Learning Scalable ℓ∞-constrained Near-lossless Image Compression via Joint Lossy Image and Residual Compression Yuanchao Bai1, Xianming Liu1,2,∗ Wangmeng Zuo1,2, Yaowei Wang1, Xiangyang Ji3 1Peng Cheng Laboratory, 2Harbin Institute of Technology, 3Tsinghua University {baiych,wangyw}@pcl.ac.cn, {csxm,wmzuo}@hit.edu.cn,
[email protected] Abstract of the decoded images, ℓ∞-constrained near-lossless image compression is developed [6, 15, 2, 47, 51] and standardized We propose a novel joint lossy image and residual in traditional codecs, e.g., JPEG-LS [47] and CALIC [51]. compression framework for learning ℓ∞-constrained near- Different from lossy image compression with Peak Signal- lossless image compression. Specifically, we obtain a lossy to-Noise Ratio (PSNR) or Multi-Scale Structural SIMilar- reconstruction of the raw image through lossy image com- ity index (MS-SSIM) [45, 46] distortion measures, ℓ∞- pression and uniformly quantize the corresponding resid- constrained near-lossless image compression requires the ual to satisfy a given tight ℓ∞ error bound. Suppose that maximum reconstruction error of each pixel to be no larger the error bound is zero, i.e., lossless image compression, than a given tight numerical bound. Lossless image com- we formulate the joint optimization problem of compress- pression is a special case of near-lossless image compres- ing both the lossy image and the original residual in terms sion, when the tight error bound is zero. of variational auto-encoders and solve it with end-to-end With the fast development of deep neural networks training. To achieve scalable compression with the error (DNNs), learning-based lossy image compression [40, 3, bound larger than zero, we derive the probability model 39, 41, 34, 24, 4, 31, 27, 22, 8, 7, 23, 25, 29] has achieved of the quantized residual by quantizing the learned prob- tremendous progress over the last four years.