  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.
