Translation:I heard the noise come from the kitchen.
Not quite. If you said "Jeg hørte, støjen kommer fra køkkenet." that would mean something more like "I heard that the noise comes from the kitchen." In this case, what you're hearing is "the noise coming from the kitchen" without a finite verb. In this case you use the infinitive. You can compare it with other sentences with sense verbs, like "I see the stars shine in the sky."
I had also wondered about this. I may be wrong, but I think this would have a different sense because the tense is changed here. Your suggestion would seem to translate to "I heard the noise, that comes from the kitchen" rather than "I heard the noise, that came from the kitchen".