Optimum word length allocation of integer DCT and its error analysis

摘要

Recently, the integer DCT (Int-DCT), which transforms an integer input to an integer output, is attracting many researchers’ attention as an effective method for DCT-based lossy/lossless unified coding. So far, there are many reports relevant to the Int-DCT, but they have been limited to a few topics such as how to reduce the number of multipliers with the four-point lossless Hadamard transform and the non-separable two-dimensional Int-DCT. However, none of them is focused on how to express the multipliers’ word length as short as possible for the reduction of hardware complexity.In this report, we define a new “SNR sensitivity” as an indicator of how the word length truncation of multiplier coefficients affects quality of a reconstructed image. Based on the sensitivity, we propose a new word length allocation method. We also theoretically analyze errors in a reconstructed signal to confirm an effectiveness of the proposed method. As a result, the optimum word length allocation, which depends on a frequency spectrum of an input signal, significantly improves quality of a reconstructed image.