NVTC: Nonlinear Vector Transform Coding

In theory, vector quantization (VQ) is always better than scalar quantization (SQ) in terms of rate-distortion (RD) performance [33]. Recent state-of-the-art methods for neural image compression are mainly based on nonlinear transform coding (NTC) with uniform scalar quantization, overlooking the benefits of VQ due to its exponentially increased complexity. In this paper, we first investigate on some toy sources, demonstrating that even if modern neural networks considerably enhance the compression performance of SQ with nonlinear transform, there is still an insurmountable chasm between SQ and VQ. Therefore, revolving around VQ, we propose a novel framework for neural image compression named Nonlinear Vector Transform Coding (NVTC). NVTC solves the critical complexity issue of VQ through (1) a multi-stage quantization strategy and (2) nonlinear vector transforms. In addition, we apply entropy-constrained VQ in latent space to adaptively determine the quantization boundaries for joint rate-distortion optimization, which improves the performance both theoretically and experimentally. Compared to previous NTC approaches, NVTC demonstrates superior rate-distortion performance, faster decoding speed, and smaller model size. Our code is available at https://github.com/USTC-IMCL/NVTC.