Theoretical Analysis on Optimum Word Length Assignment for Integer DCT (WA-L4)

Author(s) : Masahiro Iwahashi (Nagaoka University of Technology, Japan) Kohtaro Nakagawa (Nagaoka University of Technology, Japan) Somchart Chokchaitam (Thammasat University, Thailand) Yoshihide Tonomura (Nagaoka University of Technology, Japan)

Abstract : Numerous reports have demonstrated advantages of the integer transforms, which includes rounding operations in the lifting structure. The JPEG 2000 also adopts the integer wavelet for "lossless" coding of images. However DCT based "lossy" coding prevails all over the world. Therefore the integer DCT attracts researchers' attention to implement "lossless" coding maintaining compatibility to the existing DCT based "lossy" coding. So far, non-separable 2D structuring and the integer Hadamard transform reduced the number of rounding operations and multipliers respectively. We have also optimized word length of each multiplier in the integer DCT considering colored spectrum of input image signal. However it is remained unknown that 1) Is the assigned word length robust to change of input signal? 2) How does it depend on structure of the transform? This report is intended as an investigation of theoretical analysis to answer such questions. As a result, it became possible to theoretically estimate such matters with an explicit function of correlation of input image signal.

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