FLLIC: Functionally Lossless Image Compression

Recently, DNN models for lossless image coding have surpassed their traditional counterparts in compression performance, reducing the previous lossless 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 overcome the performance barrier of MLLIC, we question the very necessity of MLLIC. Considering that all digital imaging sensors suffer from acquisition noises, why should we insist on mathematically lossless coding, i.e., wasting bits to preserve noises? Instead, 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.