Image sparse approximation based on Tetrolet transform

Since most of image sparse approximation algorithms are not universal, and these algorithms could achieve optimal approximation at the special image with certain detail, a new algorithm based on the advantages of wavelet and tetrolet transform is proposed. The new algorithm exploits the advantages of the wavelet transform for the representation of smooth images and the ability of the tetrolet transform to represent details. Firstly, the smooth region are extracted and amended, then the smooth region is sparsely represented. Finally, the detail region based on the representation of smooth images is extracted, and the sparse representation of the detail region is implemented. The results of experiment show that the new algorithm is universal and it does not depend on the image detail. The image construction in quality is better than the wavelet transform by about 5.5 dB and the Tetrolet transform by about 1.0 dB at the same conditions.