Distributed Analysis Dictionary Learning Using a Diffusion Strategy

We consider the problem of distributed dictionary learning which aims to learn a global dictionary from data geographically distributed on nodes of a network. Existing works are based on sparse synthesis model while this paper is based on sparse analysis model. Two novel distributed analysis dictionary learning (ADL) algorithms are proposed by adapting the centralized ADL algorithms Analysis SimCO (ASimCO) and Incoherent Analysis SimCO (INASimCO) to distributed settings. In particular, local representation vectors and local dictionaries are introduced, and they can be updated independently on each node by distributing the sparse coding and dictionary update stages of ASimCO. A diffusion strategy is then applied to estimate a global dictionary from the local dictionaries by exchanging local information. Experimental results with synthetic data and for image denoising demonstrate that the proposed distributed ADL algorithms can obtain similar results as correpsonding centralized algorithms.