Setting an icon on a process.

In a REST response for http://localhost:8084/bonita/API/bpm/process?f=user_id%3D3, I get:

{
activationState: "ENABLED"
actorinitiatorid: "1"
configurationState: "RESOLVED"
deployedBy: "4"
deploymentDate: "2014-12-09 13:54:51.274"
description: "The description for a case"
displayDescription: "The description for a case"
displayName: "Testing"
icon: ""
id: "8505568154742351422"
last_update_date: "2014-12-09 13:54:51.692"
name: "Testing"
version: "1.0"
}

The icon is blank in the response, how do I set it in bonita studio?

You cannot set user icons from the Studio, you need to do it on the server side, since organization is exported and published as an xml flat file. The simplest is to do it as Administrator, using the Portal. You go to Organization, find your user and edit it.
It might be possible to do it using REST, as well, but it would be more complicated as you would have to upload the image first, then link it to the user and upload his professional and personal contact details.
Note, as well, that the user icon is not related to a process, it is related to a given user.
For example, if you do a GET on:

http://localhost:8080/bonita/API/identity/user/4

you would get a response containing a path to the user’s icon.