  This paper provides a comprehensive study on features and performance of
different ways to incorporate neural networks into lifting-based wavelet-like
transforms, within the context of fully scalable and accessible image
compression. Specifically, we explore different arrangements of lifting steps,
as well as various network architectures for learned lifting operators.
Moreover, we examine the impact of the number of learned lifting steps, the
number of channels, the number of layers and the support of kernels in each
learned lifting operator. To facilitate the study, we investigate two generic
training methodologies that are simultaneously appropriate to a wide variety of
lifting structures considered. Experimental results ultimately suggest that
retaining fixed lifting steps from the base wavelet transform is highly
beneficial. Moreover, we demonstrate that employing more learned lifting steps
and more layers in each learned lifting operator do not contribute strongly to
the compression performance. However, benefits can be obtained by utilizing
more channels in each learned lifting operator. Ultimately, the learned
wavelet-like transform proposed in this paper achieves over 25% bit-rate
savings compared to JPEG 2000 with compact spatial support.
