Satellite and aerial image deconvolution using an EM method with complex wavelets

In this paper we present a new deconvolution method, able to deal with noninvertible blurring functions. To avoid noise amplification, a prior model of the image to be reconstructed is used within a Bayesian framework. We use a spatially adaptive prior defined with a complex wavelet transform in order to preserve shift invariance and to better restore variously oriented features. The unknown image is estimated by an EM technique, whose E step is a Landweber update iteration, and the M step consists of denoising the image, which is achieved by wavelet coefficient thresholding. The new algorithm has been applied to high resolution satellite and aerial data, showing better performance than existing techniques when the blurring process is not invertible, like motion blur for instance.