How to set no user icons visible for unauthenticated users

Hi everybody! Not sure if this should rather be in add-on requests but then again, it's most likely just few lines of code. I'd like to set unauthenticated users see the site default user icon instead of user submitted custom ones when browsing public discussions. So help/hints how to achive this would be highly appreciated. Not afraid of modifiying core files/templates.
Thanks in advance,
Sheila
Thanks in advance,
Sheila
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