The wavelet transform of higher dimension and the Radon transform

Presents 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. The authors 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. They found applications of this approach on, for instance, multiresolution reconstruction of a 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. Also, extra properties such as the “rotated” wavelet can be easily implemented with this algorithm