In 2010, the Victorian Court of Appeal rejected Baker's application to appeal his conviction. The High Court granted him leave to appeal his conviction in 2011, but dismissed that appeal in 2012.
Now, RMIT University's Bridge of Hope Innocence Initiative, which campaigns to clear the names of people it believes have been wrongly convicted of crimes, has taken up Baker's case.
It has appealed to Victorian Attorney General Jill Hennessy for judicial mercy, asking her to refer the case to the Court of Appeal, "with a view to an acquittal".
Director Michele Ruyters said she believed Baker had "an exceptional case for an acquittal".