I did a little research and discovered how a person who has been prohibited from possessing firearms can apply to get his rights restored: and, according to U.S.C 18, Section 925 (c)...
Any person whose application for relief from disabilities is denied by the Attorney General may file a petition with the United States district court for the district in which he resides for a judicial review of such denial.
However, it looks as though there's been no funding available to review applications since 1992! Here's a story from February 2002, written before the Supreme Court reversed a 2001 United States district court decision which had restored convicted felon Thomas Lamar Bean's firearms rights, or privileges. From the 2002 Supreme Court decision U.S. et al v. Thomas Lamar Bean
"... while the Administrative Procedure Act (APA) draws a distinction between a “denial” and a “failure to act,” see 5 U.S.C. § 551(13), an applicant may obtain judicial review under §925(c) only if an application is denied."
... sneaky.
