I've read many articles about banners and text linking and which means more. The text back linking would most likely mean more, but I wouldn't go changing all your banners or buttons to text, because then the page itself does not look all that nice, and in the end, yeah you want to drive traffic, but if you're driving traffic to a website that doesn't look professional then there's no sense in putting in the time.
What is the banner? If the banner is just a link to your home page, then there is no need for it to be text because you're going to be ranking really high for your home page anyway. The text if it was for your home page would be XYZ Company Home Page, most likely, and well realistically it's pointless.
If you'd really want to help out your SEO, change the Alt tags and picture title to an SEO keyword in which you want your homepage to rank well on.
That's the best I can say without seeing the site, but it's tough, each page has it's own needs it really isn't a straightforward practice if you ask me.