<i>M</i>-Channel Fast Hartley Transform Based Integer DCT for Lossy-to-Lossless Image Coding

This paper presents an M-channel (M=2n (n ∈ N)) integer discrete cosine transforms (IntDCTs) based on fast Hartley transform (FHT) for lossy-to-lossless image coding which has image quality scalability from lossy data to lossless data. Many IntDCTs with lifting structures have already been presented to achieve lossy-to-lossless image coding. Recently, an IntDCT based on direct-lifting of DCT/IDCT, which means direct use of DCT and inverse DCT (IDCT) to lifting blocks, has been proposed. Although the IntDCT shows more efficient coding performance than any conventional IntDCT, it entails many computational costs due to an extra information that is a key point to realize its direct-lifting structure. On the other hand, the almost conventional IntDCTs without an extra information cannot be easily expanded to a larger size than the standard size M=8, or the conventional IntDCT should be improved for efficient coding performance even if it realizes an arbitrary size. The proposed IntDCT does not need any extra information, can be applied to size M=2n for arbitrary n, and shows better coding performance than the conventional IntDCTs without any extra information by applying the direct-lifting to the pre- and post-processing block of DCT. Moreover, the proposed IntDCT is implemented with a half of the computational cost of the IntDCT based on direct-lifting of DCT/IDCT even though it shows the best coding performance