Lower Complexity Lifting Structures for Hierarchical Lapped Transforms Highly Compatible With JPEG XR Standard.

This paper presents lifting structures for hierarchical lapped transforms (HLTs) that are highly compatible with the Joint Photographic Experts Group (JPEG) eXtended Range (XR) standard and that are lower in complexity in terms of the number of operations and lifting steps than the existing HLT in JPEG XR. Two structures ( \text TRR and \text THH ), called Householder-lifting structures, are obtained using a lifting factorization followed by a Householder factorization of a non-separable 2D transform of rotation matrices. The third structure ( \text THR ) is simply derived from a combination of a Hadamard transform ( \text THH ) and two rotation matrices. The floating-point lifting coefficients are approximated as dyadic values, as in the existing structures of JPEG XR, because doing so costs less, thanks to the structures having only adders and shifters without multipliers. Although the new \text THH does not outperform the existing structure, the new \text TRR has one fewer adder, one fewer shifter, and four fewer lifting steps than the existing one. Moreover, the new \text THR not only has one fewer adder, three fewer shifters, and two fewer lifting steps, but also can reuse \text THH , i.e., it can be used to make a more stylish codec. We show that these lower complexity HLTs are comparable in performance to the existing HLT at lossy-to-lossless image coding and at the same time highly compatible with JPEG XR. [ABSTRACT FROM PUBLISHER]