Satellite image deconvolution using complex wavelet packets

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Donoho (1994) has proposed to deconvolve the image without regularization and to denoise the result in a wavelet basis by thresholding the transformed coefficients. We have developed a new filtering method, consisting of using a complex wavelet packet basis. Herein, the thresholding functions associated to the proposed method are automatically estimated. The estimation is performed within a Bayesian framework, by modeling the subbands using generalized Gaussian distributions, and by applying the maximum a posteriori (MAP) estimator on each coefficient. Compared to real wavelet-packet-based algorithms, the proposed method is shift invariant, provides good directionality properties and remains of complexity O(N).