Lossy image coding is the art of computing that is principally bounded by the image's rate-distortion function. This bound, though never accurately characterized, has been approached practically via deep learning technologies in recent years. Indeed, learned image coding schemes allow direct optimization of the joint rate-distortion cost, thereby outperforming the handcrafted image coding schemes by a large margin. Still, it is observed that there is room for further improvement in the rate-distortion performance of learned image coding. In this article, we identify the gap between the ideal rate-distortion function forecasted by Shannon's information theory and the empirical rate-distortion function achieved by the state-of-the-art learned image coding schemes, revealing that the gap is incurred by five different effects: modeling effect, approximation effect, amortization effect, digitization effect, and asymptotic effect. We design simulations and experiments to quantitively evaluate the last three effects, which demonstrates the high potential of future lossy image coding technologies.

We propose an end-to-end learned image compression codec wherein the analysis transform is jointly trained with an object classification task. This study affirms that the compressed latent representation can predict human perceptual distance judgments with an accuracy comparable to a custom-tailored DNN-based quality metric. We further investigate various neural encoders and demonstrate the effectiveness of employing the analysis transform as a perceptual loss network for image tasks beyond quality judgments. Our experiments show that the off-the-shelf neural encoder proves proficient in perceptual modeling without needing an additional VGG network. We expect this research to serve as a valuable reference developing of a semantic-aware and coding-efficient neural encoder. Introduction We consider a natural image x as a point in the signal space that triggers stimuli in the brain's sensory cortex through the visual system.

Neural image compression methods have seen increasingly strong performance in recent years. However, they suffer orders of magnitude higher computational complexity compared to traditional codecs, which hinders their real-world deployment. This paper takes a step forward towards closing this gap in decoding complexity by using a shallow or even linear decoding transform resembling that of JPEG. To compensate for the resulting drop in compression performance, we exploit the often asymmetrical computation budget between encoding and decoding, by adopting more powerful encoder networks and iterative encoding. We theoretically formalize the intuition behind, and our experimental results establish a new frontier in the trade-off between rate-distortion and decoding complexity for neural image compression. Specifically, we achieve rate-distortion performance competitive with the established mean-scale hyperprior architecture of Minnen et al. (2018) at less than 50K decoding FLOPs/pixel, reducing the baseline's overall decoding complexity by 80%, or over 90% for the synthesis transform alone. Our code can be found at https://github.com/mandt-lab/shallow-ntc.

Artificial Neural-Network-based (ANN-based) lossy compressors have recently obtained striking results on several sources. Their success may be ascribed to an ability to identify the structure of low-dimensional manifolds in high-dimensional ambient spaces. Indeed, prior work has shown that ANN-based compressors can achieve the optimal entropy-distortion curve for some such sources. In contrast, we determine the optimal entropy-distortion tradeoffs for two low-dimensional manifolds with circular structure and show that state-of-the-art ANN-based compressors fail to optimally compress them.