I'm going to assume your updating the author pic, since any other picture on the page wouldn't really make sense without other changes to the site.
is that the image you replaced? did you pay close attention to capitalization? In the windows world GilbertKing.jpg Gilbertking.jpg gilbertking.jpg would all be the same file.... in the *nix world they are not. This is probably not the case as you said you removed the old file, which would mean that I would be seeing a page error most likely if this was the issue.
After seeing the page source for that page, it appears it's not being created by a dynamic web app such as wordpress as I earlier assumed. This should be as simple as changing the file as you suggested, the only real mistakes I could see that could be made are the capitialization issue mentioned, or if the original designer left some trash about the server and there are for some reason more than one /assets/images/ folders. One thing you can do to test to see if you have found the correct file to replace is to rename or remove the file and then visit the site (forcing page reload from the server with shift-f5) to see if the page breaks (shows a mess or errors, because there is a missing file)
Final thought goes back to original thoughts of image cache... When I wrote originally I was thinking about a server side image cache to improve performance, Ryo-ohki has a similar thought and suggested your local browser cache and neither appear to be the case. But just for giggles I'll take a screenshot as I see the page this morning (I've never been to the page before, so I can't have the old image in my cache, but i don't know how to tell if I'm seeing new or old.) and send you a private message on this forum with a link to my screenshot. This way we can eliminate a persistent browser caching issue for sure.