Entropy Relaxed Lattice Vector Quantization for Learned Image Compression

Learned image compression (LIC) has recently emerged as a promising alternative to realize transform-based coding. Contrary to widely studied transform and entropy modeling in LIC, most LIC methods are limited to uniform scalar quantization and existing vector quantization (VQ) methods are restricted by the soft-to-hard quantization strategy. In this paper, we propose a novel entropy relaxed lattice vector quantization (ERLVQ) scheme for LIC. ERLVQ achieves a tractable dimension-wise approximation to the probability mass function for the complex Voronoi regions in a general class of lattices. Instead of directly performing probabilistic estimation on the lattices, ERLVQ equivalently aligns complex Voronoi regions with a set of complete and non-overlapping hypercubes in a projected parametric domain. Space covering technique is then developed to generating hypercubes with their centers fixed to integer projected lattice points and their volumes equaling the Voronoi regions to enable separable dimension-wise estimation of multi-variate probability mass functions. The proposed ERLVQ is the first to adapt to arbitrary lattices for VQ based on LIC and can be embedded into existing LIC methods. Experimental results demonstrate that the proposed ERLVQ is superior to the uniform scalar quantization (USQ) and existing lattice VQ methods 1 on prevailing LIC baselines, as shown in Table 1 .