How to insert pictures without hard coded dimensions?

Question

How can I insert pictures into a post without any hard coded dimensions (e.g. <img src="" alt="" /> instead of <img src="" alt="" width="" height="" />)? I don't want my users to switch to the HTML tab and remove the parameters by themselves, so I was wondering if there is any filter I can use to achieve this?

Note: I'm already inserting them in "Full size".