Structured sparse coding for image representation based on L ₁-graph

Sparse coding seeks for over-complete bases to obtain the high-level image representation for image analysis. In many applications, the image data might reside on a low dimensional manifold embedded in high dimensional ambient space. However, standard sparse coding cannot exploit the manifold structure. In this paper, we propose a novel structured sparse coding method based on the L ₁-graph, in which the geometric structure of the image data is considered explicitly. Specifically, a new regularization term based on L ₁-graph is incorporated into the standard sparse coding framework and a fast iterative thresholding algorithm is developed to solve the optimization problem. Through this coding scheme, the codes obtained by our algorithm between the similar data points in high dimensional space are more similar than that obtained by standard sparse coding. Experiments demonstrate the the efficacy of the proposed method for image representation on two benchmark databases.