the low limit of the front derailleur so the cage moves in further towards the bike to see if it was in fact the cage, but that didn't seem to make the noise go away either. 

is there something I'm doing wrong here?

[![chain line](https://i.stack.imgur.com/gl3ys.jpg)](https://i.stack.imgur.com/gl3ys.jpg)

Answer: 
Ascertain that the chain is not visibly touching the front derailleur.

Check that your rear cassette is fitted correctly; lock-ring is tight and the correct spacers used between sprockets.

Are you using a matching chain, chain rings and rear derailleur? i.e. are they all 'n' speed; i.e. do not mix and match a 9 speed chain with a 11 speed cassette or derailleur. 

Is your rear derailleur vertically aligned correctly, not subject to crash damage.

Assuming you're on Shimano, is the b adjustment screw of your rear shimano derailleur correct such that the rear derailleur does not touch the cassette?

Is you rear derailleur compatible with the large sprockets you have on your cassette? e.g. a short arm rear derailleur may only support up to 25 tooth sprockets.

Do you have the correct length of chain to support the gear range you have.
Depending on the geometry of your frame, the noise could very well be caused by cross chaining, especially if you have very short chain stays. 

If you've ruled out rubbing, and this is in fact the problem, you don't have many options unfortunately. You can pick a cassette/crank combination that ensures you spend most of your time riding in the middle of your gear range with the chain line is as straight as possible. For most road riders this means picking up a compact crankset and pairing it with a comfortable cassette.