Apply hyperanalytic shearlet transform to geometric separation

This paper first proposes a novel image separation method based on the hyperanalytic shearlet. By combining the advantages of both the hyperanalytic wavelet transform and the shear operation, hyperanalytic shearlet is easy to implement and also has a low redundancy. By using such transform and the orthonormal wavelet, a new geometric separation dictionary is obtained which can sparsely represent points and curviline singularities, respectively. In order to get the different components of image faster and more accurate, a fast alternating direction method (FADM) is used to train the dictionary. Our algorithm can greatly improve the computational efficiency without causing damage to the accuracy of image separation. Furthermore, a proper measure to evaluate the separation performance called sep-degree is defined. The experimental results have demonstrated the proposed method’s effectiveness and