Space-frequency domain based joint dictionary learning and collaborative representation for face recognition

In this paper, we propose a novel viewpoint about dictionary learning (DL) and collaborative representation for face recognition. Different from conventional learning methods, we consider both the native spatial domain and the Fourier frequency domain of datasets for dictionary learning. Based on the Fourier spectrum of images, the proposed method provides new insights into two crucial complementations in dictionary learning: data domain complementation and classification algorithm complementation. On the one hand, we perform the dictionary learning on the original dataset and the Fourier transformed dataset respectively, which makes data complementary in both spatial and frequency domains. On the other hand, we integrate dictionary learning and collaborative representation (CRC) for classification. Specifically, CRC is conducted on frequency-domain dataset to obtain residual scores, and the residual scores are fused with the ones obtained by the previous DL algorithms as the ultimate fusion score to classify the test samples. The proposed method with two aspects of complementation promotes the discriminative ability of dictionary learning and obtains a better classification performance. The experimental results demonstrate the superior performance of our method over the original dictionary learning methods.