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

Area of Science:

• Signal Processing
• Information Theory
• Computer Vision

Background:

• Traditional near-lossless coding uses uniform quantization for error control.
• Existing methods often assume parametric source distributions, limiting adaptability.
• Controlling maximum absolute error (L∞ norm) is crucial for residual signal compression.

Purpose of the Study:

• Develop a novel framework for non-uniform, entropy-aware L∞-oriented scalar quantizers.
• Create a design that does not require parametric density function formulations.
• Enhance rate-distortion efficiency in near-lossless compression.

Main Methods:

• Introduced a tight and differentiable approximation of the L∞ distortion metric.
• Developed a framework for designing non-uniform scalar quantizers.
• Evaluated the framework on synthetic and real-world medical depth map video data.

Main Results:

• The proposed method converges to near-uniform quantizers for smoothly decaying distributions.
• For sparse or irregular sources, highly non-uniform bin allocations were produced, adapting to local structure.
• The resulting codec consistently outperformed uniform quantizers and state-of-the-art schemes like JPEG-LS and CALIC.

Conclusions:

• The novel framework enables adaptive, non-uniform quantization for improved near-lossless compression.
• The approach offers superior rate-distortion performance compared to uniform quantization and existing codecs.
• This entropy-aware design advances residual signal coding for diverse data sources.