According to Success Criterion 1.1.1 (Non-text Content), all non-text content, including images, should have a short text alternative, and (if required) a long text alternative.
When an image is used as the only content within a link, the alt text of the image should indicate the function of the link - this is slightly different to the normal requirement that it describe the image (although in a perfect environment, it should describe both). If the alt text is missing, a different message will be emitted to the usual.