Tomographic construction of a 2D wavelet transform: continuous and discrete case

The authors study some relations between the wavelet transform and image reconstruction from projections. They show how 1D wavelets may be included in the tomographic reconstruction process, in order to provide a 2D wavelet transform of the image. First, the problem is analysed using a continuous formulation. An appropriate 1D filtering may be done on the sinogram prior to reconstruction in order to recover any 2D continuous wavelet transform. Then the discrete wavelet scheme is considered. For illustration, results on a X-ray CT scan medical image are presented