Intermittent Touch Screen Non-Responsiveness

I am getting intermittent touch screen non-responsiveness from my iPhone 5s. It happens when I wake the phone for the first time--It is either completely non-responsive when I touch the screen or it does not work properly, often receiving different inputs than what I am actually touching/entering. When I put the phone to sleep and then immediately wake it, it seems to operate perfectly. This means I generally cannot answer phone calls because I cannot select the slider. However, I can sleep the phone, wake it, and call the person right back.

I have already tried restarting and resetting it with no success. I am still running iOS 7 though I don't think that is relevant.

Any help anyone can provide would be appreciated. Thanks.