Medical Image Deblurring via Lagrangian Pursuit in Frame Dictionaries

Medical image deblurring attempts to recover the original human organ boundaries prior to degradation by an optical imaging system, e.g. MRI, CT or Ultrasound. In this paper, we aim to achieve deblurring by the non-linear approximation of medical images in a well chosen basis. The proposed method decomposes medical images over elementary waveforms chosen in a redundant dictionary composed of Morlet and Curvelet frames, which are highly suitable for curved edges. It is well known that finding an ideal sparse transform adapted to all medical images is hopeless. As the dictionary is redundant, we proceed by using a Lagrangian pursuit in order to find the optimal set of the dictionary vectors which represent the few coefficients that contain the information we are looking for and give a robust geometric image description. The proposed method in most instances outperforms, common deblurring methods using translation invariant Wavelet, Tikhonov and TV regularization algorithms.