Idempotence and Perceptual Image Compression

Abstract: Idempotence is the stability of image codec to re-compression. At the first glance, it is unrelated to perceptual image compression. However, we find that theoretically: 1) Conditional generative model-based perceptual codec satisfies idempotence; 2) Unconditional generative model with idempotence constraint is equivalent to conditional generative codec. Based on this newfound equivalence, we propose a new paradigm of perceptual image codec by inverting unconditional generative model with idempotence constraints. Our codec is theoretically equivalent to conditional generative codec, and it does not require training new models. Instead, it only requires a pre-trained mean-square-error codec and unconditional generative model. Empirically, we show that our proposed approach outperforms state-of-the-art methods such as HiFiC and ILLM, in terms of Fr\'echet Inception Distance (FID). The source code is provided in https://github.com/tongdaxu/Idempotence-and-Perceptual-Image-Compression.

• The paper introduces a novel codec design that leverages idempotence to ensure stability in repeated image compressions.
• It demonstrates that conditional generative codecs naturally satisfy idempotence, while unconditional models can be constrained to mimic this behavior.
• The proposed approach simplifies codec development using pre-trained models, though it highlights challenges such as gradient-based inversion latency.

Idempotence in Perceptual Image Compression: Bridging Theory with Practical Codec Design

Introduction to Idempotence in Image Compression

The concept of idempotence in image compression refers to a codec's ability to maintain stability upon repeated compressions, a property usually overshadowed by the pursuit of reducing file sizes. Traditional codecs, including JPEG, JPEG2000, and JPEG-XL, have incorporated idempotence considerations naturally due to their design simplicity allowing for easy reversibility. However, Neural Image Compression (NIC) methods often neglect this property, owing to the non-invertibility of neural network-based transformations. Efforts to ensure idempotence in NIC typically compromise on Rate-Distortion (RD) performance or introduce complexity, making the adoption of these methods less straightforward in practical applications.

Unveiling the Connection to Perceptual Quality

Recent advancements in the field have spotlighted the significance of perceptual image compression, aiming to achieve visually pleasing compression with minimal bit rates. The majority of such efforts have revolved around conditional generative models, which have successfully approached near-lossless perceptual quality. While at first glance idempotence and perceptual image compression appear disjointed, a closer inspection reveals a profound interconnection. The contribution of this paper lies in establishing a theoretical framework that demonstrates conditional generative codecs inherently satisfy idempotence. Furthermore, it posits that unconditional generative models, when imposed with idempotence constraints, can be harnessed for perceptual image compression. This revelation not only bridges a theoretical gap but also proposes a novel perceptual image codec paradigm that employs an inversion of an unconditional generative model constrained by idempotence, marking a stride towards optimizing perceptual image compression from a fresh perspective.

Implications for Codec Development

The implications of this research are multi-faceted, ranging from theoretical contributions to practical codec implementations. On the theoretical side, the paper submits a rigorous justification for the idempotence of conditional generative codecs and elucidates the equivalence between unconditional generative models with idempotence constraints and their conditional counterparts. Practically, it introduces an innovative codec design that does not require the arduous training of new models specific to different bit rates but instead utilizes a pre-trained unconditional generative model alongside a mean-square-error (MSE) codec. This approach not only simplifies the codec development process but also showcases superior perceptual quality when benchmarked against existing state-of-the-art methods, as evidenced by the empirical results presented.

Future Directions

While the proposed codec paradigm represents a significant leap forward, it is not without limitations. The codec's reliance on gradient ascent for generative model inversion introduces latency in the decoding process, highlighting a potential area for future research aimed at optimizing computational efficiency. Additionally, the fixed resolution constraint presents challenges for flexibility, indicating another avenue where advancements could be made. However, these limitations also open the door to exciting opportunities for further exploration, particularly in accelerating generative model inversion and enhancing model flexibility.

Conclusion

This paper presents a compelling case for the interconnectedness of idempotence and perceptual image compression, proposing a new codec paradigm that leverages an unconditional generative model with idempotence constraints. The findings underscore the potential of this approach to redefine perceptual image compression, offering both theoretical insights and a practical framework for future codec development. As the community continues to explore this paradigm, it holds promise for pushing the boundaries of what's achievable in image compression technologies, paving the way for more efficient and visually appealing digital media transmission and storage solutions.