  Lossy image compression is generally formulated as a joint rate-distortion
optimization to learn encoder, quantizer, and decoder. However, the quantizer
is non-differentiable, and discrete entropy estimation usually is required for
rate control. These make it very challenging to develop a convolutional network
(CNN)-based image compression system. In this paper, motivated by that the
local information content is spatially variant in an image, we suggest that the
bit rate of the different parts of the image should be adapted to local
content. And the content aware bit rate is allocated under the guidance of a
content-weighted importance map. Thus, the sum of the importance map can serve
as a continuous alternative of discrete entropy estimation to control
compression rate. And binarizer is adopted to quantize the output of encoder
due to the binarization scheme is also directly defined by the importance map.
Furthermore, a proxy function is introduced for binary operation in backward
propagation to make it differentiable. Therefore, the encoder, decoder,
binarizer and importance map can be jointly optimized in an end-to-end manner
by using a subset of the ImageNet database. In low bit rate image compression,
experiments show that our system significantly outperforms JPEG and JPEG 2000
by structural similarity (SSIM) index, and can produce the much better visual
result with sharp edges, rich textures, and fewer artifacts.
