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In many professional fields, such as medicine, remote sensing and sciences,users often demand image compression methods to be mathematically lossless. Butlossless image coding has a rather low compression ratio (around 2:1 fornatural images). The only known technique to achieve significant compressionwhile meeting the stringent fidelity requirements is the methodology of$\ell_\infty$-constrained coding that was developed and standardized innineties. We make a major progress in $\ell_\infty$-constrained image codingafter two decades, by developing a novel CNN-based soft$\ell_\infty$-constrained decoding method. The new method repairs compressiondefects by using a restoration CNN called the $\ell_\infty\mbox{-SDNet}$ to mapa conventionally decoded image to the latent image. A unique strength of the$\ell_\infty\mbox{-SDNet}$ is its ability to enforce a tight error bound on aper pixel basis. As such, no small distinctive structures of the original imagecan be dropped or distorted, even if they are statistical outliers that areotherwise sacrificed by mainstream CNN restoration methods. More importantly,this research ushers in a new image compression system of$\ell_\infty$-constrained encoding and deep soft decoding($\ell_\infty\mbox{-ED}^2$). The $\ell_\infty \mbox{-ED}^2$ approach beats thebest of existing lossy image compression methods (e.g., BPG, WebP, etc.) notonly in $\ell_\infty$ but also in $\ell_2$ error metric and perceptual quality,for bit rates near the threshold of perceptually transparent reconstruction.Operationally, the new compression system is practical, with a low-complexityreal-time encoder and a cascade decoder consisting of a fast initial decoderand an optional CNN soft decoder.

Ultra High Fidelity Image Compression with $\ell_\infty$-constrained Encoding and Deep Decoding