A novel image sparse representation based on the hybrid transform

The sparse approximation performance of tetrolet transform to the edge and texture of image is much higher than wavelet transform, which makes it suitable for those images that rich in details. However, for the smooth images, its sparse approximation performance is weaker than wavelet transform. Focus on the problem, a novel sparse approximation method that is of some generality is proposed. First, the wavelet transform is conducted to the image, and the polyphase decomposition for each sub-band is operated using p-fold filter and some components are generated, then the PCA is applied to those components. Following, the sparse approximation is conducted to the image after two energy concentration. Secondly, the high-frequency image can be obtained based on the results above, then the tetrolet transform is applied to sparse it. Experimental result shows that, under the same condition, the quality of the reconstructed image obtained by the proposed method is better than that obtained by the wavelet transform and the tetrolet transform, either the subjective or objective quality, which indicates the effectiveness of the proposed method.