Camera manufacturers often advertise their image processors version in advertisements, such as DIGIC 6 (Canon), EXPEED 5A (Nikon) and many more. But we never see they advertise the sensor they are using.
Is the image processor more important than the sensor? Wouldn't the sensor be the most significant factor in terms of determining the image quality?

IMO, image processors may help:

1. Reduce the noise when converting to JPEG. But this can be done in photoshop as well, right?
2. Improve the burst rate. But this might vary depends on the megapixel count, despite using the same image processor, take example 5DsR 5fps Dual DIGIC 6 vs 7D Mark 2 10 fps.

Am I understanding correctly?