introduction: an efficient method of tomographic imaging in nuclear medicine is positron emission tomography (pet). compared to spect, pet has the advantages of higher levels of sensitivity, spatial resolution and more accurate quantification. however, high noise levels in the image limit its diagnostic utility. noise removal in nuclear medicine is traditionally based on fourier decomposition o...

there are two methods for identifying formation interface in oil wells: core analysis, which is a precise approach but costly and time consuming, and well logs analysis, which petrophysists perform, which is subjective and not completely reliable. in this paper, a novel coupled method was proposed to detect the formation interfaces using gr logs. second approximation level (a2) of gr log gained...

We apply the fast redundant dyadic wavelet transform to the spatial registration of two-dimensional gene expression patterns of 736 Drosophila melanogaster embryos. This method is superior to the Fourier transform or windowed Fourier transform because of its ability to reduce noise and is of high resolution. In registration of the dataset we use two cost functions based on computing the Euclide...

The free-space Green function for a two-dimensional exponentially graded elastic medium is derived. The shear modulus μ is assumed to be an exponential function of the Cartesian coordinates (x, y), i.e. μ ≡ μ(x, y) = μ0e12, where μ0, β1, and β2 are material constants, and the Poisson ratio is assumed constant. The Green function is shown to consist of a singular part, involving modified Bessel ...

The quaternion Fourier transform (QFT), which is a nontrivial generalization of the real and complex Fourier transform (FT) using quaternion algebra has been of interest to researchers for some years (see e.g. [3, 5]). It was found that many FT properties still hold but others have to be modified. Based on the (right-sided) QFT, one can extend the classical wavelet transform (WT) to quaternion ...

in this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the fourier transform. as a consequence, we extend the fundamental theorems of abelian fourier transform to non-abelian case.