  Recently learned image compression (LIC) has achieved great progress and even
outperformed the traditional approach using DCT or discrete wavelet transform
(DWT). However, LIC mainly reduces spatial redundancy in the autoencoder
networks and entropy coding, but has not fully removed the frequency-domain
correlation explicitly as in DCT or DWT. To leverage the best of both worlds,
we propose a surprisingly simple but efficient framework, which introduces the
DWT to both the convolution layers and entropy coding of CNN-based LIC. First,
in both the core and hyperprior autoencoder networks, we propose a
Wavelet-domain Convolution (WeConv) module, which performs convolution after
DWT, and then converts the data back to spatial domain via inverse DWT. This
module is used at selected layers in a CNN network to reduce the
frequency-domain correlation explicitly and make the signal sparser in DWT
domain. We also propose a wavelet-domain Channel-wise Auto-Regressive entropy
Model (WeChARM), where the output latent representations from the encoder
network are first transformed by the DWT, before applying quantization and
entropy coding, as in the traditional paradigm. Moreover, the entropy coding is
split into two steps. We first code all low-frequency DWT coefficients, and
then use them as prior to code high-frequency coefficients. The channel-wise
entropy coding is further used in each step. By combining WeConv and WeChARM,
the proposed WeConvene scheme achieves superior R-D performance compared to
other state-of-the-art LIC methods as well as the latest H.266/VVC. For the
Kodak dataset and the baseline network with -0.4% BD-Rate saving over
H.266/VVC, introducing WeConv with the simplest Haar transform improves the
saving to -4.7%. This is quite impressive given the simplicity of the Haar
transform. Enabling Haar-based WeChARM entropy coding further boosts the saving
to -8.2%.
