1. A method for deriving a transform matrix, comprising: deriving values for a 2 m ×2 m transform matrix using the following normalization constraints: 9 &AutoLeftMatch; { n 0 = norm &Sum; i = 0 2 m - 1 - 1 &it; &it; n 2 &CenterDot; i + 1 2 = 2 m - 1 &CenterDot; norm 2 &Sum; i = 0 2 m - 2 - 1 &it; &it; n 4 &CenterDot; i + 2 2 = 2 m - 2 &CenterDot; norm 2 &Sum; i = 0 2 m - 3 - 1 &it; &it; n 8 &CenterDot; i + 4 2 = 2 m - 3 &CenterDot; norm 2 &vellip; n 2 m - 1 = norm where, norm is an integer representing a normalization factor of the transform matrix; and selecting the norm that minimizes a DCT distortion function: 10 E 2 m = 1 2 m &it; &Sum; i = 0 ( 2 m - 1 ) &it; &it; &Sum; j = 0 j &NotEqual; i &it; ( 2 m - 1 ) &it; &LeftBracketingBar; d i &af; ( j ) &RightBracketingBar; &LeftBracketingBar; d i &af; ( i ) &RightBracketingBar; where d i &equals;t i ·DCT, t i is a base vector of the transform matrix, and DCT is a real Discrete Cosine Transform.