Discrete　cosine　transforms　(DCT＇s)　are　the　mainstay　of　image　signal　processing.　So　far　as　is　known,　Feig＇s　2D　DCT　requires　the　least　number　of　operations.　In　order　to　help　understanding　Feig＇s　algorithm　and　further　improve　the　algorithm,　this　paper　first　utilizes　simple　matrix　decomposition　theory　to　obtain　Feig＇s　algorithm.　In　addition,　Feig＇s　algorithm　is　extended　to　other　three　forms.　Then,　we　further　eliminates　the　inherent　49　negative　operations　of　Feig＇s　algorithm　and　regularizes　its　data　flow　diagram　which　is　suitable　for　SIMD　and　VLIW.