Wavelet transform of higher dimension and the radon transform

In this paper, we present a fast algorithm for the computation of the wavelet transform in higher dimensional Euclidean space Rn with arbitrary shaped wavelets. The algorithm is a direct consequence of the convolution property of the Radon transform and shows significant improvement in speed. We also present a novel approach for the computation of the Daubechies type wavelet transform under the Radon transform domain where the n-dimensional multiresolution Analysis (MRA) is reduced to one-dimensional MRA. We found applications of this approach on, for instance, multiresolution reconstruction of the tomographic image with the standard methods of denoising, where determination of wavelet coefficients is required under the Radon transform domain. Along with the possibility of reducing samples angularly with decreasing resolution, the efficiency can be further improved. Besides, extra property such as 'rotated' wavelet can be easily implemented with this algorithm.