Abstract. After formulating the design problem for Resampling Kernels used in Magnetic Resonance Spiral Image Reconstruction, we show that an iterative Gauss-Seidel-type interior-point optimization method is suitable (fast and light-weight) for embedded uses. In contrast to previous practice, we directly optimize a computationally efficient, piecewise-linear kernel rather than an analytic funct...

Nondiffracting beams are of interest for optical metrology applications because the size of the beam does not change as the beam propagates. However, accuracy can be increased if the diameter of the beam is smaller. One technique for accomplishing this is to use the dark axial intensity profile associated with a higher-order nondiffracting Bessel function beam. We generate these higher-order Be...

Since radial positive definite functions on R remain positive definite when restricted to the sphere, it is natural to ask for properties of the zonal series expansion of such functions which relate to properties of the Fourier-Bessel transform of the radial function. We show that the decay of the Gegenbauer coefficients is determined by the behavior of the Fourier-Bessel transform at the origi...

Abstract The normalization of the generalized Bessel functions $\mathrm{U}_{\sigma,r}$ U σ , r $(\sigma,r\in \mathbb{C}\mathbbm{)}$ ( ∈ C ) defin...