Joint coupled representation and homogeneous reconstruction for multi-resolution small sample face recognition.

• This paper proposes a novel multivariate dictionary learning framework. • A coherence enhancement term to improve the coherent representing of the coding coefficients under different resolutions. • A multivariate dictionary optimization method to solve dictionaries involving the calculation of fractional norm. • The proposed method achieves the state-of-the-art performance on several benchmark datasets. Off-the-shelf dictionary learning algorithms have achieved satisfactory results in small sample face recognition applications. However, the achieved results depend on the facial images obtained at a single resolution. In practice, the resolution of the images captured on the same target is different because of the different shooting equipment and different shooting distances. These images of the same category at different resolutions will pose a great challenge to these algorithms. In this paper, we propose a Joint Coupled Representation and Homogeneous Reconstruction (JCRHR) for multi-resolution small sample face recognition. In JCRHR, an analysis dictionary is introduced and combined with the synthetic dictionary for coupled representation learning, which better reveals the relationship between coding coefficients and samples. In addition, a coherence enhancement term is proposed to improve the coherent representation of the coding coefficients at different resolutions, which facilitates the reconstruction of the sample by its homogeneous atoms. Moreover, each sample at different resolutions is assigned a different coding coefficient in the multi-dictionary learning process, so that the learned dictionary is more in line with the actual situation. Furthermore, a regularization term based on the fractional norm is drawn into the dictionary coupled learning to remove the redundant information in the dictionary, which can reduce the negative impacts of the redundant information. Comprehensive results demonstrate that the proposed JCRHR method achieves better results than the state-of-the-art methods, on several small sample face databases. [ABSTRACT FROM AUTHOR]