  This work proposes to augment the lifting steps of the conventional wavelet
transform with additional neural network assisted lifting steps. These
additional steps reduce residual redundancy (notably aliasing information)
amongst the wavelet subbands, and also improve the visual quality of
reconstructed images at reduced resolutions. The proposed approach involves two
steps, a high-to-low step followed by a low-to-high step. The high-to-low step
suppresses aliasing in the low-pass band by using the detail bands at the same
resolution, while the low-to-high step aims to further remove redundancy from
detail bands, so as to achieve higher energy compaction. The proposed two
lifting steps are trained in an end-to-end fashion; we employ a backward
annealing approach to overcome the non-differentiability of the quantization
and cost functions during back-propagation. Importantly, the networks employed
in this paper are compact and with limited non-linearities, allowing a fully
scalable system; one pair of trained network parameters are applied for all
levels of decomposition and for all bit-rates of interest. By employing the
proposed approach within the JPEG 2000 image coding standard, our method can
achieve up to 17.4% average BD bit-rate saving over a wide range of bit-rates,
while retaining quality and resolution scalability features of JPEG 2000.
