Nonlinear Loose Coupled Non-Negative Matrix Factorization for Low-Resolution Image Recognition

Abstract In the existing coupled mapping-based methods for low-resolution image recognition (LRIR), the potential relationship between the high- and low-resolution images conforming to the nature of the image characteristics is not considered and the mapping process has no strong actual physical meaning. This paper presents a novel nonlinear loose coupled non-negative matrix factorization (NLCNMF) algorithm to deal with LRIR. The target images can be seen as composed of different local features. The local features of high- and low-resolution images are at different resolution levels, but the way different resolution images are composed of corresponding local features should be similar. The kernel trick is used to achieve the nonlinear approach. The nonlinear mapped high- and low-resolution images are represented by corresponding non-negative local features. The representation coefficient vectors of the high- and low-resolution images belonging to the same target image pair are approximately equal. The proposed NLCNMF conforms to the principle of the nonlinear approach used by the human visual system in analyzing images. When the proposed method describe the common features of the images with different resolution, the idea of ”part constitute the whole” is utilized, which has a strong interpretability. The nonlinear algorithm models based on polynomial and Gaussian kernel function are presented. The convergence of the proposed algorithm is proved theoretically. The proposed algorithm performs experiments on 5 image databases. Three different low-resolution (8 × 7, 10 × 10 and 12 × 12) images are involved in the experiment. The experimental results show that the proposed method outperforms the state-of-the-arts in LRIR task.