Non-Uniform Entropy-Constrained L∞ Quantization for Sparse and Irregular Sources

Near-lossless coding schemes traditionally rely on uniform quantization to control the maximum absolute error (L∞ norm) of residual signals, often assuming a parametric model for the source distribution. This paper introduces a novel design framework for non-uniform, entropy-aware L∞-oriented scalar quantizers that leverages a tight and differentiable approximation of the L∞ distortion metric and does not require any parametric density function formulations. The framework is evaluated on both synthetic parametric sources and real-world medical depth map video datasets. For smoothly decaying distributions, such as the continuous Laplacian or discrete two-sided geometric distributions, the proposed method naturally converges to near-uniform quantizers, consistent with theoretical expectations. In contrast, for sparse or irregular sources, the algorithm produces highly non-uniform bin allocations that adapt to the local distribution structure and improve rate-distortion efficiency. When embedded in a residual-based near-lossless compression scheme, the resulting codec consistently outperforms versions equipped with uniform or piecewise-uniform quantizers, as well as state-of-the-art near-lossless schemes such as JPEG-LS and CALIC.