A Novel Hybrid Method for Remote Sensing Image Approximation Using the Tetrolet Transform

Most existing image sparse approximation methods can reach their best performance only under the condition that the image has some certain properties. In addition, for the remote sensing image, it is difficult to obtain a good sparse result if it contains a lot of details. Focused on the two problems, in this paper, a novel hybrid method that is of some generality is proposed. The method exploits the advantages of the tensor product wavelet transform for representation of smooth images and the ability of the tetrolet transform to represent texture and edge effectively at the same time. Moreover, two specialized processes of decomposition are designed, which contribute to increasing the energy concentration further and preserving the information of the details as much as possible. The procedure of the proposed hybrid method is as follows: for a given remote sensing image, first, the usual tensor product wavelet transform is used, then the redundancy among adjacent wavelet coefficients is removed by making a polyphase decomposition to each subband with a p-fold filter, and after that, the approximation of the low frequency image can be obtained by reconstructing those preserved coefficients. Second, for the detailed image, the sparse decomposition is carried out by the tetrolet transform. For the high frequency subbands, an adaptive decomposition will be done for increasing the energy aggregation. After that, the approximation of the detailed image can be obtained by reconstructing those preserved coefficients. Numerical results indicate the high effectiveness of the procedure for remote sensing image sparse approximation.