replace gravatar with image based on category

I was wondering if (at the page that lists posts) I could replace the gravatar image in the left margin with an image that is based on which category the post is made under.

The reason is because I have a front-end posting page and I would like for the posts to not show the users information; I would like for the posts to be characterized by category rather than author.

I’m not sure if there is a plugin anyone can suggest to link an image to each category, or how I can replace the gravatar image and author name to just show the category image