Tatsuto Murayama, Masato Okada
We applied statistical mechanics to an inverse problem of linear mapping to investigate the physics of optimal lossy compressions. We used the replica symmetry breaking technique with a toy model to demonstrate Shannon’s result. The rate distortion function, which is widely known as the theoretical limit of the compression with a ﬁdelity criterion, is derived. Numerical study shows that sparse constructions of the model provide suboptimal compressions.