Recently, DNN models for lossless image coding have surpassed their traditional counterparts in compression performance, reducing the bit rate by about ten percent for natural color images. But even with these advances, mathematically lossless image compression (MLLIC) ratios for natural images still fall short of the bandwidth and cost-effectiveness requirements of most practical imaging and vision systems at present and beyond. To break the bottleneck of MLLIC in compression performance, we question the necessity of MLLIC, as almost all digital sensors inherently introduce acquisition noises, making mathematically lossless compression counterproductive. Therefore, in contrast to MLLIC, we propose a new paradigm of joint denoising and compression called functionally lossless image compression (FLLIC), which performs lossless compression of optimally denoised images (the optimality may be task-specific). Although not literally lossless with respect to the noisy input, FLLIC aims to achieve the best possible reconstruction of the latent noise-free original image. Extensive experiments show that FLLIC achieves state-of-the-art performance in joint denoising and compression of noisy images and does so at a lower computational cost.

翻译：近期，用于无损图像编码的深度神经网络模型在压缩性能上已超越传统方法，使自然彩色图像的比特率降低约10%。然而，即便取得这些进展，自然图像的数学无损图像压缩（MLLIC）比率仍难以满足当前及未来多数实际成像与视觉系统对带宽和成本效益的要求。为突破MLLIC在压缩性能上的瓶颈，我们质疑了MLLIC的必要性——几乎所有数字传感器都固有地引入采集噪声，使得数学无损压缩适得其反。因此，与MLLIC不同，我们提出了一种联合去噪与压缩的新范式，称为功能无损图像压缩（FLLIC），它对经过最优去噪后的图像（最优性可能因任务而异）执行无损压缩。尽管就含噪输入而言并非字面意义上的无损，但FLLIC旨在实现对潜在无噪原始图像的最佳可能重建。大量实验表明，FLLIC在含噪图像的联合去噪与压缩任务中达到了最先进性能，且计算成本更低。