  This paper explores learned image compression based on traditional and
learned discrete wavelet transform (DWT) architectures and learned entropy
models for coding DWT subband coefficients. A learned DWT is obtained through
the lifting scheme with learned nonlinear predict and update filters. Several
learned entropy models are proposed to exploit inter and intra-DWT subband
coefficient dependencies, akin to traditional EZW, SPIHT, or EBCOT algorithms.
Experimental results show that when the proposed learned entropy models are
combined with traditional wavelet filters, such as the CDF 9/7 filters,
compression performance that far exceeds that of JPEG2000 can be achieved. When
the learned entropy models are combined with the learned DWT, compression
performance increases further. The computations in the learned DWT and all
entropy models, except one, can be simply parallelized, and the systems provide
practical encoding and decoding times on GPUs.
