Satellite Image Deblurring Using Complex Wavelet Packets

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Direct inversion leads to unacceptable noise amplification. Usually the problem is regularized during the inversion process. Recently, new approaches have been proposed, in which a rough deconvolution is followed by noise filtering in the wavelet transform domain. Herein, we have developed this second solution, by thresholding the coefficients of a new complex wavelet packet transform; all the parameters are automatically estimated. The use of complex wavelet packets enables translational invariance and improves directional selectivity, while remaining of complexity O(N). A new hybrid thresholding technique leads to high quality results, which exhibit both correctly restored textures and a high SNR in homogeneous areas. Compared to previous algorithms, the proposed method is faster, rotationally invariant and better takes into account the directions of the details and textures of the image, improving restoration. The images deconvolved in this way can be used as they are (the restoration step proposed here can be inserted directly in the acquisition chain), and they can also provide a starting point for an adaptive regularization method, enabling one to obtain sharper edges.