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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. But lossless image coding has a rather low compression ratio (around 2:1 for natural images). The only known technique to achieve significant compression while meeting the stringent fidelity requirements is the methodology of ℓ_∞-constrained coding that was developed and standardized in nineties. We make a major progress in ℓ_∞-constrained imagearXiv:2002.03482v1 fatcat:mcyurqii4jbppcvehcjyoi4eka