Construction of wavelet decompositions for tomographic images

International audienceIn tomography an image is reconstructed from its projections from different directions. In this paper we study the reconstruction of a tomographic image from the wavelet transform of its projections with a 1-D analyzing wavelet. We then show that it allows us to reconstruct a 2-D wavelet decomposition of the image. The properties of the generated 2-D analyzing wavelet are studied. When the 1-D analyzing wavelet is even, the 2-D analyzing wavelet is isotropic. The extension of this idea to directional wavelets is also presented. The wavelet transform obtained in this case is defined with respect to a scale parameter and a rotation angle. For illustration, results on simulated and x-ray computerized tomography medical images are presented