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 and normalizing flow.In this paper, we first identify that invertibility of transform is sufficient but not necessary for idempotence. Instead, it can be relaxed into right-invertibility. And such relaxation allows wider family of transforms.Based on this identification, we 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 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.