Idempotent Learned Image Compression with Right-Inverse

We consider the problem of idempotent learned image compression (LIC). The idempotence of codec refers to the stability of codec to re-compression. To achieve idempotence, previous codecs adopt invertible transforms such as DCT [Wallace, 1991] and normalizing flow [Papamakarios et al., 2021]. In this paper, we first identify that invertibility of transform is sufficient but not necessary for idem-potence. Instead, it can be relaxed into right-invertibility. And such relaxation allows wider family of transforms. Based on this identification, we then implement an idempotent codec using our proposed blocked convolution and null-space enhancement. Empirical results show that we achieve state-of-the-art rate-distortion performance among idempotent codecs. Furthermore, our idempotent codec can be extended into near-idempotent codec by relaxing the right-invertibility. And this near-idempotent codec has significantly less quality decay after 50 rounds of re-compression compared with other near-idempotent codecs.