title: Thouless-Anderson-Palmer approach for lossy compression.
abstract: We study an ill-posed linear inverse problem, where a binary sequence will be reproduced using a sparse matrix. According to the previous study, this model can theoretically provide an optimal compression scheme for an arbitrary distortion level, though the encoding procedure remains an NP-complete problem. In this paper, we focus on the consistency condition for a dynamics model of Markov-type to derive an iterative algorithm, following the steps of Thouless-Anderson-Palmer approach. Numerical results show that the algorithm can empirically saturate the theoretical limit for the sparse construction of our codes, which is also very close to the rate-distortion function.
authors.affiliation: RIKEN Brain Science Institute, Hirosawa 2-1, Wako, Saitama 351-0198, Japan.
authors.forename: Tatsuto
authors.initials: T
authors.lastname: Murayama