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Two dimensional Fast DCT using Polynomial Transform without Complex Computations  

Park, Hwan-Serk (Myongji University, Electronics, Information & Communication Engineering)
Kim, Won-Ha (Myongji University, Electronics, Information & Communication Engineering)
Publication Information
Journal of the Institute of Electronics Engineers of Korea CI / v.40, no.6, 2003 , pp. 127-140 More about this Journal
Abstract
This paper develops a novel algorithm of computing 2 Dimensional Discrete Cosine Transform (2D-DCT) via Polynomial Transform (PT) converting 2D-DCT to the sum of 1D-DCTs. In computing N${\times}$M size 2D-DCT, the conventional row-column algorithm needs 3/2NMlog$_2$(NM)-2NM＋N＋M additions and 1/2NMlog$_2$(NM) additions and 1/2NMlog$_2$(NM) multiplications, while the proposed algorithm needs 3/2NMlog$_2$M＋NMlog$_2$N-M-N/2＋2 additions and 1/2NMlog$_2$M multiplications The previous polynomial transform needs complex operations because it applies the Euler equation to DCT. Since the suggested algorithm exploits the modular regularity embedded in DCT and directly decomposes 2D DCT into the sum of ID DCTs, the suggested algorithm does not require any complex operations.
Keywords
2D-DCT; Polynomial Transform; Fast algorithm;
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