Convergence of Cascade Algorithms in Sobolev Spaces for Perturbed Refinement Masks

In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks.     

Iterative Phase Retrieval with Sparsity Constraints

We consider the problem of iterative phase retrieval in near-field X-ray propagation imaging. Single-distance measurements ask for strong a priori information about the specimen that are not always accessible, e.g. the specimen's support. We propose to exploit sparsity of real-valued cartoon-like images using soft-thresholding of shearlet coefficients. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deterministic sparse FFT algorithms

In this paper we consider sparse signals which are known to vanish outside a support interval of length bounded by m < N. For the case that m is known, we propose a deterministic algorithm of complexity for reconstruction of x from its discrete Fourier transform (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An efficient algorithm for periodic Hermite spline interpolation with shifted nodes

Generalized Hermite spline interpolation with periodic splines of defect 2 on an equidistant lattice is considered. Then the classic periodic Hermite spline interpolation with shifted interpolation nodes is obtained as a special case.By means of a new generalization of Euler-Frobenius polynomials the symbol of the considered interpolation problem is defined. Using this symbol, a simple representation of the fundamental splines can be given. Furthermore, an efficient algorithm for the computation of the Hermite spline interpolant is obtained, which is mainly based on the fast Fourier transform.     

Cold neutron energy dependent production of ultracold neutrons in solid deuterium

A measurement of the production of ultracold neutrons from velocity-selected cold neutrons on gaseous and solid deuterium targets is reported. The expected energy dependence for two-particle collisions with well defined neutron and Maxwell-Boltzmann distributed molecular velocities is found for the gas target. The solid target data agree in shape with the phonon density-of-states curve and provide strong evidence for the phonon model including multiphonon excitations.     

How many Fourier samples are needed for real function reconstruction?

In this paper we present some new results on the reconstruction of structured functions by a small number of equidistantly distributed Fourier samples. In particular, we show that real spline functions of order m with non-uniform knots containing N terms can be uniquely reconstructed by only m+N Fourier samples. Further, linear combinations of N non-equispaced shifts of a known low-pass function Φ can be reconstructed by N+1 Fourier samples. In the bivariate case, we consider the problem of function recovering by a small amount of Fourier samples on different lines through the origin. Our methods are based on the Prony method. The proofs given in this paper are constructive. Some numerical examples show the applicability of the proposed approach.     

Radiation cryochemistry of frozen dilute aqueous solutions: influence of the extent of solute segregation on the radiolysis pathway

Polycrystalline hexagonal ice containing thymine was -irradiated at 77 K, and X-band electron paramagnetic resonance spectra of the resulting radicals were recorded at this temperature immediately after irradiation, and after thermal annealing of the samples at temperatures up to 250 K. The examined frozen samples were obtained from hyperquenched glassy aqueous solution containing 0.005 M of thymine, by using two different procedures: (i) crystallization of the glass by heating up to 250 K, and (ii) warming the glass up to room temperature to melt it, and subsequent cooling of the solution in liquid N2. Thymine-derived radicals were detectable only in the samples obtained by crystallization of the glass. We conclude that the extent of solute segregation is less for the frozen aqueous solution made by route (i) than by route (ii). Therefore, the solute is more hydrated in the frozen sample made by route (i) and the primary products of water radiolysis can react with the solute. The present results are compared with those reported for the thymine/hyperquenched glassy water system (Bednarek et al. , J. Phys. Chem. B 103 , 6824 (1999)).     

Relation between total variation and persistence distance and its application in signal processing

In this paper we establish the new notion of persistence distance for discrete signals and study its main properties. The idea of persistence distance is based on recent developments in topological persistence for assessment and simplification of topological features of data sets. Particularly, we establish a close relationship between persistence distance and discrete total variation for finite signals. This relationship allows us to propose a new adaptive denoising method based on persistence that can also be regarded as a nonlinear weighted ROF model. Numerical experiments illustrate the ability of the new persistence based denoising method to preserve significant extrema of the original signal.