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.

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