Learning Redundant Sparsifying Transform based on Equi-Angular Frame

Due to the fact that sparse coding in redundant sparse dictionary learning model is NP-hard, interest has turned to the non-redundant sparsifying transform as its sparse coding is computationally cheap. However, natural images typically contain diverse textures that cannot be sparsified well by a non-redundant system. In this paper we propose a new approach for learning redundant sparsifying transform based on equi-angular frame, where the frame and its dual frame are corresponding to applying the forward and the backward transforms. The uniform mutual coherence in the sparsifying transform is enforced by the equi-angular constraint, which better sparsifies diverse textures. In addition, an efficient algorithm is proposed for learning the redundant transform. Experimental results for image representation illustrate the superiority of our proposed method over non-redundant sparsifying transforms. The image denoising results show that our proposed method achieves superior denoising performance, in terms of subjective and objective quality, compared to the K-SVD, the data-driven tight frame method, the learning based sparsifying transform and the overcomplete transform model with block cosparsity (OCTOBOS).