Image Sparse Decomposition Based on Concatenated Dictionary

The sparse representation of signals/images plays a vital role in applications such as compression, enhancement, restoration and more. In recent years, several pioneering works suggested that signals/images could be represented sparsely by redundant dictionaries. This paper presents a novel method for image sparse decomposition by concatenating a redundant dictionary of several bases. The proposed method constructs a concatenated dictionary including cosine bases, wavelet bases and contour let bases, and applies the matching pursuit algorithm to search the optimal bases at each iterative step, thus the decomposition procedure will lead to a best sparse representation of the image. The benefit of including several bases is to overcome the poor ability in capturing the inherent structure of the natural images of conventional decomposition algorithms based on orthogonal bases. The experimental results show that the new algorithm can greatly reduce the computational complexity and generate a better sparse representation of images compared with previous method.