  Lossy image compression (LIC), which aims to utilize inexact approximations
to represent an image more compactly, is a classical problem in image
processing. Recently, deep convolutional neural networks (CNNs) have achieved
interesting results in LIC by learning an encoder-quantizer-decoder network
from a large amount of data. However, existing CNN-based LIC methods usually
can only train a network for a specific bits-per-pixel (bpp). Such a "one
network per bpp" problem limits the generality and flexibility of CNNs to
practical LIC applications. In this paper, we propose to learn a single CNN
which can perform LIC at multiple bpp rates. A simple yet effective Tucker
Decomposition Network (TDNet) is developed, where there is a novel tucker
decomposition layer (TDL) to decompose a latent image representation into a set
of projection matrices and a core tensor. By changing the rank of the core
tensor and its quantization, we can easily adjust the bpp rate of latent image
representation within a single CNN. Furthermore, an iterative non-uniform
quantization scheme is presented to optimize the quantizer, and a
coarse-to-fine training strategy is introduced to reconstruct the decompressed
images. Extensive experiments demonstrate the state-of-the-art compression
performance of TDNet in terms of both PSNR and MS-SSIM indices.
