Block-Structured Dictionary Learning For Sparse Representation-Based Recognition

Abstract:As a hot topic in the field of computer vision and pattern recognition, image recognition has been applied in public security, military, agriculture and daily life. Recently sparse representation-based classification(SRC) has gained its popularity due to its simplicity and effectiveness, it has also been applied to a variety of problems in computer vision and image processing. In the SRC framework, dictionary plays a key role in sparse coding and classification performance. It is meaningful to learn a discriminative dictionary from training samples. Current dictionary learning methods can be divided into unsupervised dictionary learning and supervised dictionary learning. Although unsupervised dictionary learning methods have achieved promising results, supervised dictionary learning often results in better performance in recognition tasks. Supervised dictionary learning methods can be roughly divided into two directions. The first direction often incorporates some discriminative terms to make the resulting representation more discriminative. The second direction focuses on learning a structured dictionary according to the class information of the training samples. Based on the theory of structured dictionary learning, this paper carry out the research work in the following two aspects:(1) Combining structured sparse representation and structured dictionary learning, this paper propose a novel Block-KSVD algorithm to learn a block-structured dictionary. Specifically, during the sparse coding stage, Block K-SVD not only collaboratively encodes training samples from the same class, but also suppose they have same block-structured representation. Simultaneous Block Orthogonal Matching Pursuit algorithm is presented in this paper to perform the structured sparse coding of training samples. During the dictionary update stage, Block-KSVD updates the dictionary atoms and the corresponding coefficients block by block base on SVD. Due to the adoption of SVD, this algorithm can naturally learn a block-structured dictionary with zero intra-block coherence. This paper also present Discriminative Block-KSVD method which can simultaneously learn a block-structured dictionary and a linear classifier.(2) Based on Block-KSVD algorithm, this paper further propose a Supervised Block K-SVD(SB-KSVD) to learn a block-structured dictionary. During the sparse coding stage, SB-KSVD not only suppose the training samples from the same class have same block-structured representation, but also force the corresponding sub-dictionary must make a contribution to represent the training samples. This paper presents a Supervised Simultaneous Block Orthogonal Matching Pursuit to perform the structured sparse coding. During the dictionary update stage, SB-KSVD find out the error matrix of the training samples from a class to updates the dictionary atoms and the corresponding coefficients block by block based on SVD. The dictionary learned by SB-KSVD guarantees each sub-dictionary is able to well represent the training samples from the same class, which improves the discrimination of the learned dictionary.This paper performs numerous experiments on two public face databases AR and Extend YaleB and one handwritten digit database Mnist to verify the effectiveness of the proposed method and comparing our method with SRC, K-SVD and many classic dictionary learning algorithms. Experiment results demonstrate that our method outperforms many state-of-the-art dictionary learning methods.