The Matrix Decomposition Representation and Modification of Feig's DCT

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 algo- rithm 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 elimi- nates the inherent 49 negative operations of Feig's algorithm and regularizes its data flow diagram which is suitable for SIMD and VLIW.