We propose a novel joint lossy image and residual compression framework for learning $\ell_\infty$-constrained near-lossless image compression. Specifically, we obtain a lossy reconstruction of the raw image through lossy image compression and uniformly quantize the corresponding residual to satisfy a given tight $\ell_\infty$ error bound. Suppose that the error bound is zero, i.e., lossless image compression, we formulate the joint optimization problem of compressing both the lossy image and the original residual…