Recently, a large family of representation-based classification methods have been proposed and attracted great interest in pattern recognition and computer vision. This paper presents a general framework, termed as atomic representation-based classifier (ARC), to systematically unify many of them. By defining different atomic sets, most popular representation-based classifiers (RCs) follow ARC as special cases. Despite good performance, most RCs treat test samples separately and fail to consider the correlation between the test samples. In this paper, we develop a structural ARC (SARC) based on Bayesian analysis and generalizing a Markov random field-based multilevel logistic prior. The proposed SARC can utilize the structural information among the test data to further improve the performance of every RC belonging to the ARC framework. The experimental results on both synthetic and real-database demonstrate the effectiveness of the proposed framework.