Abstract
In 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.
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Peyrin, F., Zaim, M. & Goutte, R. Construction of wavelet decompositions for tomographic images. J Math Imaging Vis 3, 105–122 (1993). https://doi.org/10.1007/BF01248406
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DOI: https://doi.org/10.1007/BF01248406