Cross sensor iris matching may seriously degrade the recognition performance because of the sensor mis-match problem of iris images between the enrollment and test stage. In this paper, we propose two novel patch-based heterogeneous dictionary learning method to attack this problem. The first method applies the latest sparse representation theory while the second method tries to learn the correspondence relationship through PCA in heterogeneous patch space. Both methods learn the basic atoms in iris textures across different image sensors and build connections between them. After such connections are built, at test stage, it is possible to hallucinate (synthesize) iris images across different sensors. By matching training images with hallucinated images, the recognition rate can be successfully enhanced. The experimental results showed the satisfied results both visually and in terms of recognition rate. Experimenting with an iris database consisting of 3015 images, we show that the EER is decreased 39.4% relatively by the proposed method.