Simplified DCT-lifting-based reversible lapped transforms using parallel processing of two same type lapped transforms

We present a realization of reversible lapped transforms (RevLTs) with simplified implementations, which are constructed by DCT and DST matrices, adders, and bit-shifters, for lossy-to-lossless image coding in this paper. Each DCT or DST matrix is directly used to each lifting coefficient block and it is called DCT-lifting structure. The structure is obtained by considering parallel processing of two 'same' type LTs and using DCT-lifting factorizations as our previous work. Furthermore, the Hadamard transform and scaling parts in the RevLTs are effectively implemented by extending 2D non-separable lifting structures derived from lifting-based lapped transform (L-LT) used for JPEG XR, the newest image coding standard. As a result, the proposed RevLTs achieve not only simplified implementations with any block size, but also comparable lossy-to-lossless image coding performance to the conventional RevLTs.