Discriminative analysis-synthesis dictionary learning for image classification

Dictionary learning has played an important role in the success of sparse representation. Although discriminative synthesis dictionary learning for sparse representation with a high-computational-complexity l0 or l1 norm constraint has been well studied for image classification, jointly and discriminatively learning an analysis dictionary and a synthesis dictionary is still in its infant stage. As a dual of synthesis dictionary, the recently developed analysis dictionary can provide a complementary view of data representation, which can have a much lower time complexity than sparse synthesis representation. Although several class-specific analysis-synthesis dictionary, which may have a big correlation between different classes' dictionaries, have been developed, how to learn a more compact and discriminative universal analysis-synthesis dictionary is still open. In this paper, to provide a more complete view of discriminative data representation, we propose a novel model of discriminative analysis-synthesis dictionary learning (DASDL), in which a linear classifier based on the coding coefficient is jointly learned with the dictionary pair, thus the performance of the classifier and the representational power of the dictionary pair being considered at the same time by the same optimization procedure. The size of the learned dictionaries can be very small since the analysis-synthesis dictionary is shared by all class data. An iterative algorithm to efficiently solve the proposed DASDL is presented in this paper. The experiments on face recognition, gender classification, action recognition and image classification clearly show the superiority of the proposed DASDL.