Is it possible to give the user a blank option in an image picker group - in the case a customer doesn't want an image at all?

You would need to upload a blank image file - such as a transparent pdf/png/jpg file to the image picker group.  The user could choose this blank option if they did not wish to have an image in that field.
Please see the below example of how you can provide the ability to the user to choose a blank option :